CN113361162A - Method and device for calculating node displacement of collision vibration model - Google Patents

Method and device for calculating node displacement of collision vibration model Download PDF

Info

Publication number
CN113361162A
CN113361162A CN202110617607.4A CN202110617607A CN113361162A CN 113361162 A CN113361162 A CN 113361162A CN 202110617607 A CN202110617607 A CN 202110617607A CN 113361162 A CN113361162 A CN 113361162A
Authority
CN
China
Prior art keywords
simulation
step length
simulation step
physical displacement
vibration model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110617607.4A
Other languages
Chinese (zh)
Other versions
CN113361162B (en
Inventor
卫洪涛
张峰
孙利民
徐文涛
蔡守宇
郭攀
马竞
张强
卫荣汉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhengzhou University
Original Assignee
Zhengzhou University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhengzhou University filed Critical Zhengzhou University
Priority to CN202110617607.4A priority Critical patent/CN113361162B/en
Publication of CN113361162A publication Critical patent/CN113361162A/en
Application granted granted Critical
Publication of CN113361162B publication Critical patent/CN113361162B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Theoretical Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Data Mining & Analysis (AREA)
  • Operations Research (AREA)
  • Software Systems (AREA)
  • Databases & Information Systems (AREA)
  • Algebra (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The application provides a method and a device for calculating node displacement of a collision vibration model, which comprises the steps of obtaining a finite element equation of the collision vibration model, and obtaining a simulation differential equation according to the finite element equation and a preset physical displacement calculation equation; carrying out simulation according to a preset simulation step length, modal displacement, a modal velocity initial value and a simulation differential equation; when the state of the collision vibration model is transformed once, solving a simulation differential equation according to the geometric condition and the orthogonality of the vibration mode to obtain an initial value of the modal speed after each transformation, and setting the initial value of the modal displacement after each transformation to be zero to form a simulation condition after each transformation; and simulating the collision vibration model according to the simulated differential equation after each transformation and the corresponding simulation condition after each transformation to obtain the total physical displacement vector of each node in each simulation step.

