CN112989663B - Finite element method for decoupling unsteady state vibration based on complex domain characteristic value - Google Patents
Finite element method for decoupling unsteady state vibration based on complex domain characteristic value Download PDFInfo
- Publication number
- CN112989663B CN112989663B CN202110295277.1A CN202110295277A CN112989663B CN 112989663 B CN112989663 B CN 112989663B CN 202110295277 A CN202110295277 A CN 202110295277A CN 112989663 B CN112989663 B CN 112989663B
- Authority
- CN
- China
- Prior art keywords
- vibration
- complex domain
- finite element
- characteristic value
- matrix
- 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.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 39
- 239000011159 matrix material Substances 0.000 claims abstract description 35
- 238000013461 design Methods 0.000 claims abstract description 33
- 238000004364 calculation method Methods 0.000 claims abstract description 20
- 230000009466 transformation Effects 0.000 claims abstract description 6
- 230000004044 response Effects 0.000 claims abstract description 5
- 238000004422 calculation algorithm Methods 0.000 claims description 28
- 230000035945 sensitivity Effects 0.000 claims description 16
- 238000006073 displacement reaction Methods 0.000 claims description 14
- 238000010206 sensitivity analysis Methods 0.000 claims description 11
- 238000013016 damping Methods 0.000 claims description 8
- OIGNJSKKLXVSLS-VWUMJDOOSA-N prednisolone Chemical compound O=C1C=C[C@]2(C)[C@H]3[C@@H](O)C[C@](C)([C@@](CC4)(O)C(=O)CO)[C@@H]4[C@@H]3CCC2=C1 OIGNJSKKLXVSLS-VWUMJDOOSA-N 0.000 claims description 8
- 230000008859 change Effects 0.000 claims description 7
- 238000012937 correction Methods 0.000 claims description 3
- 230000008878 coupling Effects 0.000 description 14
- 238000010168 coupling process Methods 0.000 description 14
- 238000005859 coupling reaction Methods 0.000 description 14
- 230000005284 excitation Effects 0.000 description 12
- 230000008569 process Effects 0.000 description 12
- 238000009795 derivation Methods 0.000 description 8
- 238000005457 optimization Methods 0.000 description 8
- 230000010355 oscillation Effects 0.000 description 5
- 238000005516 engineering process Methods 0.000 description 4
- 238000004891 communication Methods 0.000 description 2
- 238000010276 construction Methods 0.000 description 2
- 230000007423 decrease Effects 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 230000003287 optical effect Effects 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 238000006467 substitution reaction Methods 0.000 description 2
- 230000004913 activation Effects 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000006880 cross-coupling reaction Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
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
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- 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)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Automation & Control Theory (AREA)
- Aviation & Aerospace Engineering (AREA)
- Complex Calculations (AREA)
Abstract
The invention relates to a finite element method for decoupling unsteady vibration based on complex domain characteristic values, which comprises the following steps: the finite element method carries out complex domain solution on a time domain vibration differential equation through Laplace transformation, and the solution becomes matrix calculation with Laplace variables as characteristic values. When the calculation result captures a complex domain characteristic value, the complex domain characteristic value is essentially a vibration mode causing unstable system response, and further the essential reasons of the automobile structure vibration and brake squeal are revealed. The finite element method for decoupling unsteady vibration by the complex domain characteristic values is applied to the field of finite element numerical calculation of automobile structure design, has good calculation efficiency and precision, can reasonably predict and decouple unsteady vibration modes, and reaches the level of practical application.
Description
Technical Field
The invention relates to the field of computational mechanics, in particular to a finite element method for decoupling unsteady vibration based on complex domain characteristic values and an application process.
Background
With the continuous application and development of numerical finite element simulation in the engineering field, the designed product has larger and larger size and more complex structure. The complex structure is very easy to vibrate under the influence of the external and self friction coupling exciting force of the structure, and the phenomena of strong brake squeal, steering wheel shake and the like are generated in the design of automobile products, so that the use is influenced, and customer complaints are generated. Therefore, many automobile structural designs need measures such as changing structural design parameters to change system excitation characteristics and decouple unsteady system vibration. In the field of dynamics, matrix analysis and calculation of frequency domain characteristic values are carried out on a system time domain vibration differential equation through Laplace transformation, so that a vibration mode causing unstable system response can be deduced, and further, the essential reasons of automobile structure vibration and brake squeal are revealed. In general finite element algorithms, although matrix algorithms with relevant eigenvalues, such as power method, subspace iteration method, lanczos method, QR method, newton method, jacobi method, etc., are available for users to select, the solution principle and the application scenario are difficult for general users to understand and make correct selections.
