Origin dynamic stiffness calculation method based on structural characteristics

Abstract

The invention belongs to the technical field of structural origin dynamic stiffness calculation, and particularly relates to an origin dynamic stiffness calculation method based on structural characteristics, which comprises the following steps: designing and utilizing finite element software to output a mass matrix and a stiffness matrix of a structure, constructing a dynamic stiffness matrix, transforming a solving column formula of frequency response analysis displacement response, and calculating the origin dynamic stiffness of the structure. And multiplying the two sides of the equation by the inverse matrix of the dynamic stiffness matrix at the same time, expanding the equation to obtain an expression of displacement response on the degree of freedom corresponding to the external load, deleting the part of the degree of freedom with the load vector being zero in the expression, further obtaining an expression of the original point dynamic stiffness according to the definition of the original point dynamic stiffness, and calculating the original point dynamic stiffness of the structure.

Description

Technical Field

[0001] This application belongs to the technical field of structural origin dynamic stiffness calculation, and particularly relates to a method for calculating the origin dynamic stiffness based on structural characteristics. Background Art

[0002] The booming noise in the indoor cavity caused by the vibration of the vehicle body panel during driving has a great impact on the riding comfort. The vibration transmitted to the vehicle body through the connection point between the engine suspension and the vehicle body is the main cause of the vibration of the vehicle body panel, and the origin dynamic stiffness of the vehicle body suspension contact point is the main influencing factor of the in-vehicle noise.

[0003] The origin dynamic stiffness mainly refers to the ratio of the excitation force to the displacement at the same position and in the same direction. At present, the commonly used method for calculating the origin dynamic stiffness in engineering first performs a frequency response analysis on the structure, calculates the displacement of the external load application point at each frequency point of the structure, and then divides the external load of the corresponding degree of freedom at the corresponding frequency point by the displacement of the corresponding node to obtain the origin dynamic stiffness at each frequency point. The calculation steps are cumbersome and the calculation efficiency is low, making it difficult to quickly analyze the origin dynamic stiffness of the vehicle body suspension contact point.

[0004] In view of the existence of the above technical defects, this application is proposed. Summary of the Invention

[0005] The purpose of this application is to provide a method for calculating the origin dynamic stiffness based on structural characteristics. This calculation method does not require a frequency response analysis of the structure, does not require calculating the displacement response of each degree of freedom of the structure, only needs to transform the dynamic stiffness matrix, and can directly calculate the origin dynamic stiffness of the structure at each frequency point. The calculation steps are simple and the calculation efficiency is high. By calculating the origin dynamic stiffness of the vehicle body suspension contact point, it can realize the rapid analysis of the origin dynamic stiffness of the vehicle body suspension contact point.

[0006] The technical solution of this application is as follows:

[0007] A method for calculating the origin dynamic stiffness based on structural characteristics, comprising:

[0008] Step 1: Construct a structural finite element model and output the characteristic matrices of the structure, including the mass matrix and the stiffness matrix;

[0009] Step 2: Determine the position and direction of the external load applied on the structure to obtain the degrees of freedom of the external load application;

[0010] Step 3: Construct a dynamic stiffness matrix of the frequency point with the mass matrix and the stiffness matrix and find the inverse matrix;

[0011] Step 4: Transform the displacement response solution formula of the frequency response analysis of the structure. Multiply the left and right sides of the transformed frequency response analysis formula by the inverse matrix of the dynamic stiffness matrix of the frequency point respectively to obtain the expression of the displacement response of the degrees of freedom where the external load is applied;

[0012] Step 5: Expand the expression of the displacement response of the degrees of freedom where the external load is applied, and delete the content of the degrees of freedom where the external load is 0;

[0013] Step 6: Based on the displacement expression corresponding to the degrees of freedom where the external load is applied at the frequency point, calculate the origin dynamic stiffness of the structure according to the definition of the origin dynamic stiffness.

[0014] According to at least one embodiment of the present application, in the above origin dynamic stiffness calculation method based on the structural characteristics, step 1 is specifically:

[0015] Use Hypermesh to build a structural finite element model and export the structural finite element model in the "BDF" format;

[0016] Add the statement "param,extout,kaax" to the BDF file, save it and submit it to NASTRAN for solution to obtain a file with the suffix ".pch";

[0017] Read the file with the suffix ".pch" into the MATLAB program, and assemble the groups of the read "pch" file into the mass matrix [M] and the stiffness matrix [K] through the program for output.