Description

Method and device for calculating node displacement of collision vibration model
Technical Field
The application relates to the technical field of collision vibration of a continuum, in particular to a method and a device for calculating node displacement of a collision vibration model.
Background
At present, three methods for studying impact vibration of a continuum are respectively as follows: the force integration method, the method based on vibration mode conversion and the coefficient recovery method are used for obtaining better results no matter numerical solution or analytic solution based on modal analysis when objects with regular shapes, such as regular beams and plates, are processed by adopting the three methods; however, if the shape and structure of the object to be studied are complex, such as an irregular beam, a beam with additional mass, etc., and such a continuum collision vibration solution has a problem that the vibration mode equation of the complex structure needs to be solved, it is difficult to obtain an accurate analytical equation.
The finite element method well solves the modeling problem of a non-regular object, but the force integration method is only realized in a finite element frame at present, and when the force integration method and the finite element realization method are used for researching the vibration problem of other non-linear boundary conditions of a continuum, if the boundary conditions cannot be simply converted into force, the force integration method cannot process the problem, for example, a cantilever beam which can be stretched and contracted while vibrating, the non-linear boundary conditions cannot be simply embodied in a vibration equation.
Therefore, under the condition that the boundary conditions cannot be simply converted into force, the problem that the real displacement of each node of the impact vibration model cannot be solved by the conventional method for realizing the force integration method in the finite element frame exists.
Disclosure of Invention
An object of the embodiments of the present application is to provide a method and an apparatus for calculating node displacement of a collision vibration model, so as to solve a problem that it is difficult to find an analytic vibration mode expression when a non-regular model is faced, and meanwhile, under a condition that a boundary condition cannot be simply converted into a force, the present application is expected to solve such a problem, and an existing force integration method cannot solve the problem.
In a first aspect, an embodiment of the present application provides a method for calculating node displacement of a crash vibration model, including: acquiring a finite element equation of a collision vibration model, wherein the finite element equation is different according to different current states of the collision vibration model, and the current states of the collision vibration model comprise a non-contact blocking state or a contact blocking state; obtaining a simulation differential equation of the collision vibration model according to a preset physical displacement calculation equation and the finite element equation; simulating the collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value and the simulation differential equation; in the simulation process, when the state of the collision vibration model is transformed every time, solving the simulation differential equation according to the geometric condition and the vibration mode orthogonality to obtain the initial value of the modal velocity after each transformation, and setting the initial value of the modal displacement after each transformation to be zero to form the simulation condition after each transformation; and simulating the crash vibration model from the simulation moment of state transformation according to the simulated differential equation after each transformation and the corresponding simulation condition after each transformation to obtain a total physical displacement vector of each node on the crash vibration model at the end of each simulation step length, wherein the total physical displacement vector is obtained by substituting modal displacement obtained by simulation at the end of the corresponding simulation step length into the physical displacement calculation equation, and is equal to the sum of the physical displacement vector of the current simulation step length and the physical displacement vector of the corresponding simulation step length before the current simulation step length and the state at each transformation.
The method for calculating the node displacement of the collision vibration model realizes modeling solution of a relative vibration mode conversion method under a finite element frame, so that the corresponding simulated differential equation and the corresponding simulated condition are transformed at each transformation of the boundary condition, further, the real displacement of each node of the impact vibration model can be calculated under the condition that the boundary condition can not be simply converted into force, the problem that the real displacement of each node of the impact vibration model can not be solved in the existing method for realizing the force integration method in a finite element frame under the condition that the boundary condition can not be simply converted into force is solved, a novel method for modeling and solving the displacement of the node of the impact vibration model by a relative vibration mode conversion method under the finite element frame is provided, the solving problem of the situation that the irregular object and the boundary condition can not be simply converted into the force can be accurately solved.
In an alternative embodiment of the first aspect, the preset physical displacement calculation equation comprises:
Figure RE-GDA0003153839070000031
Figure RE-GDA0003153839070000032
Figure RE-GDA0003153839070000033
wherein the content of the first and second substances,
Figure RE-GDA0003153839070000034
is ti-1～tiThe nth order mode of the time interval; etani(t) is the corresponding modal displacement,
Figure RE-GDA0003153839070000035
is tj-1～tjN-th order mode of time interval, etanj(tj) Is at the tjModal displacement of the nth order mode at the moment; deltai(t) model of impact vibration at ti-1～tiSimulating a physical displacement vector at the end of the step length;
Figure RE-GDA0003153839070000036
representing the model of impact vibration at ti-1～tiBefore the simulation step length, the sum of the physical displacement vectors of the simulation step length when the state is changed, tjThe time point when the state changes; delta(t)Represents ti-1～tiAnd simulating the total physical displacement vector at the end of the step length.
In an alternative embodiment of the first aspect, the finite element equations of the crash vibration model include:
Figure RE-GDA0003153839070000037
wherein [ C ] represents a damping matrix, { δ } represents a node displacement vector, { P (t) } represents an excitation vector; [ M ] represents a quality matrix; [K] and representing a rigidity matrix which is different according to the current state of the crash vibration model.
In an optional implementation manner of the first aspect, the obtaining a simulated differential equation of the impact vibration model according to the finite element equation and a preset physical displacement calculation equation includes: substituting the preset physical displacement calculation equation into the finite element equation, and obtaining the simulated differential equation through the orthogonality of the vibration mode, wherein the simulated differential equation is as follows:
Figure RE-GDA0003153839070000041
wherein, tjFor the point in time when the state change occurs,
Figure RE-GDA0003153839070000042
is a constant number of times, and is,
Figure RE-GDA0003153839070000043
can be expressed as:
Figure RE-GDA0003153839070000044
when the state changes
Figure RE-GDA0003153839070000045
Change in value of, xiiIs the damping ratio.
In an optional implementation manner of the first aspect, the solving the simulated differential equation according to the orthogonality of the mode shape to obtain an initial value of the modal velocity after each transformation includes: solving the simulation differential equation according to the orthogonality of the vibration mode to obtain the initial value of the modal velocity after each transformation
Figure RE-GDA0003153839070000046
Wherein, the
Figure RE-GDA0003153839070000047
Comprises the following steps:
Figure RE-GDA0003153839070000048
wherein the content of the first and second substances,
Figure RE-GDA0003153839070000049
for the mode shape of the P-th order at the time of state transition,
Figure RE-GDA00031538390700000410
the modal velocity at the moment of the corresponding state transition.
In an optional implementation of the first aspect, the method further comprises: in the simulation process, judging whether the polarity of subtracting a clearance value from a total physical displacement vector of a node corresponding to a blocking position at the end of the current simulation step length is opposite to the polarity of subtracting the clearance value from the total physical displacement vector at the end of the previous simulation step length, wherein the clearance value represents the distance between a collision vibration model and a blocking piece; if so, judging whether the absolute value of the difference value between the total physical displacement vector of the node corresponding to the current simulation step length and the blockage and the gap value is larger than a set error threshold value or not; if the current simulation step length is larger than the set error threshold, refining the current simulation step length by adopting a dichotomy method to determine a time point in the current simulation step length, wherein the total physical displacement vector of the node corresponding to the blocking is subtracted by the gap value, the polarity of the total physical displacement vector of the point corresponding to the blocking is opposite to that of the gap value subtracted by the total physical displacement vector of the previous simulation step length, and the absolute value of the difference value of the total physical displacement vector of the node corresponding to the blocking and the gap value is smaller than the threshold; and determining the simulation time of the state transition as the time point when the absolute value of the difference value of the total physical displacement vector of the opposite polarity blocking the corresponding node minus the gap value is smaller than the threshold value.
