CN113361162B - 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

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CN113361162B
CN113361162B CN202110617607.4A CN202110617607A CN113361162B CN 113361162 B CN113361162 B CN 113361162B CN 202110617607 A CN202110617607 A CN 202110617607A CN 113361162 B CN113361162 B CN 113361162B
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卫洪涛
张峰
孙利民
徐文涛
蔡守宇
郭攀
马竞
张强
卫荣汉
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Zhengzhou University
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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 as follows: the method comprises a force integration method, a method based on vibration mode conversion and a recovery coefficient method, wherein when objects with regular shapes, such as regular beams and plates, are processed by adopting the three methods, a better result can be obtained no matter numerical solution or analytic solution is adopted on the basis of modal analysis; 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 problem of modeling of a non-regular object, but only a force integration method is 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 vibrated and stretched simultaneously cannot be simply embodied in a vibration equation under the non-linear boundary conditions.
Therefore, 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 under the condition that the boundary condition cannot be simply converted into the force can be solved.
Disclosure of Invention
The embodiment of the application aims to provide a method and a device for calculating node displacement of a collision vibration model, which are used for solving the problem that an analytic vibration mode expression is difficult to find when a non-regular model is faced, and meanwhile, under the condition that boundary conditions cannot be simply converted into force, the problem can be hopefully solved, but the problem cannot be solved by an existing force integral method.
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; acquiring 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.
According to the designed method for calculating the node displacement of the impact vibration model, the modeling solution of the relative vibration mode conversion method is realized under a finite element frame, so that the corresponding simulation differential equation and the simulation condition are converted when the boundary condition is converted every time, the real displacement of each node of the impact vibration model can be calculated 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 in the conventional method for realizing the force integral method in the finite element frame under the condition that the boundary condition cannot be simply converted into force is solved, a novel method for modeling the relative vibration mode conversion method under the finite element frame to solve the node displacement of the impact vibration model is provided, and the problem of solving the condition that a non-regular object and the boundary condition cannot be simply converted into 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 t i-1 ～t i The nth order mode of the time interval; eta ni (t) is the corresponding modal displacement,
Figure RE-GDA0003153839070000035
is t j-1 ～t j N-th order mode of time interval, eta nj (t j ) Is at the t th j Modal displacement of the nth order mode at the moment; delta i (t) model of impact vibration at t i-1 ～t i Simulating a physical displacement vector at the end of the step length;
Figure RE-GDA0003153839070000036
represents the collision vibration model at t i-1 ～t i Before the simulation step length, the sum of the physical displacement vectors of the simulation step length when each state is converted, t j The time point when the state changes; delta. For the preparation of a coating (t) Represents t i-1 ～t i And 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 ] denotes a damping matrix, { δ } denotes a node displacement vector, { P (t) } denotes 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, t j For 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, xi i Is 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 first and the second end of the pipe are connected with each other,
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 and the 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 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 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 collision 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 collision 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 state conversion.
In the device for calculating the node displacement of the collision vibration model, the scheme realizes modeling solution of the relative vibration mode conversion method under the finite element frame, so that the corresponding simulation differential equation and simulation conditions are converted when the boundary conditions are converted each time, the real displacement of each node of the collision vibration model is calculated, a novel method for modeling the relative vibration mode conversion method under the finite element frame to solve the node displacement of the collision vibration model is provided, and the solution problem of the non-regular object condition can be accurately solved. 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 obtained by subtracting the gap value from the total physical displacement vector of the corresponding blocking node is smaller than a threshold value as the simulation time of 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, 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 barrier when the simulation step length is updated is larger than a set error threshold value or not; 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, an embodiment provides 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.
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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 embodiment of 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 the method for calculating node displacement of the crash vibration model provided in 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 displacement of a collision vibration model according to the present application, and the method combines a relative vibration mode transformation method and a finite element to solve real displacement of each node of the collision 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 the state after the boundary condition transition, which can be understood as the state in the event of a collision between the node of the crash vibration model and the blocking. As a possible implementation mode, assuming that the application adopts a typical cantilever beam unilateral 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 freedom in translation and 1 degree of freedom in rotation, then the displacement vector delta of the unit is e Can be expressed as:
δ e ＝{Y i ,θ Zi ,Y j ,θ Zj } T ；
on the basis of the designed impact vibration model, the finite element equation of the impact 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 collision vibration model, E represents the elastic modulus, A represents the cross-sectional area, l represents the length of the collision vibration model, and I Z Representing the inertia matrix about the Z-axis.