In the structural design of automobile engineering, complex structures and excitation characteristics are often involved, so comprehensive evaluation on characteristics such as matrix dimension, solving precision and sparse singularity of a stiffness matrix is required to ensure that the algorithm and the program thereof have higher precision and faster convergence speed. The application provides a set of flow and a method for judging and decoupling unsteady vibration based on complex domain characteristic values, which can automatically pre-judge and capture the basic characteristics of the complex domain characteristic values, further select and adopt a related complex domain characteristic value optimization algorithm, and complete the design optimization of decoupling unsteady vibration by a design parameter sensitivity method. The invention provides a theoretical derivation and application process of the technology, introduces the theoretical derivation and application process into the field of finite element calculation, realizes algorithm programming, and lays the foundation of an independent structural mechanics finite element solver ProStruct complex domain characteristic value decoupling unsteady state vibration algorithm.
Disclosure of Invention
The invention overcomes the defects of the prior art and provides a finite element method for decoupling unsteady vibration based on complex domain characteristic values and an application process.
In order to achieve the purpose, the invention adopts the technical scheme that: a finite element method for decoupling unsteady state vibration based on complex domain characteristic values comprises the following steps:
performing complex domain solution on a time domain vibration differential equation by using Laplace transformation to obtain a matrix calculation result taking a Laplace variable as a characteristic value;
if the complex domain characteristic value is captured by the matrix calculation result, sensitivity analysis is carried out on the design parameters through an algorithm to obtain sensitivity information;
comparing the sensitivity information with preset sensitivity information to obtain a deviation rate;
judging whether the deviation rate is larger than a preset deviation rate threshold value or not,
if the number is larger than the preset value, generating correction parameters to correct the design parameters;
if the difference is smaller than the preset threshold value, deducing a modal frequency domain and a modal characteristic value of unstable system response in the complex domain characteristic value, and predicting the vibration and brake squeal of the automobile structure.
In a preferred embodiment of the present invention, the time domain vibration differential equation in the complex domain solution of the time domain vibration differential equation using the laplace transform is as follows:
[M]{X}+[C]{X}+[K s +K c ]{X}＝ΔF f (1)
[M]and [ C]Respectively representing the structural mass and the damping matrix of the system, { X } is the system displacement, delta F f For friction exciting force, [ K ] s ]And [ K ] c ]Respectively representing the system structure and the stiffness matrix of the internal connections.
In a preferred embodiment of the invention, the friction force Ff is proportional to the change in the normal force Δ N and the coefficient of friction μ, which can be expressed as Δ F f = μ Δ N. The normal force N then depends linearly on the spring rate K f And the relative displacement between the bearing surface and the bearing surface is delta X, and the normal displacement delta X and the spring stiffness K are obtained through delta N f Instead, the change in friction force can be rewritten as:
ΔF f ＝μK f ΔX (2)
in a preferred embodiment of the present invention, the complex domain eigenvalues captured by the matrix calculation result are represented by the following formula:
P k ＝σ k ±jω k (k =1, …, m) formula σ k Complex domain eigenvalues, ω, representing k-order modes k Representing the modal frequencies of the k-order modes.
In a preferred embodiment of the present invention, the sensitivity analysis of the design parameters is performed by an algorithm, which is formulated as follows:
wherein
Is a characteristic singular matrix, x i Are design parameters.
The second aspect of the present invention further provides an application process applied to a finite element algorithm for decoupling unsteady state vibration based on complex domain eigenvalue, comprising the following steps:
constructing a friction force coupling model, and establishing an inclined double-cantilever beam model of a friction excitation source related to unsteady vibration generation;
analyzing a linear one-way friction stiffness spring through a friction force model of unsteady state vibration, and describing oscillation information excited by friction force;
resolving the complex domain characteristic value, and judging the unsteady vibration to obtain an unsteady vibration influence factor;
carrying out sensitivity analysis on the unsteady vibration influence factors to obtain feedback information;
and optimizing the finite element algorithm through the feedback information.