In an optional implementation manner of the first aspect, the refining the current simulation step size by using the bisection method includes: taking the starting time point to the middle time point of the current simulation step length as an updated simulation step length; simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state to obtain a total physical displacement vector corresponding to the updated simulation step length; judging whether the polarity of the total physical displacement minus the clearance value of the node corresponding to the blocking position at the end of updating the simulation step length is opposite to the polarity of the total physical displacement vector minus the clearance value at the end of the last simulation step length; if the polarities are opposite, whether the absolute value of the difference value between the total physical displacement vector and the gap value of the node corresponding to the barrier when the simulation step length updating is finished is larger than a set error threshold value is judged; if the difference is larger than the set error threshold, taking the initial time point and the middle time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the crash vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain a total physical displacement vector corresponding to the updated simulation step length; if the simulation step length is smaller than the set error threshold, determining the end time point of updating the simulation step length as the simulation time of state conversion; and if the polarities are not opposite, taking the middle time point and the end time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain a total physical displacement vector corresponding to the updated simulation step length.
In a second aspect, an embodiment of the present application further provides an apparatus for calculating a node displacement of a crash vibration model, including: the acquisition module is used for acquiring a finite element equation of the collision vibration model, the finite element equation is different according to different current states of the collision vibration model, and the current states of the collision vibration model comprise a non-contact blocking state or a contact blocking state; obtaining a simulation differential equation of the collision vibration model according to a preset physical displacement calculation equation and the finite element equation; the simulation module is used for simulating the collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value and the simulation differential equation; in the simulation process, when the state of the collision vibration model is transformed every time, solving the simulation differential equation according to the geometric condition and the vibration mode orthogonality to obtain the initial value of the modal velocity after each transformation, and setting the initial value of the modal displacement after each transformation to be zero to form the simulation condition after each transformation; and according to the physical displacement calculation equation and the finite element equation after each conversion, obtaining a simulation differential equation after each conversion through vibration mode orthogonality calculation, simulating the impact vibration model from the simulation moment of state conversion according to the simulation differential equation after each conversion and the corresponding simulation condition after each conversion to obtain a total physical displacement vector of each node on the impact vibration model at the end of each simulation step, substituting modal displacement obtained through simulation at the end of the corresponding simulation step into the physical displacement calculation equation to obtain the total physical displacement vector, wherein the total physical displacement vector is equal to the sum of the physical displacement vector of the current simulation step and the physical displacement vector of the corresponding simulation step before the current simulation step and at each conversion of the state.
In the designed device for calculating the node displacement of the collision vibration model, the scheme realizes modeling solution of the relative vibration mode conversion method under a finite element frame, so that the corresponding simulation differential equation and simulation conditions are converted when the boundary conditions are converted each time, and the real displacement of each node of the collision vibration model is calculated. Meanwhile, for the vibration problem with the nonlinear boundary condition, under the condition that the boundary condition cannot be simply converted into force, the problem that the real displacement of each node of the impact vibration model cannot be solved by the existing method for realizing the force integration method in the finite element frame exists, and the method provided by the application can also be used for processing.
In an optional implementation manner of the second aspect, the apparatus further includes a determining module, configured to determine, in the simulation process, whether a polarity of a gap value subtracted from a total physical displacement vector of a node corresponding to the blocking position at the end of the current simulation step is opposite to a polarity of a gap value subtracted from a total physical displacement vector of a node corresponding to the blocking position at the end of the previous simulation step, where the gap value represents a distance between the impact vibration model and the blocking member; after the polarity is judged to be opposite, whether the absolute value of the difference value between the total physical displacement vector of the node corresponding to the current simulation step length and the blocking and the gap value is larger than a set error threshold value or not is judged; the refinement processing module is used for performing refinement processing on the current simulation step length by adopting a bisection method after the absolute value of the difference value is larger than the set error threshold value so as to determine a time point when the polarity of the gap value subtracted from the total physical displacement vector of the node corresponding to the block in the current simulation step length is opposite to the polarity of the gap value subtracted from the total physical displacement vector of the point corresponding to the block in the previous simulation step length and the absolute value of the difference value subtracted from the gap value subtracted from the total physical displacement vector of the node corresponding to the block is smaller than the threshold value; and the determining module is used for determining a time point with opposite polarity and the absolute value of the difference value of the total physical displacement vector of the blocked corresponding node minus the gap value smaller than a threshold value as the simulation time of the state transformation.
In an optional implementation manner of the second aspect, the refinement processing module is specifically configured to use a starting time point to a middle time point of a current simulation step size as an updated simulation step size; simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state to obtain a total physical displacement vector corresponding to the updated simulation step length; judging whether the polarity of the total physical displacement minus the clearance value of the node corresponding to the blocking position at the end of updating the simulation step length is opposite to the polarity of the total physical displacement vector minus the clearance value at the end of the last simulation step length; if the polarities are opposite, whether the absolute value of the difference value between the total physical displacement vector and the gap value of the node corresponding to the barrier when the simulation step length updating is finished is larger than a set error threshold value is judged; if the difference is larger than the set error threshold, taking the initial time point and the middle time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the crash vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain a total physical displacement vector corresponding to the updated simulation step length; if the simulation step length is smaller than the set error threshold, determining the end time point of updating the simulation step length as the simulation time of state conversion; and if the polarities are not opposite, taking the middle time point and the end time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain a total physical displacement vector corresponding to the updated simulation step length.
In a third aspect, an embodiment provides an electronic device, including a memory and a processor, where the memory stores a computer program, and the processor executes the computer program to perform the method in the first aspect or any optional implementation manner of the first aspect.
In a fourth aspect, the embodiments provide a storage medium, on which a computer program is stored, where the computer program, when executed by a processor, performs the method in the first aspect or any optional implementation manner of the first aspect.
In a fifth aspect, embodiments provide a computer program product, which when run on a computer, causes the computer to execute the method of the first aspect or any optional implementation manner of the first aspect.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments of the present application will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that those skilled in the art can also obtain other related drawings based on the drawings without inventive efforts.
Fig. 1 is a first flowchart of a method for calculating node displacement of a crash vibration model provided by the present application.
Fig. 2 is a schematic view of a crash vibration model provided in the present application.
Fig. 3 is a schematic view of a planar beam unit according to an embodiment of the present application.
Fig. 4 is a schematic view of a crash vibration process provided in an embodiment of the present application.
FIG. 5 is a second flowchart of a method for calculating node displacement of a crash vibration model provided by the present application;
FIG. 6 is a third flowchart of a method for calculating node displacement of a crash vibration model provided by the present application;
FIG. 7 is a schematic structural diagram of a device for calculating node displacement of a crash vibration model provided by the present application;
fig. 8 is a schematic structural diagram of an electronic device according to an embodiment of the present application;
fig. 9 is a schematic diagram of a combination of a mass array and a stiffness array provided in an embodiment of the present application.
Icon: 700-an obtaining module; 710-a simulation module; 720-judging module; 730-fine processing module; 740-a determination module; 8-an electronic device; 801-a processor; 802-a memory; 803 — communication bus.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application.
Referring to fig. 1, fig. 1 is a flowchart of a method for calculating node displacements of a crash vibration model according to the present application, which combines a relative vibration mode transformation method and a finite element to solve for real displacements of each node of the crash vibration model. Wherein, the method comprises the following steps:
s100: and acquiring a finite element equation of the collision vibration model.
S110: and obtaining a simulation differential equation of the collision vibration model according to the finite element equation and a preset physical displacement calculation equation.