The mass array and stiffness array combination is shown in fig. 9:
when the cantilever beam contacts with the barrier, the influence of the barrier rigidity needs to be added into the rigidity array [ 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 state j Then the value of the element after contact with the barrier is K j + 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
wherein, 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. The diagonal elements corresponding to the node displacement in the stiffness array need to be added with blocking stiffness when in contact blocking, so that a finite element equation is different according to different current states 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 t i-1 ～t i The nth order mode of the time interval; eta ni (t) is the corresponding modal displacement,
Figure RE-GDA0003153839070000126
is t j-1 ～t j N-th order of oscillation, eta, of time interval nj (t j ) Is at the t th j Modal displacement of the nth order vibration mode at the moment; delta. For the preparation of a coating i (t) model of impact vibration at t i-1 ～t i Simulating a physical displacement vector of a step length;
Figure RE-GDA0003153839070000127
representing the model of impact vibration at t i-1 ～t i Before the simulation step length, the sum of the physical displacement vectors of the simulation step length when each state is converted, t j The point in time 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, t 0 Representing the time of zero, any point displacement on the beam can be expressed as { δ (t) } = 1 (t) }, as can be seen in the figure, let t 1 When the time begins, the displacement of the end point is larger than the clearance, and the receiving end of the system isThe counter force effect of the point block, 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, namely { delta (t) } = { delta (t) = wherein the displacement before the boundary condition is converted is superposed with the displacement after the conversion 1 (t 1 )}+{δ 2 (t) }, whereby the analogy is to t i Time of day t i The 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, t j For the point in time when the state changes,
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, xi i For the damping ratio, it should be noted that when the simulated differential equation is transformed, the parameters are used
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 a geometric condition 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 method for 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 specifically includes: 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 t 1 ～t i In 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 t 1 When the step length is long, each order modal displacement obtained by simulating the simulated differential equation is eta ni (t 1 ) Shifting the mode η ni (t 1 ) By substitution into the physical displacement calculation equation
Figure RE-GDA0003153839070000151
In (1), calculating to obtain 0-t 1 The physical displacement vector of the step size is assumed to be { δ } i (t 1 ) 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 (t 1 ) I.e., the total physical displacement vector is { delta } i (t 1 ) }; continuing the simulation when starting from t 1 ～t 2 When the step length is long, the modal displacement obtained by simulating the simulation differential equation is eta ni (t 2 ) D, the modal displacement eta ni (t 2 ) By substitution into the physical displacement calculation equation
Figure RE-GDA0003153839070000154
In (1), calculating to obtain t 1 ～t 2 The physical displacement vector of the step size is { delta } i (t 2 ) Before this, since the state of the knock-up model has not changed yet, therefore,
Figure RE-GDA0003153839070000155
thus, the method can obtain the result that,
Figure RE-GDA0003153839070000156
in this case, δ (t) = { δ = i (t 2 ) I.e. t 1 ～t 2 The total physical displacement vector of step length is { delta i (t 2 ) }; continuing the simulation when starting from t 2 ～t 3 When the step length is long, the modal displacement obtained by simulating the simulation differential equation is eta ni (t 3 ) D, the modal displacement eta ni (t 3 ) By substitution into the physical displacement calculation equation
Figure RE-GDA0003153839070000157
Figure RE-GDA0003153839070000158
In (1), calculating to obtain t 2 ～t 3 The physical displacement vector of the step size is now δ i (t 3 ) 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 time i (t 3 ) 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 y L Let the gap between the node and the barrier at the initial vibration be Δ if at t 2 Time y L -Δ>0 and at t 3 Time y L -Δ<0, then, is illustrated at t 2 ～t 3 The polarity of the difference between the total physical displacement vector of the point corresponding to the block obtained at the end of the step length and the gap value is the same as that described aboveThe polarity of this value obtained by simulating the step is opposite, so t can be determined 2 ～t 3 And the state of the impact vibration model is changed from a cantilever beam state to a contact blocking state during the step.
