CN110858256A - Sensitivity analysis method for rigidity performance of vehicle body - Google Patents
Sensitivity analysis method for rigidity performance of vehicle body Download PDFInfo
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Abstract
The invention relates to the technical field of vehicle design, in particular to a sensitivity analysis method for vehicle body rigidity performance. The sensitivity analysis method for the rigidity performance of the vehicle body comprises the following steps: acquiring a plurality of characteristic structures of an automobile body to be analyzed; wherein the feature comprises a beam structure and/or a joint structure; determining simplified models corresponding to a plurality of characteristic structures; carrying out preliminary test design on the automobile body according to the plurality of simplified models to obtain preliminary design values corresponding to the plurality of simplified models; and analyzing the sensitivity of the rigidity performance of the automobile body of the automobile according to the plurality of simplified models and the initial design values thereof, and determining the sensitive structure in the plurality of characteristic structures. The sensitivity analysis method for the rigidity performance of the vehicle body can quickly and efficiently identify the sensitive structure influencing the rigidity performance of the vehicle body, and provides a basis for further structure optimization design.
Description
Technical Field
The invention relates to the technical field of vehicle design, in particular to a sensitivity analysis method for rigidity performance of a vehicle body.
Background
The structural rigidity of the automobile body can reflect the overall structural performance of the automobile body and is an important target in the design of new automobile types, the structural rigidity and the light weight are mutually influenced to a certain extent, and the structural rigidity can be reduced when a light weight scheme is implemented. Therefore, the sensitivity analysis method can be used for identifying the parts of the automobile body which have large influence on the structural rigidity, and further the design of the targeted Jinxin light weight scheme is carried out, so that the influence on the structural rigidity is avoided.
The conventional method for analyzing the sensitivity of the automobile body mainly uses the part with the minimum assembly level as an analysis object, uses the thickness of each part as an independent design variable, and analyzes the sensitivity of each part thickness to the overall rigidity performance.
However, in addition to the thickness of the parts, the joint and the main cross section are also important objects for reducing the weight of the vehicle body, and it is necessary to identify the sensitive structural characteristics of the joint and the cross section and use the characteristics as the target or boundary condition for the optimum design. However, the conventional automobile body sensitivity is lack of an analysis method for directly acquiring the sensitivity of the automobile body rigidity performance to the joint and section structure characteristics.
Therefore, in order to solve the problems of the conventional method for analyzing the sensitivity of the automobile body, it is necessary to provide a method for analyzing the sensitivity of the rigidity of the automobile body, which can directly analyze the influence of the structural characteristics of the joint and the cross section on the rigidity of the automobile body.
Disclosure of Invention
In order to solve the problems, the invention provides a sensitivity analysis method for the rigidity performance of the vehicle body, which can quickly and efficiently identify a sensitive structure influencing the rigidity performance of the vehicle body and provide a basis for further structure optimization design.
In order to achieve the above object, the present invention provides a sensitivity analysis method for vehicle body stiffness performance, comprising:
acquiring a plurality of characteristic structures of an automobile body to be analyzed; wherein the feature comprises a beam structure and/or a joint structure;
determining simplified models corresponding to a plurality of characteristic structures;
carrying out preliminary test design on the automobile body according to the plurality of simplified models to obtain preliminary design values corresponding to the plurality of simplified models;
and analyzing the sensitivity of the rigidity performance of the automobile body of the automobile according to the plurality of simplified models and the initial design values thereof, and determining the sensitive structure in the plurality of characteristic structures.
Further, when the feature is a beam structure, the method for determining the simplified model corresponding to the feature includes:
the beam structure is simplified into a simplified model in the form of one-dimensional beam elements.
Further, when the feature structure is a joint structure, the method for determining the simplified model corresponding to the feature structure includes:
the joint structure is simplified into a simplified model in the form of a combination of one-dimensional beam units and one-dimensional spring units.
Further, the method for carrying out preliminary experimental design on the automobile body according to the plurality of simplified models to obtain preliminary design values corresponding to the plurality of simplified models comprises the following steps:
assigning a first design variable to each simplified model;
assigning a first design value to the plurality of first design variables to complete a preliminary test design of the automobile body;
the first design value is taken as a preliminary design value of the corresponding simplified model.