S120: and simulating the collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value and a simulation differential equation.
S130: in the simulation process, when the state of the collision vibration model is transformed every time, a simulation differential equation is solved according to the geometric condition and the vibration mode orthogonality to obtain an initial value of the modal velocity after each transformation, and the initial value of the modal displacement after each transformation is set to be zero to form a simulation condition after each transformation.
S140: and simulating the collision vibration model from the transformation moment according to the simulation differential equation after each transformation and the corresponding simulation condition after each transformation so as to obtain the total physical displacement vector of each node on the collision vibration model in each simulation step length.
In the step S100, the finite element equation is different according to the current state of the impact vibration model, wherein the current state of the impact vibration model includes a non-contact blocking state or a contact blocking state, wherein the non-contact blocking state includes a cantilever beam state, which can be regarded as a state before boundary condition transition, and which can be correspondingly understood as a state before a node of the impact vibration model contacts with the blocking member; the contact-blocking state can be regarded as a state after the boundary condition transition, which can be understood as a state when the node of the impact vibration model collides with the blocking. As a possible implementation mode, assuming that the application adopts a typical cantilever beam single-side blocking collision vibration model, as shown in FIG. 2, the blocking is arranged at the end point of the beam, and when finite element dispersion is carried out, N finite elements, N +1 nodes are taken, wherein, assuming that the beam is a plane beam element as shown in FIG. 3, each element has 2 nodes, each node has 2 degrees of freedom, including 1 degree of translational freedom and 1 degree of rotational freedom, the displacement vector delta of the unit iseCan be expressed as:
δe＝{Yi,θZi,Yj,θZj}T；
on the basis of the designed collision vibration model, the finite element equation of the collision vibration model is obtained by the following process: firstly, adopting a concentrated mass array, wherein the mass array of the beam unit is as follows:
Figure RE-GDA0003153839070000111
the stiffness matrix is represented as:
Figure RE-GDA0003153839070000112
wherein ρ represents the density of the impact vibration model, E represents the elastic modulus, A represents the cross-sectional area, l represents the length of the impact vibration model, and IZRepresenting the inertia matrix about the Z-axis.
The mass array and stiffness array combination is shown in fig. 9:
when the cantilever beam contacts the barrier, the effect of barrier stiffness needs to be added to the stiffness matrix [ K1 ]]In the method, if the position of the jth node of the beam corresponds to the barrier, the barrier stiffness needs to be added to a diagonal element corresponding to the displacement of the node in the stiffness array, and the diagonal element is assumed to have a value of K in the cantilever beam statejThen the value of the element after contact with the barrier is Kj+ k, where k is the barrier stiffness, where the barrier stiffness is related to the material of the barrier.
On the basis, a finite element equation of the collision vibration model can be obtained after finite element dispersion:
Figure RE-GDA0003153839070000121
in the finite element equation, [ C ] represents a damping matrix, { δ } represents a node displacement vector, { P (t) } represents an excitation vector, [ M ] represents a mass matrix, and [ K ] represents a stiffness matrix. And the barrier stiffness is required to be added when the diagonal elements corresponding to the node displacement in the stiffness array are in contact with the barrier, so that the finite element equation is different according to the current state of the collision vibration model.
In step S100, the preset physical displacement calculation equation may specifically be:
Figure RE-GDA0003153839070000122
Figure RE-GDA0003153839070000123
Figure RE-GDA0003153839070000124
wherein the content of the first and second substances,
Figure RE-GDA0003153839070000125
is ti-1～tiThe nth order mode of the time interval; etani(t) is the corresponding modal displacement,
Figure RE-GDA0003153839070000126
is tj-1～tjN-th order mode of time interval, etanj(tj) Is at the tjModal displacement of the nth order mode at the moment; deltai(t) model of impact vibration at ti-1～tiSimulating a physical displacement vector of a step length;
Figure RE-GDA0003153839070000127
representing the model of impact vibration at ti-1～tiBefore the simulation step length, the sum of the physical displacement vectors of the simulation step length when the state is changed, tjThe time point when the state changes; delta(t)Representing the total physical displacement vector.
The principle of the physical displacement calculation equation is as follows:
as shown in FIG. 4, in one vibration cycle, assume that the impact vibration model starts vibrating from rest, t0Representing the time zero, any point displacement on the beam can be expressed as { δ (t) } ═ δ (t) }1(t) }, as can be seen in the figure, let t1When the moment begins, the displacement of the end point is larger than the gap, the system is subjected to the action of the counterforce blocked by the end point, namely the boundary condition is changed, so that the vibration mode of the beam is changed, and the transverse displacement of any point on the beam can be regarded as the displacement before the boundary condition is converted and the displacement after the conversion is superposed, namely { delta (t) } (delta (t) } is the displacement after the conversion, namely { delta (t) } is superposed with the displacement after the conversion1(t1)}+{δ2(t) }, whereby the analogy is to tiTime of day tiThe displacement of the node on the beam is the above-mentioned physical displacement calculation equation at the time point when the boundary condition of the system changes.
After the finite element equation and the preset physical displacement calculation equation are obtained in the above manner, step S110 may be executed to obtain a simulated differential equation of the impact vibration model according to the finite element equation and the preset physical displacement calculation equation; as a possible implementation manner, the simulated differential equation may be obtained by substituting a preset physical displacement calculation equation into the finite element equation, and specifically, the simulated differential equation may be:
Figure RE-GDA0003153839070000131
wherein, tjFor the point in time when the state change occurs,
Figure RE-GDA0003153839070000132
is a constant number of times, and is,
Figure RE-GDA0003153839070000133
can be expressed as:
Figure RE-GDA0003153839070000134
when the state changes
Figure RE-GDA0003153839070000135
Change in value of, xiiFor the damping ratio, it should be noted here that when the simulated differential equation is transformedIs to the parameter
Figure RE-GDA0003153839070000136
And (6) updating.
After obtaining the simulated differential equation, the simulation process from step S120 to step S140 may be executed, specifically: simulating a collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value and a simulation differential equation, solving the simulation differential equation according to geometric conditions and vibration mode orthogonality to obtain a modal velocity initial value after each transformation when the state of the collision vibration model is transformed in the simulation process, and setting the modal displacement initial value after each transformation to be zero to form a simulation condition after each transformation; and simulating the crash vibration model according to the simulated differential equation after each transformation and the corresponding simulation condition after each transformation to obtain a total physical displacement vector of each simulation step length of each node on the crash vibration model, wherein the total physical displacement vector is obtained by substituting modal displacement obtained by simulating the corresponding simulation step length into the physical displacement calculation equation and is equal to the sum of the physical displacement vector of the current simulation step length and the physical displacement vector of the corresponding simulation step length before the current simulation step length and when each transformation occurs.
The above-mentioned solving of the simulation differential equation according to the geometric condition and the orthogonality of the mode shape to obtain the initial value of the modal velocity after each transformation may specifically be: solving the simulation differential equation according to the geometric condition and the orthogonality of the vibration mode to obtain the initial value of the modal velocity after each transformation
Figure RE-GDA0003153839070000141
Wherein, the
Figure RE-GDA0003153839070000142
Can be expressed by the following formula:
Figure RE-GDA0003153839070000143
wherein the content of the first and second substances,
Figure RE-GDA0003153839070000144
for the mode shape of the P-th order at the time of state transition,
Figure RE-GDA0003153839070000145
the modal velocity at the moment of the corresponding state transition.
The above simulation process can be illustrated by way of example as follows: assuming that the initial state of the collision vibration model is a cantilever beam state, and the preset simulation step length is t1～tiIn the simulation process, for each simulation step length t, the simulation differential equation can calculate a modal displacement of each step length, and the modal displacement of each step length obtained by each step length is substituted into the preset physical displacement calculation equation to calculate a total physical displacement vector of each step length, for example, from 0 to t1When the step length is long, the modal displacement of each order obtained by simulating the simulated differential equation is etani(t1) Shifting the mode ηni(t1) By substitution into the physical displacement calculation equation
Figure RE-GDA0003153839070000151
In (1), calculating to obtain 0-t1The physical displacement vector of the step size is assumed to be { δ }i(t1) Before that, since the state of the knock model has not changed, therefore,
Figure RE-GDA0003153839070000152
then it is determined that,
Figure RE-GDA0003153839070000153
in this case, δ (t) { δ }i(t1) I.e., the total physical displacement vector is { delta }i(t1) }; continuing the simulation when starting from t1～t2At step length, the simulated differentialThe modal displacement obtained by simulating the equation is etani(t2) Shifting the mode ηni(t2) By substitution into the physical displacement calculation equation