After the state is determined to be changed, the scheme transforms the simulation conditions 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 condition 2 ～t 3 In the simulation step, when the difference value between the total physical displacement vector and the clearance calculated in a certain simulation step changes relative to the polarity of the value calculated in the previous simulation step in the subsequent simulation step, the simulation condition and the simulation differential equation are changed, and then 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 changes is repeated until the simulation step is completely finished or the set simulation step 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 is opposite to the polarity of the gap value subtracted from the total physical displacement vector at the end of the previous simulation step, 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 blocking the corresponding node minus the gap value is smaller than the threshold value.
In the simulation process, when each simulation step size simulation is finished, the method compares the polarity of the difference between the total physical displacement vector of the node corresponding to the blocking position calculated when the current step size is finished and the gap value subtracted from the current physical displacement vector of the node corresponding to the blocking position when the current simulation step size is finished with the difference when the previous simulation step size is finished, and if the polarity is opposite, the state is changed, the method executes step S510 to further judge whether the absolute value of the difference between the total physical displacement vector of the node corresponding to the blocking position of the current simulation step size and the gap value is greater than the set error threshold value; if the current simulation step length is smaller than the set error threshold value, determining the termination time point of the current simulation step length as a 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 and 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 state transition, and then accurately obtains the time point of state transition in the simulation step length of state transition, 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 greater than the set error threshold, continuing to halve 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 and the polarity of the total physical displacement vector minus gap value at the end of the previous simulation step length are not opposite, it is indicated that the state transformation time is not between the starting time point and the middle time point of the simulation step length of the state transformation, then the middle time point and the ending time point of the simulation step length of the state transformation 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 used for acquiring a finite element equation of the 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 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 a physical displacement calculation equation and a finite element equation after each conversion, calculating the vibration mode orthogonality to obtain a simulation differential equation after each conversion, simulating the collision 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 collision vibration model at the end of each simulation step, substituting modal displacement obtained by 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 state conversion.
In the designed device for calculating the node displacement of the impact vibration model, the scheme realizes that the relative vibration mode conversion method is modeled and solved under a finite element frame, so that the corresponding simulation differential equation and simulation condition are converted when the boundary condition is converted every time, further the real displacement of each node of the impact vibration model can be calculated 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 in the conventional method for realizing the force integral method in the finite element frame under the condition that the boundary condition cannot be simply converted into force is solved, a novel method for modeling and solving the node displacement of the impact vibration model under the finite element frame by the relative vibration mode conversion method is provided, and the problem of solving under the condition that a non-regular object and the boundary condition cannot be simply converted into 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, 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 blocking and the gap value is larger than a set error threshold value or not; 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 the determining module 740 is 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 and a middle time point of the current simulation step as the updated simulation step; 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 time is smaller than the set error threshold, determining a termination time point for updating the simulation step length as the simulation time of state change; 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: acquiring a finite element equation of a 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 execute the method of the first embodiment or any alternative implementation of the first embodiment.
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 solutions of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several 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 methods described in 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 to the present application 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 (9)

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 condition and the vibration mode orthogonality to obtain the 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 the simulation condition after each transformation;
according to the physical displacement calculation equation and the finite element equation after each conversion, a simulation differential equation after each conversion is obtained through vibration mode orthogonality calculation, and according to the simulation differential equation after each conversion and the corresponding simulation condition after each conversion, the collision vibration model is simulated from the simulation moment of state conversion so as to obtain a total physical displacement vector of each node on the collision vibration model when each simulation step length is finished, wherein the total physical displacement vector is obtained through substituting modal displacement obtained through simulation when the corresponding simulation step length is finished 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 when the state is converted before the current simulation step length;
in the simulation process, judging whether the polarity of the total physical displacement vector minus the clearance value of the node corresponding to the blocking position at the end of the current simulation step length is opposite to the polarity of the total physical displacement vector minus the clearance value at the end of the previous simulation step length, wherein the clearance value represents the distance between the collision vibration model and the 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 greater than the set error threshold value, refining the current simulation step length by adopting a dichotomy method to determine a time point when the absolute value of the difference value of the total physical displacement vector of the node corresponding to the blocking minus the gap value in the current simulation step length is smaller than the threshold value, wherein the polarity of the subtraction of the total physical displacement vector of the node corresponding to the blocking minus the gap value is opposite to that of the total physical displacement vector of the point corresponding to the blocking minus the gap value in the previous simulation step length;
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.