In a preferred embodiment of the present invention, the complex domain eigenvalue is solved, and the unsteady-state vibration is evaluated at the same time, so as to obtain an unsteady-state vibration influence factor, which specifically is:
the unsteady vibration characteristics of the finite element model can be analyzed and judged by the complex domain feature vector distribution obtained by analyzing the finite element model; the equations of vibrational motion for the finite element model can be expressed as:
[M]{X}+[C]{X}+[K]{X}＝{0}
and M and C respectively represent the mass and damping matrix of the system structure, { X } represents the system displacement, and K represents the rigidity matrix of the system structure.
The invention solves the defects in the background technology, and has the following beneficial effects:
the invention provides a flow and a method for judging and decoupling unsteady vibration based on complex domain characteristic values, which can automatically pre-judge and capture the basic characteristics of the complex domain characteristic values, further select and adopt a related complex domain characteristic value optimization algorithm, and complete the design optimization of decoupling unsteady vibration by a design parameter sensitivity method. The invention provides a theoretical derivation and application process of the technology, introduces the theoretical derivation and application process into the field of finite element calculation, realizes algorithm programming, and lays the foundation of an independent structural mechanics finite element solver ProStruct complex domain characteristic value decoupling unsteady state vibration algorithm.
Drawings
The invention is further illustrated by the following examples in conjunction with the drawings.
FIG. 1 shows the construction of the Sprag-slip frictional coupling model of the present invention;
FIG. 2 illustrates a model of frictional coupling between a force-bearing surface and an excitation source;
FIG. 3 shows a distribution diagram of a complex domain eigenvalue solution;
FIG. 4 shows a flow chart of an algorithm and application for decoupling unsteady vibration based on a complex domain eigenvalue method;
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
FIGS. 1 to 4 show a finite element algorithm for decoupling unsteady vibration based on complex domain eigenvalue and an application flow thereof.
A finite element algorithm for decoupling unsteady state vibration based on complex domain characteristic values comprises the following steps:
performing complex domain solution on a time domain vibration differential equation by using Laplace transformation to obtain a matrix calculation result taking a Laplace variable as a characteristic value;
if the complex domain characteristic value is captured by the matrix calculation result, sensitivity analysis is carried out on the design parameters through an algorithm to obtain sensitivity information;
comparing the sensitivity information with preset sensitivity information to obtain a deviation rate;
judging whether the deviation rate is larger than a preset deviation rate threshold value or not,
if so, generating a correction parameter to correct the design parameter;
if the difference is smaller than the preset threshold value, deducing a modal frequency domain and a modal characteristic value of unstable system response in the complex domain characteristic value, and predicting the vibration and brake squeal of the automobile structure.
In a preferred embodiment of the present invention, the time domain vibration differential equation in complex domain solution of the time domain vibration differential equation using Laplace transform is as follows:
[M]{X}+[C]{X}+[K s +K c ]{X}＝ΔF f
[M]and [ C]Respectively representing the structural mass and the damping matrix of the system, { X } is the system displacement, delta F f For friction exciting force, [ K ] s ]And [ K ] c ]Respectively representing the system structure and the stiffness matrix of the internal connections.
It should be noted that, applying the discussed concept of the frictional coupling model to the stiffness matrix of the unsteady vibration finite element model is a reasonable application manner of the frictional coupling contact model. The present application introduces a group of spring units which are linearly related to displacement and are uniformly distributed on the contact surfaces of a force bearing surface and an excitation source (as shown in figure 2). Consider the hypothetical non-interacting coupling friction term Δ F f The associated unsteady vibration finite element differential equation can be expressed as
[M]{X}+[C]{X}+[K s +K c ]{X}＝ΔF f (3)
Here [ K ] s ]And [ K ] c ]Respectively representing the system structure and the stiffness matrix of the internal connections. The coupling friction in this equation is expressed as Δ F of formula (2) f Alternatively, then equation (3) can be expressed as:
in the above equation, the resulting system stiffness matrix becomes an asymmetric structure, which results in a complex domain eigenvalue solution problem, and the magnitude of the real part determines the amplitude of the vibration near the limit, and an unstable state may occur.