Figure RE-GDA0003153839070000154
In (1), calculating to obtain t1～t2The physical displacement vector of the step size is { delta }i(t2) Before that, since the state of the crash model has not changed yet, therefore,
Figure RE-GDA0003153839070000155
thus, the method can obtain the product,
Figure RE-GDA0003153839070000156
in this case, δ (t) { δ }i(t2) I.e. t1～t2The total physical displacement vector of step length is { deltai(t2) }; continuing the simulation when starting from t2～t3When the step length is long, the modal displacement obtained by simulating the simulation differential equation is etani(t3) Shifting the mode ηni(t3) By substitution into the physical displacement calculation equation
Figure RE-GDA0003153839070000157
Figure RE-GDA0003153839070000158
In (1), calculating to obtain t2～t3The physical displacement vector of the step size is now { δ }i(t3) Since the state of the bump model has not changed before, therefore,
Figure RE-GDA0003153839070000159
then the total physical displacement vector is δ (t) ═ δ at this timei(t3) If in the delta (t) vector, the lateral physical displacement value of the node corresponding to the block is found, assuming that this displacement value is yLLet the gap between the node and the barrier at the initial vibration be Δ if at t2Time yL-Δ>0 and at t3Time yL-Δ<0, then, is illustrated at t2～t3The polarity of the difference between the total physical displacement vector of the point corresponding to the blockage and the gap value obtained at the end of the step length is opposite to the polarity of the value obtained by the simulation step length, and therefore, t can be determined2～t3And the state of the impact vibration model is changed from a cantilever beam state to a contact blocking state during the step length.
After the state is determined to be changed, the method transforms the simulation condition and the differential simulation equation, and the transformation process specifically comprises the following steps: solving the simulation differential equation according to the geometric condition and the vibration mode orthogonality to obtain an initial value of the transformed modal velocity, setting the initial value of the transformed modal displacement to be zero to form a transformed simulation condition, meanwhile, calculating the simulation differential equation according to the physical displacement calculation equation and the finite element equation after each transformation through the vibration mode orthogonality calculation to obtain the simulation differential equation after each transformation, and further calculating the simulation step length t from the simulation step length t according to the transformed simulation differential equation and the transformed simulation condition2～t3In the simulation step length, when the difference value between the total physical displacement vector and the clearance calculated in a certain simulation step length is changed relative to the polarity of the value calculated in the previous simulation step length in the subsequent simulation step length, the simulation condition and the simulation differential equation are changed, the simulation is continued from the state conversion time point, and the mode of changing the simulation condition and the simulation differential equation when the boundary condition is changed is repeated until the simulation step length is completely finished or the set simulation step length is reached.
In an optional implementation manner of this embodiment, the present solution may further determine a time point of the transformation in a refined manner from the simulation step size of the state transformation, as shown in fig. 5, specifically including the following steps:
step S500: in the simulation process, it is determined whether the polarity of the gap value subtracted from the total physical displacement vector of the node corresponding to the blocking position at the end of the current simulation step length is opposite to the polarity of the gap value subtracted from the total physical displacement vector at the end of the previous simulation step length, if yes, the process goes to step S510.
Step S510: and judging whether the absolute value of the difference between the total physical displacement vector of the node corresponding to the current simulation step length and the blockage and the gap value is greater than a set error threshold value, if so, turning to the step S520.
Step S520: and refining the current simulation step length by adopting a bisection method to determine a time point when the polarity of the gap value subtracted from the total physical displacement vector of the node corresponding to the blockage in the current simulation step length is opposite to the polarity of the gap value subtracted from the total physical displacement vector of the point corresponding to the blockage in the previous simulation step length, and the absolute value of the difference value of the gap value subtracted from the total physical displacement vector of the node corresponding to the blockage is smaller than a threshold value.
Step S530: and determining the simulation time of the state transition as the time point when the absolute value of the difference value of the total physical displacement vector of the opposite polarity blocking the corresponding node minus the gap value is smaller than the threshold value.
In the simulation process, when each simulation step length simulation is finished, the scheme compares the polarity of the difference value obtained by subtracting the clearance value from the total physical displacement vector of the node corresponding to the blocking position at the end of the current simulation step length, which is obtained by calculation at the end of the current step length, with the difference value at the end of the previous simulation step length, and if the polarity is opposite, the state is changed, the step S510 is executed to further judge whether the absolute value of the difference value between the total physical displacement vector of the node corresponding to the blocking position at the current simulation step length and the clearance value is greater than the set error threshold value; if the current simulation step length is smaller than the set error threshold, determining the termination time point of the current simulation step length as the time point of the state change; if the absolute value of the difference value between the total physical displacement vector of the node corresponding to the block and the gap value subtracted in the current simulation step length is larger than the error threshold, fine processing is needed, and the moment point when the absolute value of the difference value between the total physical displacement vector of the node corresponding to the block and the gap value subtracted in the previous simulation step length is smaller than the threshold is further determined, and the moment point is the simulation moment of state transformation.
As a possible implementation manner, the refinement of the current simulation step size by using the bisection method may be implemented by the following manner, as shown in fig. 6, including:
step S600: and taking the starting time point to the middle time point of the current simulation step length as the updated simulation step length.
Step S610: and simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state to obtain a total physical displacement vector corresponding to the updated simulation step length.
Step S620: judging whether the polarity of the total physical displacement minus gap value of the node corresponding to the blocking position at the end of updating the simulation step length is opposite to the polarity of the total physical displacement vector minus gap value at the end of the previous simulation step length, if so, turning to the step S630; if not, go to step S640.
Step S630: judging whether the absolute value of the difference value between the total physical displacement vector and the gap value of the node corresponding to the block when the simulation step length updating is finished is larger than a set error threshold value, if so, turning to the step S6310; if not, the flow proceeds to step S6320.
Step S6310: and taking the starting time point and the middle time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and going to step S610.
Step S6320: and determining the end time point of updating the simulation step length as the simulation time of state transition.
Step S640: the middle time point and the end time point of the updated simulation step are used as new simulation steps, the updated simulation steps are updated, and the process goes to step S610.
In the above steps, the present solution adopts a bisection method to process the simulation step length of the state transformation, and then accurately obtains the time point of the state transformation in the simulation step length of the state transformation, specifically: and then judging whether the polarity of the total physical displacement minus gap value of the node corresponding to the blocking position at the end of the simulation step updating is opposite to the polarity of the total physical displacement minus gap value at the end of the last simulation step.
If the difference value of the total physical displacement vector and the gap value of the node corresponding to the block at the end of updating the simulation step length is not greater than the set error threshold, the ending time point of updating the simulation step length is the time point of state conversion; if the updated simulation step length is still larger than the set error threshold, continuing halving the updated simulation step length, namely, taking the initial time point and the middle time point of the updated simulation step length as new simulation step lengths to update the updated simulation step length, and further repeatedly executing the steps of the simulation of the step S610, the polarity judgment of the step S620 and the error threshold judgment of the step S630 until the updated simulation step length smaller than the error threshold is found; and determining the end time point of the updated simulation step length as the time point of state transition.
If the polarity of the total physical displacement minus gap value of the node corresponding to the blocking position at the end of updating the simulation step length is not opposite to the polarity of the total physical displacement vector minus gap value at the end of the last simulation step length, it indicates that the time of state transition is not between the starting time point and the middle time point of the simulation step length of the state transition, then the middle time point and the ending time point of the simulation step length of the state transition are used as the updated simulation step length, and the steps of the simulation of the step S610, the polarity judgment of the step S620 and the error threshold judgment of the step S630 are repeatedly executed until the updated simulation step length smaller than the error threshold is found; and determining the end time point of the updated simulation step length as the time point of state transition.