[0018] According to at least one embodiment of the present application, in the above origin dynamic stiffness calculation method based on the structural characteristics, in step 2, determine that the degree of freedom where the external load is applied is k.

[0019] According to at least one embodiment of the present application, in the above origin dynamic stiffness calculation method based on the structural characteristics, in step 3, the dynamic stiffness matrix of the frequency point is constructed as:

[0020] [K d j =-ω j 2 [M]+iω j [B]+[K], where [K d j is the dynamic stiffness matrix of the jth frequency point, ω j is the jth frequency point, and i is the imaginary unit.

[0021] According to at least one embodiment of the present application, in the above origin dynamic stiffness calculation method based on the structural characteristics, in step 4, transform the displacement response solution formula of the frequency response analysis of the structure, and the transformed frequency response analysis formula is:

[0022] ​​[K d j {x(ω j )} = {f(ω j )}, where {x(ω j )} is the displacement response at the j-th frequency point, and {f(ω j )} is the external load at the j-th frequency point;

[0023] The expression for the displacement response of the degree of freedom where the external load is applied is obtained as:

[0024] {x(ω j )} = [K d j -1 {f(ω j )}.

[0025] According to at least one embodiment of the present application, in step five of the above method for calculating the origin dynamic stiffness based on structural characteristics, the expression for the displacement response of the degree of freedom where the external load is applied is expanded, and the content of the degree of freedom with the external load being 0 is deleted, and the expression for the displacement response of the degree of freedom where the external load is applied is obtained as:

[0026] where {x k} j is the displacement of the k-th degree of freedom at the j-th frequency point, {f k} j is the external load of the k-th degree of freedom at the j-th frequency point, is the k-th element of the k-th row at the j-th frequency point, and is the inverse matrix of the dynamic stiffness matrix [K d j at the j-th frequency point.

[0027] According to at least one embodiment of the present application, in step six of the above method for calculating the origin dynamic stiffness based on structural characteristics, calculating the origin dynamic stiffness of the structure specifically includes:

[0028] where is the origin dynamic stiffness of the structure at the j-th frequency point.

[0029] According to at least one embodiment of the present application, the above method for calculating the origin dynamic stiffness based on structural characteristics further includes:

[0030] Step seven, drawing the dynamic stiffness curve of each frequency point of the structure.

[0031] The present application has at least the following beneficial technical effects:

[0032] ​​​A method for calculating the origin dynamic stiffness based on structural characteristics is provided. This method does not require calculating the frequency response of the structure. The origin dynamic stiffness can be directly obtained through the transformation of the dynamic stiffness matrix. The calculation steps are simple and the calculation efficiency is relatively high. By calculating the origin dynamic stiffness of the suspension contact points of the vehicle body, a rapid analysis of the origin dynamic stiffness of the suspension contact points of the vehicle body can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 FIG. is a schematic diagram of the method for calculating the origin dynamic stiffness based on structural characteristics provided by an embodiment of the present application;

[0034] Figure 2 FIG. is a schematic diagram of the finite element model of the three-layer plate structure provided by an embodiment of the present application;

[0035] Figure 3 FIG. is a schematic diagram of a part of the stiffness matrix of the finite element model provided by an embodiment of the present application;

[0036] Figure 4 FIG. is a schematic diagram of the dynamic stiffness curve in the X direction of the 40-node finite element model calculated by the method for calculating the origin dynamic stiffness based on structural characteristics provided by an embodiment of the present application;

[0037] Figure 5 FIG. is a schematic diagram of the dynamic stiffness curve in the X direction of the 40-node finite element model calculated by the current calculation method.

[0038] For better illustration of this embodiment, some contents in the drawings are omitted, enlarged or reduced, and are only used for exemplary illustration and should not be construed as a limitation to the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] To make the technical solutions of the present application and their advantages clearer, the technical solutions of the present application will be further described clearly and completely below in conjunction with the drawings. It can be understood that the specific embodiments described herein are only part of the embodiments of the present application, which are only used to explain the present application and are not intended to limit the present application. It should be noted that for the convenience of description, only the parts related to the present application are shown in the drawings, and other related parts can refer to the usual design.

[0040] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of the present application should have the ordinary meanings understood by those of ordinary skill in the art to which the present application belongs. The "including" used in the description of the present application means that the concept appearing before this word covers the concepts listed after this word and their equivalents, without excluding other related concepts.

[0041] A method for calculating the origin dynamic stiffness based on structural characteristics is as Figure 1 shown.

[0042] Step 1: Construct a structural finite element model and output the characteristic matrices of the structure, including the mass matrix and the stiffness matrix.

[0043] Generally, commercial finite element analysis software such as MSC PATRAN and ANSYS is used to construct the structural finite element model. The structural finite element model includes information such as nodes, elements, attributes, materials, and boundary conditions. Commercial software such as MSC NASTRAN and ANSYS can be used to output the characteristic matrices of the structure.

[0044] In a specific example, Hypermesh is used to create a Figure 2 three-layer plate structural finite element model as shown. The struts in the three-layer plate structure are composed of beam elements CBEAM, and the plates in the three-layer plate structure are composed of shell elements CAUAD4. These two types of elements use the same material parameters. After setting the material and attribute parameters, the degrees of freedom in six directions (Tx, Ty, Tz, Rx, Ry, Rz) of the four fulcrums (nodes 71, 76, 81, 86 as shown Figure 2 in) of the three-layer plate structure are constrained.

[0045] Use Hypermesh to export the structural finite element model in the "BDF" format that NASTRAN can recognize to obtain the input file of NASTRAN. Add the statement "param,extout,kaax" to the BDF file, save it and submit it to NASTRAN for solution, and a file with the suffix "pch" can be obtained. The "pch" file contains the numerical and position information of the mass matrix and the stiffness matrix of the established Figure 2 structural finite element model shown after eliminating the single-point constraints.

[0046] Read the "pch" file containing the stiffness matrix and mass matrix information into the MATLAB program, and assemble the groups of the read "pch" file into a mass matrix [M] and a stiffness matrix [K] through the program, as Figure 3 shown.

[0047] Step 2: Determine the positions and directions of the external loads applied to the structure to obtain the degrees of freedom of the external load application.

[0048] When a concentrated force is applied to the nodes on the structure, the degrees of freedom k of the external load application can be determined according to the positions and directions of the nodes.

[0049] The expression of the external load vector is f j ={0…f k …0} j T , and except for the degrees of freedom where the concentrated external force is applied, the external load vector is 0 on other degrees of freedom. Among them, f jThe subscript j of f represents the external load at the j-th frequency point. k The subscript k represents the k-th degree of freedom of the structure.

[0050] As Figure 2 shown, the position where the external load is applied is in the X direction of Node No. 40. Each node has 6 degrees of freedom, and the X direction is the first degree of freedom of the node. Thus, it can be determined that the external load is applied to the 39×6 + 1 = 235-th degree of freedom of the structure.

[0051] Step 3: Construct the dynamic stiffness matrix of the frequency point with the mass matrix and stiffness matrix and find the inverse matrix.

[0052] In frequency response analysis, a dynamic stiffness matrix is generated for each solved frequency point. This dynamic stiffness matrix is a combination of the stiffness matrix [K], the mass matrix [M], the damping matrix [B], and the solved frequency point.

[0053] The expression for the dynamic stiffness matrix is [K d j =-ω j 2 [M]+iω j [B]+[K], where [K d j is the dynamic stiffness matrix at the j-th frequency point, ω j is the j-th frequency point, and i is the imaginary unit.

[0054] Taking Figure 2 the three-layer plate structure shown as an example, the damping is the global structural damping, and the damping coefficient G is 0.05. For the overall structural damping in frequency response analysis, the treatment method is to multiply the stiffness matrix [K] by the overall damping coefficient G, multiply it by the imaginary unit i, and then add it to the structural stiffness matrix [K] through [K fu =[K]+iG[K] to form the complex stiffness matrix [K fu . The complex stiffness matrix [K fu is a complex stiffness matrix containing the damping term. Therefore, the dynamic stiffness matrix [K d j at the j-th frequency point can be expressed as: [K d j =-ω j 2 [M]+[K fu . Through this formula, the dynamic stiffness matrix at each frequency point can be obtained.

[0055] Invert the dynamic stiffness matrix at each obtained frequency point to obtain the inverse matrix of the dynamic stiffness matrix at each frequency point.

[0056] is the dynamic stiffness matrix [K at the j-th frequency point​​​​d j The inverse matrix of, can also be expressed as [K d j -1 .

[0057] Step 4: Transform the displacement response solution formula for the frequency response analysis of the structure. Multiply both the left and right sides of the transformed frequency response analysis formula by the inverse matrix of the dynamic stiffness matrix at the frequency point to obtain the expression for the displacement response of the degrees of freedom where the external load is applied.

[0058] The main purpose of this step is to theoretically derive the origin dynamic stiffness. The displacement response solution formula for the frequency response analysis of the structure is:[[]] where, {x(ω j )} is the displacement response at the j-th frequency point, {f(ω j )} is the external load at the j-th frequency point, and the transformed expression is: [K d j {x(ω j )} = {f(ω j )}. Multiply both the left and right sides of the equation by the dynamic stiffness matrix at the frequency point and find the inverse matrix to obtain the expression for the displacement response of the degrees of freedom where the external load is applied: {x(ω j )} = [K d j -1 {f(ω j )}.

[0059] Step 5: Expand the expression for the displacement response of the degrees of freedom where the external load is applied, and delete the content of the degrees of freedom where the external load is 0.

[0060] The main purpose of this step is also to theoretically derive the origin dynamic stiffness. Expand the expression for the displacement response of the degrees of freedom where the external load is applied {x(ω j )} = [K d j -1 {f(ω j )} as follows:

[0061]

[0062] In the above formula, k is the k-th degree of freedom, j is the j-th frequency point, n is the size of the dynamic stiffness matrix, and k dkk is the element in the k-th row and k-th column of the dynamic stiffness matrix.

[0063] According to the rule of matrix-vector multiplication, the expression for the frequency response displacement of the k-th degree of freedom {x k} j ​​​​​, that is, the expression of the displacement response of the degrees of freedom to which the external load is applied, is obtained by multiplying the k-th row of the inverse matrix of the dynamic stiffness matrix by the load vector respectively, as follows:

[0064] where {x k} j is the displacement of the k-th degree of freedom at the j-th frequency point, and {f k} j is the external load of the k-th degree of freedom at the j-th frequency point. is the inverse matrix of the dynamic stiffness matrix [K d j at the j-th frequency point, that is is the first element of the k-th row of at the j-th frequency point, is the k-th element of the k-th row of at the j-th frequency point, is the n-th element of the k-th row of at the j-th frequency point.

[0065] Delete the content corresponding to the degrees of freedom to which no external load is applied, that is, the degrees of freedom with an external load of 0, and the displacement expression corresponding to the degrees of freedom to which the external load is applied at the frequency point is obtained as:

[0066] Step 6: Based on the displacement expression corresponding to the degrees of freedom to which the external load is applied at the frequency point, calculate the origin dynamic stiffness of the structure according to the definition of the origin dynamic stiffness.

[0067] The purpose of this step is to derive the expression of the origin dynamic stiffness. The definition of the origin dynamic stiffness is: the ratio of the excitation force to the displacement in the same position and the same direction. According to the definition, the expression of the origin dynamic stiffness is: The physical meaning of

[0068] is the origin dynamic stiffness of the structure at the j-th frequency point.

[0069] For Figure 2 the finite element model shown, the frequency domain range can be the first thirty natural frequencies, 0 - 3.82 Hz.

[0070] Step 7: Plot the dynamic stiffness curves of each frequency point of the structure.

[0071] Taking the frequency as the horizontal axis and the origin dynamic stiffness of each frequency point of the structure as the vertical axis, plot the origin dynamic stiffness curves of each frequency point of the structure.​

[0072] The origin dynamic stiffness calculation method based on structural characteristics disclosed in the above embodiments is designed to utilize the finite element software to output the mass matrix and stiffness matrix of the structure, construct the dynamic stiffness matrix, transform the solution formula for the displacement response of the frequency response analysis, multiply both sides of the equation by the inverse matrix of the dynamic stiffness matrix, expand the equation, obtain the expression for the displacement response of the external load corresponding to the degrees of freedom, delete the part of the degrees of freedom where the load vector is zero in the expression, and then obtain the expression for the origin dynamic stiffness according to the definition of the origin dynamic stiffness, so as to calculate the origin dynamic stiffness of the structure.

[0073] Using the origin dynamic stiffness calculation method based on structural characteristics disclosed in the above embodiments, the Figure 2 origin dynamic stiffness curve in the X direction of node 40 of the finite element model of the structure shown is calculated, as Figure 4 shown. The frequency response results are calculated using NASTRAN, and the origin dynamic stiffness curve in the X direction of node 40 of the finite element model of the structure shown is calculated using the current method through Hyperview, as Figure 2 shown. The two are basically the same, which can prove the effectiveness of the origin dynamic stiffness calculation method based on structural characteristics disclosed in the above embodiments. Figure 5

[0074] So far, the technical solutions of the present application have been described in combination with the preferred embodiments shown in the drawings. Those skilled in the art should understand that the protection scope of the present application is obviously not limited to these specific embodiments. Without departing from the principle of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present application.​

Claims

1. A method for calculating the origin dynamic stiffness based on structural characteristics, characterized in that: include: Step 1: Build a structural finite element model and output the structural characteristic matrix, including mass matrix and stiffness matrix; Step 2: Determine the position and direction of the external load applied on the structure and obtain the degree of freedom of the external load application; Step 3: Use the mass matrix and stiffness matrix to construct the dynamic stiffness matrix of the frequency point and calculate the inverse matrix; Step 4: Transform the frequency response analysis displacement response solution formula of the structure, multiply the left and right ends of the transformed frequency response analysis formula by the inverse matrix of the dynamic stiffness matrix of the frequency point, and obtain the expression of the displacement response of the degree of freedom applied by the external load; Step 5: Expand the expression of displacement response of the degree of freedom when external load is applied, and delete the content of the degree of freedom when the external load is 0; Step 6. Based on the displacement expression corresponding to the degree of freedom applied by the external load at the frequency point, and according to the definition of the origin dynamic stiffness, calculate the origin dynamic stiffness of the structure.

2. The method for calculating the origin dynamic stiffness based on structural characteristics according to claim 1, characterized in that: Step 1 is as follows: Use Hypermesh to build a structural finite element model and export the structural finite element model in "BDF" format; Add "param,extout,kaax" statements in the BDF file, save it and submit it to NASTRAN for solution, and get a file with the suffix "pch"; Read the file with the suffix "pch" into the MATLAB program, and assemble the read "pch" file groups into mass matrix [M] and stiffness matrix [K] for output through the program.

3. The method for calculating the origin dynamic stiffness based on structural characteristics according to claim 2, characterized in that: In step 2, the degree of freedom for applying the external load is determined as k.

4. The method for calculating the origin dynamic stiffness based on structural characteristics according to claim 3, characterized in that: In step three, the dynamic stiffness matrix is ​​constructed as: [K d ] j =-ω j 2 [M]+iω j [B]+[K], where [K d ] j is the dynamic stiffness matrix of the jth frequency point, ω j is the jth frequency point, and i is an imaginary unit.

5. The method for calculating the origin dynamic stiffness based on structural characteristics according to claim 4, characterized in that: In step 4, the frequency response analysis displacement response solution formula of the structure is transformed, and the transformed frequency response analysis formula is: [K d ] j {x(ω j )}={f(ω j )}, where {x(ω j )} is the displacement response of the jth frequency point, {f(ω j )} is the external load at the jth frequency point; The expression of the displacement response of the degree of freedom under external load is obtained as follows: {x(ω j )}=[K d ] j -1 {f(ω j )}。 6. The method for calculating the origin dynamic stiffness based on structural characteristics according to claim 5, characterized in that: In step 5, the expression of displacement response of the degree of freedom applied by external load is expanded, and the content of the degree of freedom with external load of 0 is deleted, and the expression of displacement response of the degree of freedom applied by external load is obtained as follows: Among them, {x k } j is the displacement of the kth degree of freedom at the jth frequency, {f k } j is the external load of the kth degree of freedom at the jth frequency point, For the jth frequency point The k-th element of the k-th row of is the dynamic stiffness matrix of the jth frequency point [K d ] j The inverse matrix of .

7. The method for calculating the origin dynamic stiffness based on structural characteristics according to claim 6, characterized in that: In step 6, the origin dynamic stiffness of the structure is calculated, specifically: in, is the origin dynamic stiffness of the structure at the jth frequency point.

8. The method for calculating the origin dynamic stiffness based on structural characteristics according to claim 7, characterized in that: Also includes: Step 7: Draw the dynamic stiffness curve of each frequency point of the structure.

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