2. The method of claim 1, wherein the preset physical displacement calculation equation comprises:
Figure FDA0003889322260000021
Figure FDA0003889322260000022
Figure FDA0003889322260000023
wherein the content of the first and second substances,
Figure FDA0003889322260000024
is t i-1 ～t i The nth order mode of the time interval; eta ni (t) is corresponding toThe displacement of the mode shape is realized,
Figure FDA0003889322260000025
is t j-1 ～t j N-th order mode of time interval, eta nj (t j ) Is at the t j Modal displacement of the nth order mode at the moment; delta i (t) model of impact vibration at t i-1 ～t i Simulating a physical displacement vector at the end of the step length;
Figure FDA0003889322260000026
representing the model of impact vibration at t i-1 ～t i Before the simulation step length, the sum of the physical displacement vectors of the simulation step length when the state is changed, t j The time point when the state changes; delta. For the preparation of a coating (t) Represents t i-1 ～t i And 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 FDA0003889322260000027
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 simulation differential equation according to the orthogonality of the vibration mode, wherein the simulation differential equation is as follows:
Figure FDA0003889322260000031
wherein, t j For the point in time when the state change occurs,
Figure FDA0003889322260000032
is a constant number of times, and is,
Figure FDA0003889322260000033
can be expressed as:
Figure FDA0003889322260000034
Figure FDA0003889322260000035
when the state changes
Figure FDA0003889322260000036
Change in value of, xi i Is 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 FDA0003889322260000037
Wherein, the
Figure FDA0003889322260000038
Comprises the following steps:
Figure FDA0003889322260000039
wherein the content of the first and second substances,
Figure FDA00038893222600000310
for the mode shape of the P-th order at the time of state transition,
Figure FDA00038893222600000311
the modal velocity at the moment of the corresponding state transition.
6. The method of claim 1, wherein the refining the current simulation step size by using 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 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 the polarities are opposite, 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 barrier when the simulation step length is updated is larger than a set error threshold value or not;
if the simulation step length is larger than the set error threshold value, 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 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.
7. 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, and according to the simulation differential equation after each conversion and the corresponding simulation condition after each conversion, simulating the crash vibration model from the simulation moment of state conversion 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 through substituting modal displacement obtained through 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 at each conversion of the state;
the device also comprises a judging module, a judging module and a judging module, wherein the judging module is used for judging whether the polarity of the gap value subtracted by 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 by the total physical displacement vector at the end of the previous simulation step length in the simulation process, and the gap value represents the distance between the collision vibration model and the 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 blocking and the gap value is larger than a set error threshold value or not;
the fine processing module is used for performing fine 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 in the current simulation step length, wherein the polarity of the gap value subtracted from the total physical displacement vector of the node corresponding to the block 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 of the gap value subtracted from the total physical displacement vector of the node corresponding to the block is smaller than the threshold value;
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.
8. An electronic device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the method of any of claims 1 to 6 when executing the computer program.
9. A storage medium on which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1-6.
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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 (5)

* Cited by examiner, † Cited by third party
Title
Stability and bifurcation analysis of two-degrees-of-freedom vibro-impact system with fractional-order derivative;Ruyu Liu 等;《International Journal of Non-Linear Mechanics》;20201130;全文 *
两种求解连续体撞振响应方法对比研究;李丙涛等;《航天器环境工程》;20170215(第01期);全文 *
基于Hertz接触理论的带冠叶片碰撞振动数值仿真研究;董福王等;《汽轮机技术》;20170825(第04期);全文 *
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》.2013,(第21期), *
相对振型转换法求解具有多点限制连续体振动响应;孔宪仁等;《振动与冲击》;20130215(第03期);全文 *

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