In the embodiment of the design, the exact state change time point can be found out through the dichotomy refinement treatment, so that the simulation conditions and the transformation time of the simulation equation are more accurate, and the simulation result is more accurate.
Fig. 7 shows a schematic structural block diagram of an apparatus for calculating node displacement of a crash vibration model provided in the present application, and it should be understood that the apparatus corresponds to the embodiment of the method executed in fig. 1 to 6, and can execute the steps related to the foregoing method, and the specific functions of the apparatus can be referred to the description above, and detailed description is appropriately omitted here to avoid repetition. The device includes at least one software function that can be stored in memory in the form of software or firmware (firmware) or solidified in the Operating System (OS) of the device. Specifically, the apparatus includes: the acquisition module 700 is configured to acquire a finite element equation of the impact vibration model, where the finite element equation is different according to different current states of the impact vibration model, and the current states of the impact vibration model include a non-contact blocking state or a contact blocking state; obtaining a simulation differential equation of the collision vibration model according to the finite element equation and a preset physical displacement calculation equation; the simulation module 710 is configured to simulate the collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value, and a simulation differential equation; in the simulation process, when the state of the collision vibration model is transformed every time, solving an equation according to the geometric condition and the vibration mode orthogonality to obtain an initial value of modal velocity after each transformation, and setting the initial value of modal displacement after each transformation to be zero to form a simulation condition after each transformation; and according to the physical displacement calculation equation and the finite element equation after each conversion, obtaining a simulation differential equation after each conversion through vibration mode orthogonality calculation, simulating the crash vibration model from the simulation moment of state conversion according to the simulation differential equation after each conversion and the corresponding simulation condition after each conversion to obtain a total physical displacement vector of each node on the crash vibration model at the end of each simulation step length, substituting modal displacement obtained through simulation at the end of the corresponding simulation step length into the physical displacement calculation equation to obtain the total physical displacement vector, wherein the total physical displacement vector is equal to the sum of the physical displacement vector of the current simulation step length and the physical displacement vector of the corresponding simulation step length before the current simulation step length and each state conversion.
In the device for calculating the node displacement of the collision vibration model, the scheme realizes modeling solution of a relative vibration mode conversion method under a finite element frame, so that the corresponding simulated differential equation and the corresponding simulated condition are transformed at each transformation of the boundary condition, further, the real displacement of each node of the impact vibration model can be calculated under the condition that the boundary condition can not be simply converted into force, the problem that the real displacement of each node of the impact vibration model can not be solved in the existing method for realizing the force integration method in a finite element frame under the condition that the boundary condition can not be simply converted into force is solved, a novel method for modeling and solving the displacement of the node of the impact vibration model by a relative vibration mode conversion method under the finite element frame is provided, the solving problem of the situation that the irregular object and the boundary condition can not be simply converted into the force can be accurately solved.
In an optional implementation manner of this embodiment, the apparatus further includes a determining module 720, configured to determine, in the simulation process, whether a polarity of a gap value subtracted from a total physical displacement vector of a node corresponding to the blocking position at the end of the current simulation step is opposite to a polarity of a gap value subtracted from a total physical displacement vector of a node corresponding to the blocking position at the end of the previous simulation step, where the gap value represents a distance between the impact vibration model and the blocking member; after the polarity is judged to be opposite, whether the absolute value of the difference value between the total physical displacement vector of the node corresponding to the current simulation step length and the blocking and the gap value is larger than a set error threshold value or not is judged; the refining processing module 730 is configured to perform refining processing on the current simulation step length by using a bisection method after the absolute value of the difference is greater than the set error threshold, so as to determine a time point at which the polarity of the gap value subtracted from the total physical displacement vector of the node corresponding to the block in the current simulation step length is opposite to the polarity of the gap value subtracted from the total physical displacement vector of the point corresponding to the block in the previous simulation step length, and the absolute value of the difference value subtracted from the gap value subtracted from the total physical displacement vector of the node corresponding to the block is smaller than the threshold; and a determining module 740, configured to determine, as the simulation time of the state transition, a time point at which the polarity is opposite and the absolute value of the difference between the total physical displacement vector blocking the corresponding node and the gap value is smaller than a threshold.
In an optional implementation manner of this embodiment, the refinement processing module 730 is specifically configured to use a starting time point to a middle time point of the current simulation step length as the updated simulation step length; simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state to obtain a total physical displacement vector corresponding to the updated simulation step length; judging whether the polarity of the total physical displacement minus the clearance value of the node corresponding to the blocking position at the end of updating the simulation step length is opposite to the polarity of the total physical displacement vector minus the clearance value at the end of the last simulation step length; if the polarities are opposite, whether the absolute value of the difference value between the total physical displacement vector and the gap value of the node corresponding to the barrier when the simulation step length updating is finished is larger than a set error threshold value is judged; if the total physical displacement vector is larger than the set error threshold, taking the initial time point and the middle time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain the total physical displacement vector corresponding to the updated simulation step length; if the simulation step length is smaller than the set error threshold, determining the end time point of updating the simulation step length as the simulation time of state conversion; and if the polarities are not opposite, taking the middle time point and the end time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the crash vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain the total physical displacement vector corresponding to the updated simulation step length.
As shown in fig. 8, the present application provides an electronic device 8 comprising: the processor 801 and the memory 802, the processor 801 and the memory 802 being interconnected and communicating with each other via a communication bus 803 and/or other form of connection mechanism (not shown), the memory 802 storing a computer program executable by the processor 801, the computer program being executed by the processor 801 when the computing device is running to perform the method of the first embodiment, any alternative implementation of the first embodiment, such as the steps S100 to S130: obtaining a finite element equation of the collision vibration model; obtaining a simulation differential equation of the collision vibration model according to a finite element equation and a preset physical displacement calculation equation; simulating the collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value and a simulation differential equation; in the simulation process, when the state of the collision vibration model is transformed every time, solving a simulation differential equation according to the geometric condition and the vibration mode orthogonality to obtain an initial value of modal velocity after each transformation, and setting the initial value of modal displacement after each transformation to be zero to form a simulation condition after each transformation; and simulating the collision vibration model from the transformation moment according to the simulation differential equation after each transformation and the corresponding simulation condition after each transformation so as to obtain the total physical displacement vector of each node on the collision vibration model in each simulation step length.
The present application provides a storage medium having a computer program stored thereon, where the computer program is executed by a processor to perform the method of the first embodiment or any alternative implementation manner of the first embodiment.
The storage medium may be implemented by any type of volatile or nonvolatile storage device or combination thereof, such as a Static Random Access Memory (SRAM), an Electrically Erasable Programmable Read-Only Memory (EEPROM), an Erasable Programmable Read-Only Memory (EPROM), a Programmable Read-Only Memory (PROM), a Read-Only Memory (ROM), a magnetic Memory, a flash Memory, a magnetic disk, or an optical disk.
The present application provides a computer program product which, when run on a computer, causes the computer to perform the method of the first embodiment, any of its alternative implementations.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
In addition, units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Furthermore, the functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
It should be noted that the functions, if implemented in the form of software functional modules and sold or used as independent products, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.
The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (10)