Further, still include:
carrying out accurate test design on the automobile body according to the simplified model corresponding to the sensitive structure to obtain an accurate design value corresponding to the simplified model of the sensitive structure;
and analyzing the sensitivity of the rigidity performance of the automobile body of the automobile according to the characteristic structure and the initial design value thereof, the sensitive structure and the accurate design value thereof, and determining the characteristic parameters of the sensitive structure.
Further, the method for obtaining the accurate design value corresponding to the simplified model of the sensitive structure comprises the following steps:
respectively endowing key structure characteristic parameters of the simplified model of the sensitive structure with second design variables;
giving a second design value to the plurality of second design variables to complete the accurate test design of the automobile body;
the second design value is taken as an accurate design value of the corresponding simplified model.
Further, when the sensitive structure is a beam structure, the key structural characteristic parameters are characteristic parameters corresponding to the bending characteristic and the torsion characteristic of the simplified model of the beam structure.
Further, when the sensitive structure is a joint structure, the key structural characteristic parameter is a stiffness value of each branch of the simplified model of the joint structure in three directions in a stereo coordinate system.
Further, when the sensitive structure is a beam structure, the characteristic parameter of the sensitive structure is a characteristic parameter corresponding to bending characteristic and/or torsion characteristic.
Further, when the sensitive structure is a joint structure, the sensitive structure characteristic parameter is a stiffness value of at least one branch of the simplified model of the joint structure in at least one direction in a stereo coordinate system.
According to the sensitivity analysis method for the rigidity performance of the automobile body, disclosed by the invention, the beam structure and the joint structure are respectively simplified into the corresponding simplified models, the initial test design is carried out on the automobile body according to the corresponding simplified models, and the sensitivity of the rigidity performance of the automobile body is analyzed, so that the rigidity sensitivity of the beam structure and the joint structure of the automobile body can be quickly and efficiently analyzed, the sensitive structure influencing the integral performance of the automobile body can be quickly and efficiently identified, and a basis is provided for further structural optimization design.
Drawings
FIG. 1 is a flow chart of a method for sensitivity analysis of vehicle body stiffness performance in accordance with one embodiment of the present invention;
FIG. 2 is a schematic view of a beam structure and joint structure of an automobile body according to an embodiment of the present invention;
FIG. 3 is a schematic view of a beam structure and simplified model thereof according to an embodiment of the present invention;
FIG. 4 is a schematic illustration of key structural characteristic parameters of a beam structure according to an embodiment of the present invention;
FIG. 5 is a schematic view of a joint structure and a simplified model thereof according to an embodiment of the present invention;
FIG. 6 is a flow chart of a method for sensitivity analysis of vehicle body stiffness performance in accordance with another embodiment of the present invention;
FIG. 7 is an overall flow chart of assay design and sensitivity analysis according to an embodiment of the present invention;
fig. 8 is a schematic view of a joint structure of an automobile body according to one specific example of the present invention.
Detailed Description
The structure, operation principle and the like of the present invention will be further explained with reference to the accompanying drawings.
As shown in fig. 1, a sensitivity analysis method for vehicle body stiffness performance according to an embodiment of the present invention includes:
s10, acquiring a plurality of characteristic structures of the automobile body to be analyzed; wherein the feature comprises a beam structure and/or a joint structure.
And S20, determining simplified models corresponding to the plurality of characteristic structures.
And S30, carrying out preliminary test design on the automobile body according to the plurality of simplified models to obtain preliminary design values corresponding to the plurality of simplified models.
And S40, analyzing the sensitivity of the rigidity performance of the automobile body of the automobile according to the plurality of simplified models and the initial design values thereof, and determining the sensitive structure in the plurality of characteristic structures. Wherein the sensitive structure is one or more characteristic structures which have the greatest influence on the rigidity performance of the automobile body.
In the embodiment of the present invention, in step S10, as shown in fig. 2, different area structures may be divided into the beam structure 10 and the joint structure 20 according to the geometric features of the different structures, wherein the beam structure 10 refers to the area structure with continuous geometric section and uniform structural characteristics on the automobile body, and the joint structure 20 refers to the connection structure between the different beam features on the automobile body. When the classification of the different region structures is completed, the beam structure 10 and/or the joint structure 20 can be selected and used as the feature structure to be analyzed.