The finite element algorithm for solving the unsteady state vibration based on the complex domain eigenvalue is to perform Laplace transformation on a differential equation (4), and the solution becomes a solving problem with a Laplace variable as an eigenvalue. The characteristic values of these complex fields are what cause unstable system responseModal frequency omega k And modal characteristic values, which may be expressed as:
P k ＝σ k ±jω k (k＝1,…,m) (5)
in the formula sigma k Complex domain eigenvalues, ω, representing k-order modes k Representing the modal frequencies of the k-order modes. Each eigenvalue corresponds to a eigenvector representing the predicted mode shape of the unstable system. Thus, σ k And ω k Respectively representing the damping coefficient and the natural frequency describing the motion of the damping curve. Theoretically the magnitude of the real part in equation (5) determines the amplitude of the vibration near the limit. The test data of simulation and experiment shows that the model with higher positive damping is likely to generate unstable mechanical vibration phenomena, including shaking of the steering wheel of the automobile, braking noise and the like. In fig. 3, the unsteady vibration characteristics of the finite element model to be solved can be analyzed and judged by analyzing the complex domain feature vector distribution obtained by analyzing the finite element model.
In a preferred embodiment of the present invention, as shown in FIG. 2, the friction force Ff is proportional to the change in the normal force Δ N and the coefficient of friction μ, which can be expressed as Δ F f = μ Δ N. The normal force N then depends linearly on the spring rate K f And the relative displacement between the bearing surface and the bearing surface is delta X, and the normal displacement delta X and the spring stiffness K are obtained through delta N f Instead, the change in friction force can be rewritten as:
ΔF f ＝μK f ΔX
in a preferred embodiment of the present invention, the complex domain eigenvalues captured by the matrix calculation result are represented by the following formula: p k ＝σ k ±jω k (k =1, …, m) formula σ k Complex domain eigenvalues, ω, representing k-order modes k Representing the modal frequencies of the k-order modes.
In a preferred embodiment of the present invention, the sensitivity analysis of the design parameters is performed by an algorithm, which is formulated as follows:
wherein
Is a characteristic singular matrix, x i For design parameters, see the description of the embodiments for details.
The second aspect of the invention also provides an application process, which is applied to a finite element algorithm for decoupling unsteady vibration based on complex domain eigenvalue, and comprises the following steps:
constructing a friction force coupling model, and establishing an inclined double-cantilever beam model of a friction excitation source related to unsteady vibration generation;
analyzing a linear one-way friction stiffness spring through a friction force model of unsteady state vibration, and describing oscillation information excited by friction force;
resolving the complex domain characteristic value, and judging unsteady vibration to obtain an unsteady vibration influence factor;
carrying out sensitivity analysis on the unsteady vibration influence factors to obtain feedback information;
and optimizing the finite element algorithm through feedback information.
It should be noted that, the construction of the frictional coupling model is based on the theoretical derivation of the Sprag-Slip,
FIG. 1 sets up a tilted double cantilever model of the frictional excitation source associated with unsteady state vibration generation. The force-bearing surface and the excitation source of the vibrating system structure are represented by the moving surface AB and the support O' P/O "P, respectively. The definition of the rigid strut O 'P pivot angle at the friction activation source O' and the force-bearing surface AB is defined herein as β, in which case the associated friction force F can be expressed as:
where L is the load and μ is the coefficient of friction. As μ approaches cot β, the frictional resistance F becomes infinite and the rigid strut is considered to be in a locked state. In this case, the flexible support that actuates O 'may be replaced with another rigid support O' P. As the moving surface AB continues to move to the right, the elastic moment of the pivot O 'will compress the O' P further, the moment resistance of which finally becomes very large, the PO 'O "becomes comparable to a rigid strut O" P, and decreases β to β', the friction force F also decreases, which causes the wiping tip P to slide back causing oscillation. The oscillation of the rigid strut is caused by frictional contact coupling at the strut pivot point and repeated storage and release of elastic energy. Since the frictional force has non-cross coupling, that is, displacement in the normal direction generates tangential force (frictional force), but the tangential displacement does not generate normal force (contact force), the frictional force model of unsteady vibration in the present invention uses a linear one-way frictional stiffness spring to describe the oscillation phenomenon excited by the frictional force. Linear spring elements are selected among excitation surfaces of the finite element modeling, are uniformly distributed in the whole area of the excitation surfaces, and are used for simulating excitation contact conditions.