1. A method for calculating node displacement of a collision vibration model is characterized by comprising the following steps:
acquiring a finite element equation of a collision vibration model, wherein the finite element equation is different according to different current states of the collision vibration model, and the current states of the collision vibration model comprise a non-contact blocking state or a contact blocking state;
obtaining a simulation differential equation of the collision vibration model according to a preset physical displacement calculation equation and the finite element equation;
simulating the collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value and the simulation differential equation;
in the simulation process, when the state of the collision vibration model is transformed every time, solving the simulation differential equation according to the geometric conditions and the vibration mode orthogonality to obtain the initial value of the modal velocity after each transformation, and setting the initial value of the modal displacement after each transformation to be zero to form the simulation condition after each transformation;
and simulating the crash vibration model from the simulation moment of state transformation according to the simulated differential equation after each transformation and the corresponding simulation condition after each transformation to obtain a total physical displacement vector of each node on the crash vibration model at the end of each simulation step length, wherein the total physical displacement vector is obtained by substituting modal displacement obtained by simulation at the end of the corresponding simulation step length into the physical displacement calculation equation, and is equal to the sum of the physical displacement vector of the current simulation step length and the physical displacement vector of the corresponding simulation step length before the current simulation step length and the state at each transformation.
2. The method of claim 1, wherein the preset physical displacement calculation equation comprises:
Figure FDA0003098316170000021
Figure FDA0003098316170000022
Figure FDA0003098316170000023
wherein the content of the first and second substances,
Figure FDA0003098316170000024
is ti-1～tiThe nth order mode of the time interval; etani(t) is the corresponding modal displacement,
Figure FDA0003098316170000025
is tj-1～tjN-th order mode of time interval, etanj(tj) Is at the tjModal displacement of the nth order mode at the moment; deltai(t) model of impact vibration at ti-1～tiSimulating a physical displacement vector at the end of the step length;
Figure FDA0003098316170000026
representing the model of impact vibration at ti-1～tiBefore the simulation step length, the sum of the physical displacement vectors of the simulation step length when the state is changed, tjThe time point when the state changes; delta(t)Represents ti-1～tiAnd simulating the total physical displacement vector at the end of the step length.
3. The method of claim 2, wherein the finite element equations of the buff vibration model comprise:
Figure FDA0003098316170000027
wherein [ C ] represents a damping matrix, { δ } represents a node displacement vector, { P (t) } represents an excitation vector; [ M ] represents a quality matrix; [K] and representing a rigidity matrix which is different according to the current state of the crash vibration model.
4. The method of claim 3, wherein obtaining the simulated differential equation of the crash vibration model according to the finite element equation and the preset physical displacement calculation equation comprises:
substituting the preset physical displacement calculation equation into the finite element equation, and obtaining the simulated differential equation according to the orthogonality of the vibration modes, wherein the simulated differential equation is as follows:
Figure FDA0003098316170000028
wherein, tjFor the point in time when the state change occurs,
Figure FDA0003098316170000029
is a constant number of times, and is,
Figure FDA00030983161700000210
can be expressed as:
Figure FDA0003098316170000031
when the state changes
Figure FDA0003098316170000032
Change in value of, xiiIs the damping ratio.
5. The method according to claim 4, wherein solving the simulated differential equation according to geometric conditions and mode orthogonality to obtain an initial value of modal velocity after each transformation comprises:
solving the simulation differential equation according to the orthogonality of the vibration mode to obtain the initial value of the modal velocity after each transformation
Figure FDA0003098316170000033
Wherein, the
Figure FDA0003098316170000034
Comprises the following steps:
Figure FDA0003098316170000035
wherein the content of the first and second substances,
Figure FDA0003098316170000036
for the mode shape of the P-th order at the time of state transition,
Figure FDA0003098316170000037
the modal velocity at the moment of the corresponding state transition.
6. The method of claim 1, further comprising:
in the simulation process, judging whether the polarity of subtracting a clearance value from a total physical displacement vector of a node corresponding to a blocking position at the end of the current simulation step length is opposite to the polarity of subtracting the clearance value from the total physical displacement vector at the end of the previous simulation step length, wherein the clearance value represents the distance between a collision vibration model and a blocking piece;
if so, judging whether the absolute value of the difference value between the total physical displacement vector of the node corresponding to the current simulation step length and the blockage and the gap value is larger than a set error threshold value or not;
if the current simulation step length is larger than the set error threshold, refining the current simulation step length by adopting a dichotomy method to determine a time point in the current simulation step length, wherein the polarity of the subtraction of the gap value from the total physical displacement vector of the node corresponding to the block is opposite to the polarity of the subtraction of the gap value from the total physical displacement vector of the point corresponding to the block in the previous simulation step length, and the absolute value of the subtraction difference value of the gap value from the total physical displacement vector of the node corresponding to the block is smaller than the threshold;
and determining the simulation time of the state transition as the time point when the absolute value of the difference value of the total physical displacement vector of the opposite polarity blocking the corresponding node minus the gap value is smaller than the threshold value.
7. The method of claim 6, wherein the refining the current simulation step size by the bisection method comprises:
taking the starting time point to the middle time point of the current simulation step length as an updated simulation step length;
simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state to obtain a total physical displacement vector corresponding to the updated simulation step length;
judging whether the polarity of the total physical displacement minus the clearance value of the node corresponding to the blocking position at the end of updating the simulation step length is opposite to the polarity of the total physical displacement vector minus the clearance value at the end of the last simulation step length;
if the polarities are opposite, whether the absolute value of the difference value between the total physical displacement vector and the gap value of the node corresponding to the barrier when the simulation step length updating is finished is larger than a set error threshold value is judged;
if the difference is larger than the set error threshold, taking the initial time point and the middle time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the crash vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain a total physical displacement vector corresponding to the updated simulation step length;
if the simulation step length is smaller than the set error threshold, determining the end time point of updating the simulation step length as the simulation time of state conversion;
and if the polarities are not opposite, taking the middle time point and the end time point of the updated simulation step length as new simulation step lengths, updating the updated simulation step length, and returning to execute the step of simulating the collision vibration model according to the updated simulation step length and the simulation differential equation of the current state so as to obtain a total physical displacement vector corresponding to the updated simulation step length.
8. An apparatus for calculating node displacement of a crash vibration model, comprising:
the acquisition module is used for acquiring a finite element equation of the collision vibration model, the finite element equation is different according to different current states of the collision vibration model, and the current states of the collision vibration model comprise a non-contact blocking state or a contact blocking state; obtaining a simulation differential equation of the collision vibration model according to the finite element equation and a preset physical displacement calculation equation;
the simulation module is used for simulating the collision vibration model according to a preset simulation step length, a preset modal displacement, a preset modal velocity initial value and the simulation differential equation; in the simulation process, when the state of the collision vibration model is transformed every time, solving the simulation differential equation according to the geometric conditions and the vibration mode orthogonality to obtain the initial value of the modal velocity after each transformation, and setting the initial value of the modal displacement after each transformation to be zero to form the simulation condition after each transformation; and according to the physical displacement calculation equation and the finite element equation after each conversion, obtaining a simulation differential equation after each conversion through vibration mode orthogonality calculation, simulating the impact vibration model from the simulation moment of state conversion according to the simulation differential equation after each conversion and the corresponding simulation condition after each conversion to obtain a total physical displacement vector of each node on the impact vibration model at the end of each simulation step, substituting modal displacement obtained through simulation at the end of the corresponding simulation step into the physical displacement calculation equation to obtain the total physical displacement vector, wherein the total physical displacement vector is equal to the sum of the physical displacement vector of the current simulation step and the physical displacement vector of the corresponding simulation step before the current simulation step and at each conversion of the state.
9. An electronic device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the method of any one of claims 1 to 7 when executing the computer program.
10. A storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, performs the method according to any of claims 1-7.
CN202110617607.4A 2021-06-03 2021-06-03 Method and device for calculating node displacement of collision vibration model Active CN113361162B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110617607.4A CN113361162B (en) 2021-06-03 2021-06-03 Method and device for calculating node displacement of collision vibration model