For example, in one embodiment, only the beam structure 10 of the automobile body may be selected as the characteristic structure to be analyzed, and in this case, only one or several beam structures 10, which affect the sensitivity of the body rigidity performance of the automobile body, among the plurality of beam structures 10 are analyzed as the sensitive structure. For another example, in still another embodiment, only the joint structure 20 of the automobile body may be selected as the characteristic structure to be analyzed, in which case, only one or several joint structures 20 that affect the sensitivity of the body rigidity performance of the automobile body among the plurality of joint structures 20 are analyzed as the sensitive structure. For another example, in another embodiment, the beam structure 10 and the joint structure 20 of the automobile body may be selected as the characteristic structure to be analyzed, in which case, only one or several of the plurality of beam structures 10 and the joint structure 20 that affect the sensitivity of the body rigidity performance of the automobile body are analyzed as the sensitive structure.
In an embodiment of the present invention, when the feature structure is a beam structure, the method for determining the simplified model corresponding to the feature structure includes:
the beam structure is simplified into a simplified model in the form of one-dimensional beam elements.
Specifically, as shown in fig. 3, a finite element mesh of the beam structure 10 can be determined, and then a simplified equivalent is performed by using one-dimensional beam elements, and two elements are equivalent to a straight line segment, i.e. a beam simplified model 10'. Since the spatial position of the beam structure 10 is determined by placing the finite element mesh into the geometric center of the cross-section, the key structural characteristics considered may include bending and torsion characteristics in order to ensure that the key structural characteristics of the beam simplified model 10' are consistent with the finite element mesh.
The above-mentioned key structural characteristic parameters can be calculated from the geometric section features of the beam structure, and the calculation formula is shown in table 1 below.
TABLE 1 formula for calculating key structural characteristics of beam structure
The parameters of the equations in Table 1 are illustrated as shown in FIG. 4, where t isiThickness, l, of the jth geometrical feature of the ith beam structure 30ijDenotes the length, θ, of the jth geometrical feature of the ith beam structureijRepresents the angle between the jth geometrical feature of the ith beam structure and the inertia axis y, (cy)ij, czij) Is the center coordinate of the jth geometric feature of the ith beam structure.
In an embodiment of the present invention, when the feature structure is a joint structure, the method for determining the simplified model corresponding to the feature structure includes:
the joint structure is simplified into a simplified model in the form of a combination of one-dimensional beam units and one-dimensional spring units.
Specifically, as shown in fig. 5, the vehicle body B-pillar lower joint is taken as an example, and includes three branches, i.e., a left branch 1, an upper branch 2, and a right branch 3. Firstly, determining a finite element grid of a joint structure 20, then adopting a joint model in a one-dimensional beam unit and one-dimensional spring unit combination form to carry out simplification equivalence, adopting a one-dimensional beam unit 21' to carry out simplification equivalence on each joint branch, and determining the geometric position of each joint branch by the section centroid and the joint central point; and every two branches 21 ' are connected by a spring unit 22 ', so that it is equivalent to a joint simplification model 20 '. Wherein the angular displacement of each branch in the system coordinate system can be obtained by applying x, y, z three-directional unit loads in the stereo coordinate system to each branch of the finite element mesh model of the joint structure 20. Obtaining a stiffness matrix M of the branches 1, 2, 3 from the applied unit load and angular displacement1、M2、M3Each matrix is subjected to similar diagonal transformation to obtain diagonal matrices, i.e.
[Rn]T[Mn][Rn]＝[Ωn]n＝1,2,3
Wherein [ omega ]n]Is a diagonal matrix of the branches and,
is the eigenvector matrix of the stiffness matrix of the branches,
for the stiffness value of the nth branch in the direction of its corresponding local coordinate system 23', the local coordinate system xn-yn-znDirection is defined by a feature vector
And (4) determining. The overall stiffness value of the joint simplification model 20 'can be expressed by the stiffness values of 3 sets of zero-sized spring units 22', and satisfies the following formula:
in the formula, K12＝diag(λ11,λ12,λ13)，λ11Local coordinate system x corresponding to the 1 st branch1To spring unit stiffness value, λ12Local coordinate system y corresponding to the 1 st branch1To spring unit stiffness value, λ13Local coordinate system z corresponding to the 1 st branch1Stiffness value to spring unit; k23＝diag(λ21,λ22,λ23)，λ21Local coordinate system x corresponding to the 2 nd branch2To spring unit stiffness value, λ22Local coordinate system y corresponding to the 2 nd branch2To the stiffness value, lambda, of the spring unit23Local coordinate system z corresponding to the 2 nd branch2A stiffness value to the spring unit; k13＝diag(λ31,λ32,λ33)，λ31Local coordinate system x corresponding to the 3 rd branch3To spring unit stiffness value, λ32Local coordinate system y corresponding to the 3 rd branch3To a spring unit stiffness value, λ33Part corresponding to the 3 rd branchCoordinate system z3And (4) a rigidity value towards the spring unit.
In the embodiment of the present invention, in step S30, the method for performing preliminary trial design on the automobile body according to the plurality of simplified models to obtain preliminary design values corresponding to the plurality of simplified models includes:
s31, a first design variable is assigned to each simplified model.
And S32, assigning first design values to the first design variables to complete the preliminary test design of the automobile body.
And S33, taking the first design value as a preliminary design value of the corresponding simplified model.
Because the whole of every simplified model is as first design variable, consequently, when carrying out preliminary test design to automobile body, can reduce preliminary test design's calculated amount, improve preliminary test design's efficiency, make preliminary test design's process more simplified.
As shown in fig. 6, in the embodiment of the present invention, the sensitivity analysis method for the vehicle body rigidity performance further includes:
and S50, carrying out accurate test design on the automobile body according to the simplified model corresponding to the sensitive structure, and obtaining an accurate design value corresponding to the simplified model of the sensitive structure.
S60, analyzing the sensitivity of the rigidity performance of the automobile body of the automobile according to the characteristic structure and the initial design value thereof, the sensitive structure and the accurate design value thereof, and determining the characteristic parameters of the sensitive structure.
When the sensitive structure is a beam structure, the characteristic parameters of the sensitive structure are characteristic parameters corresponding to the bending characteristic and/or the torsion characteristic. When the sensitive structure is a joint structure, the sensitive structure-specific parameter is a stiffness value of at least one branch of the simplified model of the joint structure in at least one direction in a stereo coordinate system.
In the embodiment of the present invention, in step S50, the method for performing an accurate test design on an automobile body according to a simplified model corresponding to a sensitive structure to obtain an accurate design value corresponding to the simplified model of the sensitive structure includes:
and S51, respectively assigning the key structure characteristic parameters of the simplified model of the sensitive structure to second design variables.
And S52, giving a second design value to the plurality of second design variables to complete the accurate test design of the automobile body.
And S53, taking the second design value as the accurate design value of the corresponding simplified model.
When the sensitive structure is a beam structure, the key structural characteristic parameters are characteristic parameters corresponding to the bending characteristic and the torsion characteristic of the simplified model of the beam structure. When the sensitive structure is a joint structure, the key structural characteristic parameter is the stiffness value of each branch of the simplified model of the joint structure in three directions in the three-dimensional coordinate system.
In the embodiment of the invention, the initial test design is firstly carried out, then the sensitive structure is analyzed, then the precise test design is carried out on the sensitive structure, and the characteristic parameters of the sensitive structure are analyzed, so that the efficiency of sensitivity analysis can be effectively improved.
As shown in fig. 7, the sensitivity analysis method for the vehicle body rigidity performance according to the embodiment of the present invention performs the analysis in two stages, i.e., stage 1 and stage 2. The operation flow is shown in fig. 7. In stage 1, first, design variables 1 … … j and k … … m are respectively assigned to simplified models of a joint structure 1 … … joint structure j and a beam structure k … … beam structure m, thereby forming a set of design variables. And carrying out preliminary test design aiming at the set of design variables, wherein when the first design value of any design variable is changed, all structural performances of the corresponding joint structure or beam structure are changed according to the same amplitude. And then, carrying out sensitivity analysis according to a preliminary design value obtained by the preliminary test design to obtain a sensitive structure. In stage 2, each critical structural characteristic parameter of the sensitive structure is assigned a corresponding design variable, and a set of design variables is formed therefrom, for example, the critical structural characteristic parameter I of the beam structureY、IZ、IYZ、EtDesign variables S1, S2, S3 and S4 are respectively assigned to the joint structure, and design variables are respectively assigned to key structural characteristic parameters λ 11, λ 12, λ 13 and … … of the joint structureAmounts j1, j2, j3, … …. And carrying out accurate test design aiming at the group of design variables, and carrying out sensitivity analysis according to an accurate design value obtained by the accurate test design, so that sensitive structural characteristic parameters which have important influence on the rigidity performance of the vehicle body can be identified and used as an optimization target or boundary condition in the structural optimization design.
Next, a method for analyzing the sensitivity of the vehicle body rigidity performance according to the embodiment of the present invention will be specifically described with respect to the vehicle body shown in fig. 8. Specifically, the characteristic structure to be analyzed is taken as an example of the joint structure. The vehicle body shown in the drawing has 12 key joint structures, such as a-pillar lower joint left 207, a-pillar lower joint right 201, a-pillar upper joint left 210, a-pillar upper joint right 204, B-pillar upper joint left 211, B-pillar upper joint right 205, B-pillar lower joint left 208, B-pillar lower joint right 202, C-pillar upper joint left 212, C-pillar upper joint right 206, C-pillar lower joint left 209, and C-pillar lower joint right 203. Because the vehicle body joint is designed symmetrically, when the design variable corresponding to the left joint structure changes, the corresponding parameters of the right corresponding joint structure also change in the same way, and six joints, namely a left joint 207 of a left column A lower joint, a left joint 210 of an A column, a left joint 211 of a B column, a left joint 208 of a B column, a left joint 212 of a C column and a left joint 206 of a C column, are used as analysis objects.
Taking the left 206 of the C-pillar lower joint as an example, the stiffness values of the branches of the simplified model of the joint structure obtained by the simplified equivalent method of the embodiment of the present invention are shown in table 2.
TABLE 2C statistical table of stiffness values of left branches of lower joints of columns
When the rigidity values of the respective branches of the respective joint structures are determined, 1 design variable is assigned to each joint structure, whereby 6 design variables can be established. Then, 2-level orthogonal trial design, i.e., preliminary trial design, was performed on the 6 design variables using the orthogonal trial design table L8. Wherein, the 1 level represents that the performance parameter associated with the design variable takes the initial value, and the 2 level represents that the performance parameter associated with the design variable increases by 10% on the initial value, which is the first design value. Taking bending stiffness as an example, the method for calculating the bending stiffness sensitivity coefficient of the design variable comprises the following steps:
the results of simulation analysis according to the preliminary test design table of the joint structure shown in table 3 are shown in table 4.
Table 3 preliminary test design table of joint structure
TABLE 4 sensitivity analysis results of joint structure Table
As can be seen from table 4, the C-pillar lower joint left 206 has the greatest influence on the overall torsional stiffness of the vehicle, and the B-pillar lower joint left 208 has the greatest influence on the overall bending stiffness of the vehicle, and the overall stiffness performance of the vehicle body can be effectively improved by performing targeted optimization design on the two joint structures.
Taking the torsional rigidity as an example, the precise experimental design will be described by taking 6 rigidity values λ 11, λ 12, λ 13, λ 21, λ 22, λ 23 in the three directions of the upper and lower 2 branches x, y, z of the C-pillar lower joint left 206 as design variables. Specifically, a 2-level test design is performed using the orthogonal test design table L8, where a 1-level represents that the performance parameter associated with the design variable takes an initial value, and a 2-level represents that the performance parameter associated with the design variable increases by 10% from the initial value, i.e., a second design value, and the result of the precise test design is shown in table 5.
Table 5 accurate test design table for left lower joint of C column
The simulation analysis was performed according to the accurate test design table of the C column lower joint left 206 shown in table 5, and the results are shown in table 6.
TABLE 6C table of sensitivity analysis results of column lower joint left
From the analysis of table 6, it can be seen that for the left side of the C-pillar lower joint 206, the z-direction stiffness of the lower branch is optimized, which is helpful to improve the overall torsional stiffness performance of the automobile body.
In summary, compared with the prior art, the sensitivity analysis method for the rigidity performance of the vehicle body provided by the embodiment of the invention has the following advantages:
1) the method not only can identify the sensitive structure in the characteristic structure to be analyzed, but also can further identify the key structure characteristic of the sensitive structure so as to carry out targeted structure optimization design and finally determine the sensitive structure characteristic parameter of the sensitive structure.
2) The method has simple and efficient operation process, and can automatically generate the simplified model of the characteristic structure to be analyzed according to the test design table.
It should be noted that the joint structure and the beam structure provided by the invention can be further expanded to a group of space structures on the automobile body, and the method can be used for sensitivity analysis of commercial automobiles and other structures except automobiles besides passenger automobiles, and has wider application prospect and economic value.
The foregoing is merely illustrative of the present invention, and it will be appreciated by those skilled in the art that various modifications may be made without departing from the principles of the invention, and the scope of the invention is to be determined accordingly.
Claims (10)
1. A sensitivity analysis method for rigidity performance of a vehicle body is characterized by comprising the following steps:
acquiring a plurality of characteristic structures of an automobile body to be analyzed; wherein the feature comprises a beam structure and/or a joint structure;
determining a plurality of simplified models corresponding to the characteristic structures;
carrying out preliminary test design on the automobile body according to the simplified models to obtain preliminary design values corresponding to the simplified models;
and analyzing the sensitivity of the rigidity performance of the automobile body according to the plurality of simplified models and the initial design values thereof, and determining the sensitive structure in the plurality of characteristic structures.
2. The method for sensitivity analysis of vehicle body stiffness performance according to claim 1, wherein when the feature is a beam structure, the method for determining the simplified model corresponding to the feature comprises:
the beam structure is simplified into a simplified model in the form of one-dimensional beam units.
3. The method for sensitivity analysis of vehicle body stiffness performance according to claim 1, wherein when the feature is a joint structure, the method of determining the simplified model corresponding to the feature includes:
and simplifying the joint structure into a simplified model in a combined form of a one-dimensional beam unit and a one-dimensional spring unit.
4. The sensitivity analysis method for the rigidity performance of the automobile body according to claim 1, wherein the method for carrying out preliminary experimental design on the automobile body according to the plurality of simplified models and obtaining preliminary design values corresponding to the plurality of simplified models comprises the following steps:
assigning a first design variable to each of the simplified models;
assigning a first design value to a plurality of the first design variables to complete a preliminary test design for the automotive body;
the first design value is taken as the preliminary design value of the corresponding simplified model.
5. The method for sensitivity analysis of vehicle body stiffness performance according to claim 1, further comprising:
carrying out accurate test design on the automobile body according to the simplified model corresponding to the sensitive structure to obtain an accurate design value corresponding to the simplified model of the sensitive structure;
and analyzing the sensitivity of the rigidity performance of the automobile body of the automobile according to the characteristic structure and the initial design value thereof, the sensitive structure and the accurate design value thereof, and determining the characteristic parameters of the sensitive structure.
6. The sensitivity analysis method for the rigidity performance of the automobile body according to claim 5, wherein the accurate experimental design is carried out on the automobile body according to the simplified model corresponding to the sensitive structure, and the method for obtaining the accurate design value corresponding to the simplified model of the sensitive structure comprises the following steps:
respectively assigning second design variables to key structure characteristic parameters of the simplified model of the sensitive structure;
assigning a second design value to a plurality of the second design variables to complete an accurate test design for the automotive body;
the second design value is taken as the precise design value of the corresponding simplified model.
7. The method for sensitivity analysis of vehicle body stiffness performance according to claim 5, wherein when the sensitive structure is a beam structure, the key structural characteristic parameters are characteristic parameters corresponding to bending characteristics and torsion characteristics of a simplified model of the beam structure.
8. The method for sensitivity analysis of the rigidity performance of a vehicle body according to claim 5, wherein when the sensitive structure is a joint structure, the key structural characteristic parameter is a rigidity value of each branch of the simplified model of the joint structure in three directions in a three-dimensional coordinate system.
9. The sensitivity analysis method for the rigidity performance of the vehicle body according to claim 5, wherein when the sensitive structure is a beam structure, the characteristic parameter of the sensitive structure is a characteristic parameter corresponding to a bending characteristic and/or a torsion characteristic.
10. The method for sensitivity analysis of the rigidity performance of a vehicle body according to claim 6, wherein when the sensitive structure is a joint structure, the characteristic parameter of the sensitive structure is a rigidity value of at least one branch of the simplified model of the joint structure in at least one direction in a stereo coordinate system.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114841037A (en) * | 2022-05-09 | 2022-08-02 | 桂林电子科技大学 | Cab stiffness modal optimization method based on joint sensitivity analysis |
| CN114841037B (en) * | 2022-05-09 | 2024-04-02 | 桂林电子科技大学 | Cab rigidity modal optimization method based on joint sensitivity analysis |
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