In a preferred embodiment of the present invention, the complex domain characteristic value is solved, and the unsteady state vibration is evaluated at the same time, so as to obtain an unsteady state vibration influence factor, which is specifically:
the unstable vibration characteristics of the finite element model to be solved can be analyzed and judged through the complex domain characteristic vector distribution obtained by analyzing the finite element model; the equation of vibrational motion for the finite element model can be expressed as:
[M]{X}+[C]{X}+[K]{X}＝{0}
and M and C respectively represent the mass and damping matrix of the system structure, { X } represents the system displacement, and K represents the rigidity matrix of the system structure.
It should be noted that, when the complex domain eigenvalue is solved, the application performs the sensitivity analysis according to the correlation on the predicted unsteady vibration mode eigenvalue. The objective of the unsteady vibration influence factor sensitivity analysis is to find a way to most effectively eliminate the unstable vibration modes among all the designable system parameters. This will derive a set of coefficients for the design parameters that relate the variation of the complex domain characteristic values to the system non-stationary mode of the design parameter set. The coefficients of this set of design parameters are referred to as sensitivity coefficients. The result shows that the derived sensitivity coefficient can identify the contribution of each design parameter to exciting the unstable vibration mode, so that a design optimization suggestion can be fed back, and the unstable vibration excitation can be eliminated and decoupled most effectively. The sensitivity calculation method is deduced and integrated into a complex domain characteristic value calculation process, and algorithm programming is realized.
Further from the derivation in the previous section, the equations of vibration motion for the finite element model can be expressed as:
let
Equation (6) can then be rewritten as follows:
[I] is a feature matrix. It is assumed that,
the equations of motion thus associated can be transformed into:
by making assumptions
And instead of the above equation, the first order eigenvalue problem may be expressed as
To find the derivative of the eigensolution, the eigenvector should have unique orthogonal matrix properties, with the corresponding orthogonalization conditions:
by applying the design parameters (variable x) of equations (9) - (10) i ) Performing a differential calculation yields:
the derivative of the final eigenvalue eigenvalues may be determined by
Multiplying by equation (12) to obtain:
as can be seen from equation (14), to obtain the derivative of the characteristic solution lambda,
the solution should be obtained first. If the design parameter (variable x) i ) And system matrix [ A]And [ B]The clear relationship between the parameters is known, so that the sensitivity coefficient of the system design parameter of the complex domain solution eigensolution can be easily calculated. In the finite element program, the design parameter (variable x) i ) Relation to system matrix [ A ]]，[B]The method can be used for deducing and obtaining the non-steady-state vibration influence factor from a specific solution FE model by a conventional method, so that the sensitivity analysis of the non-steady-state vibration influence factor can be completed by using an equation (14), and further, the design optimization task of decoupling the non-steady-state vibration of the automobile structure is completed by an automatic iterative application process.
The invention provides a flow and a method for judging and decoupling unsteady vibration based on complex domain characteristic values, which can automatically pre-judge and capture the basic characteristics of the complex domain characteristic values, further select and adopt a related complex domain characteristic value optimization algorithm, and complete the design optimization of decoupling unsteady vibration by a design parameter sensitivity method. The invention provides a theoretical derivation and application process of the technology, introduces the theoretical derivation and application process into the field of finite element calculation, realizes algorithm programming, and lays the foundation of an independent structural mechanics finite element solver ProStruct complex domain characteristic value decoupling unsteady state vibration algorithm.
In the several 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 device embodiments are merely illustrative, for example, the division of a unit is only one logical function division, and there may be other division ways in actual implementation, such as: multiple units or components may be combined, or may be integrated into another system, or some features may be omitted, or not implemented. In addition, the coupling, direct coupling or communication connection between the components shown or discussed may be through some interfaces, and the indirect coupling or communication connection between the devices or units may be electrical, mechanical or other forms.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units; can be located in one place or 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.
In addition, all the functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately regarded as one unit, or two or more units may be integrated into one unit; the integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.
Those of ordinary skill in the art will understand that: all or part of the steps for realizing the method embodiments can be completed by hardware related to program instructions, the program can be stored in a computer readable storage medium, and the program executes the steps comprising the method embodiments when executed; and the aforementioned storage medium includes: a mobile storage device, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Alternatively, the integrated unit of the present invention may be stored in a computer-readable storage medium if it is implemented in the form of a software functional module and sold or used as a separate product. Based on such understanding, the technical solutions of the embodiments of the present invention may be essentially implemented or a part contributing 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 enabling a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the methods of the embodiments of the present invention. And the aforementioned storage medium includes: a removable storage device, a ROM, a RAM, a magnetic or optical disk, or various other media that can store program code.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. A finite element method for decoupling unsteady state vibration based on complex domain characteristic values is characterized by comprising the following steps:
performing complex domain solution on the time domain vibration differential equation by using Laplace transformation to obtain a matrix calculation result taking Laplace variables as eigenvalues;
if the complex domain characteristic value is captured by the matrix calculation result, sensitivity analysis is carried out on the design parameters through an algorithm to obtain sensitivity information;
comparing the sensitivity information with preset sensitivity information to obtain a deviation rate;
judging whether the deviation rate is larger than a preset deviation rate threshold value or not,
if so, generating a correction parameter to correct the design parameter;
if the number of the detected signals is less than the preset value, deducing a modal frequency domain and a modal characteristic value of unstable system response in the complex domain characteristic value, and predicting the vibration and brake squeal of the automobile structure;
and (3) carrying out complex domain solution on the time domain vibration differential equation by using Laplace transform, wherein the time domain vibration differential equation is as follows:
[M]{X}+[C]{X}+[K s +K c ]{X}＝ΔF f
[M]and [ C]Respectively representing the structural mass and the damping matrix of the system, { X } is the system displacement, delta F f Is a friction exciting force, [ K s ]And [ K ] c ]Respectively representing the system structure and the rigidity matrix of internal connection;
frictional force F f Proportional to the change in normal force Δ N and coefficient of friction μ, which can be expressed as Δ F f = μ Δ N, the normal force N then depends linearly on the spring rate K f And the relative displacement between the bearing surface and the bearing surface, the normal displacement delta X and the spring stiffness K are obtained through delta N f Instead, the change in friction force can be rewritten as:
ΔF f ＝μK f ΔX
the complex domain eigenvalue of the matrix calculation result is represented by the following formula:
P k ＝σ k ±jω k (k =1, …, m) formula σ k Complex domain eigenvalues, ω, representing k-order modes k A modal frequency representing a k-order mode;
sensitivity analysis is carried out on the design parameters through an algorithm, and the algorithm formula is as follows:
wherein
[I]Is a characteristic singular matrix, x i Is a design parameter;
[K]a stiffness matrix representing the system structure, [ K ]]＝[K S +K C -μK f ]。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110295277.1A CN112989663B (en) | 2021-03-19 | 2021-03-19 | Finite element method for decoupling unsteady state vibration based on complex domain characteristic value |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110295277.1A CN112989663B (en) | 2021-03-19 | 2021-03-19 | Finite element method for decoupling unsteady state vibration based on complex domain characteristic value |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112989663A CN112989663A (en) | 2021-06-18 |
| CN112989663B true CN112989663B (en) | 2023-03-24 |
Family
ID=76333879
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110295277.1A Active CN112989663B (en) | 2021-03-19 | 2021-03-19 | Finite element method for decoupling unsteady state vibration based on complex domain characteristic value |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112989663B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114626141A (en) * | 2022-02-22 | 2022-06-14 | 中国第一汽车股份有限公司 | Method and device for acquiring component contribution amount of unstable mode of brake system, readable storage medium, noise optimization method and computer |
| EP4293228A1 (en) * | 2022-06-14 | 2023-12-20 | Burckhardt Compression AG | Method for predicting the remaining service life of a sealing arrangement of a piston compressor |
| CN116167187B (en) * | 2023-03-20 | 2024-01-05 | 黑龙江大学 | Vibration characteristic analysis method for arbitrary-shape plate coupling structure |
| CN117668597B (en) * | 2023-11-13 | 2024-06-11 | 华南理工大学 | Structural modal parameter identification method and system considering excitation non-stationarity |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109902404A (en) * | 2019-03-06 | 2019-06-18 | 中国工程物理研究院总体工程研究所 | The unified recurrence calculation method of the structure time-histories data integral of different damping form |
| WO2020115386A1 (en) * | 2018-12-03 | 2020-06-11 | Psa Automobiles Sa | Prediction of squeal instability for a vehicle brake |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN111767668B (en) * | 2020-07-03 | 2024-03-29 | 衢州职业技术学院 | Steering knuckle characteristic-based disc brake squeal noise prediction method and storage medium |
-
2021
- 2021-03-19 CN CN202110295277.1A patent/CN112989663B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2020115386A1 (en) * | 2018-12-03 | 2020-06-11 | Psa Automobiles Sa | Prediction of squeal instability for a vehicle brake |
| CN109902404A (en) * | 2019-03-06 | 2019-06-18 | 中国工程物理研究院总体工程研究所 | The unified recurrence calculation method of the structure time-histories data integral of different damping form |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112989663A (en) | 2021-06-18 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112989663B (en) | Finite element method for decoupling unsteady state vibration based on complex domain characteristic value | |
| CN107016154B (en) | Method and system for modeling mechanical features of a structural dynamics system | |
| Liu et al. | Time‐domain Galerkin method for dynamic load identification | |
| Poudou et al. | Hybrid frequency-time domain methods for the analysis of complex structural systems with dry friction damping | |
| Sulsky et al. | Implicit dynamics in the material-point method | |
| Soize | Maximum entropy approach for modeling random uncertainties in transient elastodynamics | |
| Giagopoulos et al. | Computational framework for model updating of large scale linear and nonlinear finite element models using state of the art evolution strategy | |
| Lesoinne et al. | A linearized method for the frequency analysis of three-dimensional fluid/structure interaction problems in all flow regimes | |
| Kuran et al. | A modal superposition method for non-linear structures | |
| CN106372278A (en) | Sensitivity analysis method jointly considering input parameter uncertainty and proxy model uncertainty | |
| Li et al. | Nonlinear friction-induced vibration of a slider–belt system | |
| Meyer et al. | Co-simulation: Error estimation and macro-step size control | |
| JP2021101330A (en) | Geometrical dimension control in optimization | |
| CN104620010B (en) | Disk brake vibration evaluation method and disk brake vibration estimation device | |
| Yuan et al. | A novel hybrid Neumann expansion method for stochastic analysis of mistuned bladed discs | |
| Stanford et al. | Computational strategies for reliability-based structural optimization of aeroelastic limit cycle oscillations | |
| Holland et al. | A component damping identification method for mistuned blisks | |
| Holland et al. | Measurement point selection and modal damping identification for bladed disks | |
| Li et al. | A novel reduced basis method for adjoint sensitivity analysis of dynamic topology optimization | |
| Zhang et al. | A novel technique to predict harmonic response of Particle-damping structure based on ANSYS® secondary development technology | |
| JP2002215680A (en) | Method of designing structure, and recording medium | |
| Warwick et al. | Multi-objective model updating optimization considering orthogonality | |
| Hussein | Inverse force problems for the wave equation | |
| Mahmoodi et al. | Shift-independent model reduction of large-scale second-order mechanical structures | |
| Liao et al. | Maximization of the vibration amplitude and bifurcation analysis of nonlinear systems using the constrained optimization shooting 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 | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20230907 Address after: 215000 station 19, room 1303, floor 13, building 4, No. 209, Zhuyuan Road, high tech Zone, Suzhou, Jiangsu Province (cluster registration) Patentee after: Zhongsheng Yiwei software technology (Suzhou) Co.,Ltd. Address before: No.50, Yixian Road, Hongkou District, Shanghai Patentee before: Dai Die |
|
| TR01 | Transfer of patent right |