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110617607.4A CN113361162B (en) 2021-06-03 2021-06-03 Method and device for calculating node displacement of collision vibration model

Publications (2)

Publication Number Publication Date
CN113361162A true CN113361162A (en) 2021-09-07
CN113361162B CN113361162B (en) 2022-11-22

Family

ID=77531585

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110617607.4A Active CN113361162B (en) 2021-06-03 2021-06-03 Method and device for calculating node displacement of collision vibration model

Country Status (1)

Country Link
CN (1) CN113361162B (en)

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2007015688A1 (en) * 2005-08-01 2007-02-08 Georgij Ivanovich Prokopenko Method for ultrasound vibro-impact processing of long-length product surface
CN102339350A (en) * 2011-09-16 2012-02-01 南京航空航天大学 Complete automobile collision simulation method on basis of parameterization design
CN104268342A (en) * 2014-09-28 2015-01-07 中航工业哈尔滨轴承有限公司 Method for analyzing vibration characteristics of bearing retainer based on finite elements
CN106227922A (en) * 2016-07-14 2016-12-14 燕山大学 Real-time emulation method at Laplace Beltrami shape space elastomeric material based on sample
CN106777630A (en) * 2016-12-07 2017-05-31 同济大学 For the determination method of the mode finite element simulation precision of machine components
KR101861122B1 (en) * 2016-12-12 2018-07-02 인천대학교 산학협력단 Method for analysis of vibro-impacts in a torsional system under both wide open throttle and coast conditions with focus on the multi-staged clutch damper
CN109740216A (en) * 2018-12-24 2019-05-10 南京航空航天大学 One kind being used for the modified modal separation degree method of discrimination of structural model
CN110334371A (en) * 2019-04-18 2019-10-15 朱思宇 A kind of Train-bridge coupling system vibration calculation method based on finite element model

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2007015688A1 (en) * 2005-08-01 2007-02-08 Georgij Ivanovich Prokopenko Method for ultrasound vibro-impact processing of long-length product surface
CN102339350A (en) * 2011-09-16 2012-02-01 南京航空航天大学 Complete automobile collision simulation method on basis of parameterization design
CN104268342A (en) * 2014-09-28 2015-01-07 中航工业哈尔滨轴承有限公司 Method for analyzing vibration characteristics of bearing retainer based on finite elements
CN106227922A (en) * 2016-07-14 2016-12-14 燕山大学 Real-time emulation method at Laplace Beltrami shape space elastomeric material based on sample
CN106777630A (en) * 2016-12-07 2017-05-31 同济大学 For the determination method of the mode finite element simulation precision of machine components
KR101861122B1 (en) * 2016-12-12 2018-07-02 인천대학교 산학협력단 Method for analysis of vibro-impacts in a torsional system under both wide open throttle and coast conditions with focus on the multi-staged clutch damper
CN109740216A (en) * 2018-12-24 2019-05-10 南京航空航天大学 One kind being used for the modified modal separation degree method of discrimination of structural model
CN110334371A (en) * 2019-04-18 2019-10-15 朱思宇 A kind of Train-bridge coupling system vibration calculation method based on finite element model

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
RUYU LIU 等: "Stability and bifurcation analysis of two-degrees-of-freedom vibro-impact system with fractional-order derivative", 《INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS》 *
孔宪仁等: "相对振型转换法求解具有多点限制连续体振动响应", 《振动与冲击》 *
李丙涛等: "两种求解连续体撞振响应方法对比研究", 《航天器环境工程》 *
董福王等: "基于Hertz接触理论的带冠叶片碰撞振动数值仿真研究", 《汽轮机技术》 *

Also Published As

Publication number Publication date
CN113361162B (en) 2022-11-22

Similar Documents

Publication Publication Date Title
Liu et al. Explicit form of an implicit method for inverse force identification
Zhang et al. A response surface approach for structural reliability analysis using evidence theory
Andreaus et al. Numerical simulation of the soft contact dynamics of an impacting bilinear oscillator
US20080312882A1 (en) Structural analysis apparatus and structural analysis method
CN112889058A (en) Method and device for analyzing sensitivity of vehicle body member, and method for determining material characteristics of vehicle body member
Downey et al. Millisecond model updating for structures experiencing unmodeled high-rate dynamic events
Ding et al. Uncertainty quantification of spatially uncorrelated loads with a reduced-order stochastic isogeometric method
He et al. A deep learning energy-based method for classical elastoplasticity
WO2018150798A1 (en) Model estimation system, method, and program
Azam et al. Output-only schemes for joint input-state-parameter estimation of linear systems
CN112949065A (en) Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass
Fehr et al. Interface and model reduction for efficient explicit simulations-a case study with nonlinear vehicle crash models
Li et al. Sparse Bayesian technique for load identification and full response reconstruction
CN113361162B (en) Method and device for calculating node displacement of collision vibration model
JP7018993B2 (en) Fast way for computer-based simulation
Mráz et al. Solution of three key problems for massive parallelization of multibody dynamics
EP2787457B1 (en) Contact simulation method for rubber material
JP2020095400A (en) Simulation device, simulation method, and program
JP2020064450A (en) Fiber behavior calculation device, method, and program
Tuan et al. A fuzzy finite element algorithm based on response surface method for free vibration analysis of structure
Staiger et al. Extending the dynamic response of structural input estimation by combining sensors with unmatched bandwidth
Ray Elasto-plastic analysis of plate using ABAQUS
JP7381892B2 (en) Model conversion method, model conversion device, program and recording medium
Ebrahimian et al. A nonlinear model inversion method for joint system parameter, noise, and input identification of civil structures
JP2009053900A (en) Oscillation analyzing system and oscillation analyzing method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant