Rigid-flexible coupling multi-body dynamics analysis method based on new modal flexible body

Abstract

The invention discloses a rigid-flexible coupling multi-body dynamics analysis method based on a new modal flexible body, which comprises the following steps: large-range rigid body motion based on a moving contact elastomer is effectively separated by a floating coordinate description method, and deformation response relative to a floating coordinate system is a result of combined action of a moving contact load and an inertia distribution load. The method can be decomposed into a group of complete superposition of elastic free interface modal responses, and the group of complete elastic free interface modal sets are converted into a combination of a few key global main modals and static equivalent interface residual modals, so as to ensure the completeness and convergence of modal characterization of the moving contact elastomer. According to the method, the completeness and convergence of the modal representation of the moving contact body can be ensured, and the model scale can be greatly reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of multibody dynamics analysis, and particularly relates to a rigid-flexible coupling multibody dynamics analysis method based on a new modal flexible body. Background Art

[0002] Calculating the motion deformation of mechanical components, such as gears and bearings, under working conditions by numerical simulation methods helps to clarify the cause of failures and optimize the component design.

[0003] In the finite element method calculation, in order to capture the local contact characteristics, it is necessary to encrypt the mesh in the contact area. However, the movement of the moving contact body will cause changes in the local contact area. Therefore, only by arranging precise meshes in all potential contact areas can the local response generated during the global moving contact process be accurately calculated, which will lead to an overly large model size and make it difficult to perform long-term dynamic simulations.

[0004] In multibody dynamics, the use of the floating coordinate description method combined with the modal synthesis method can decouple the model size from the mesh density and effectively separate the large-scale motion and linear elastic deformation of the elastic body. The commonly used fixed interface modal synthesis method can ensure the completeness and convergence of the modal representation of the interface-constrained elastic body. However, when representing the moving contact elastic body, the modal sets corresponding to different contact states are different, and it is difficult to switch the modal sets during dynamic simulations. Therefore, only by retaining the constraint modes corresponding to the global potential contact interfaces and the fixed interface main modes can the completeness and convergence of the modal representation of the elastic body in any contact state be ensured, and this will greatly increase the model size. Summary of the Invention

[0005] Aiming at the above problems, the present invention provides a rigid-flexible coupling multibody dynamics analysis method based on a new modal flexible body, aiming to ensure the completeness and convergence of the modal representation of the moving contact body and achieve a significant reduction in the model size.

[0006] According to an embodiment of the present disclosure, there is provided a rigid-flexible coupling multibody dynamics analysis method based on a new modal flexible body. The method includes that the large-scale rigid body motion of the moving contact elastic body is effectively separated by the floating coordinate description method, and the deformation response relative to the floating coordinate system is the result of the combined action of the moving contact load and the inertial distributed load, and can be decomposed into the superposition of a set of complete elastic free interface modal responses. This set of complete elastic free interface modal sets is converted into the synthesis of a few key global main modes and statically equivalent interface residual modes to ensure the completeness and convergence of the modal representation of the moving contact elastic body.

[0007] In some embodiments, the elastomer deformation response is decomposed into a low-frequency mode and a high-frequency mode according to the system excitation frequency, and then the completeness and convergence of the mobile contact body mode representation are ensured in a way of superimposing the global response and the local response, where the global response is represented by retaining a few key principal modes, and the local quasi-static contribution caused by the contact interface force is compensated by introducing the current interface residual modes equivalent to static force.

[0008] In some embodiments, each mode response is a decoupled single-degree-of-freedom vibration equation, where the low-frequency mode generates a dynamic response and the high-frequency mode generates a quasi-static response.

[0009] In some embodiments, when the inertial force distribution form is similar to the high-frequency mode, the high coupling of the inertial force and the high-frequency mode will generate a global quasi-static response.

[0010] In some embodiments, it is assumed that the m-th mode of the mobile contact elastomer is φ m , and the inertial force generated by the main motion form is denoted as f i , then the degree of coupling between the inertial force and the mode is judged by the dot product value φ m ·f i ; according to the main motion form of the elastomer under specific working conditions, some key high-frequency modes are retained and combined with the low-frequency modes to form a set of retained free interface modes, denoted as where the subscript represents the high-frequency mode set where the inertial distribution force cannot be ignored, and l represents the low-frequency mode set. This set of free interface modes ensures the convergence of the global response of the elastomer.

[0011] In some embodiments, in the decoupled single-degree-of-freedom mode equation, the modal generalized force is divided into a local interface force and an inertial distribution force, where the modal generalized force generated by the local interface force is converted from the interface node load vector F b =[0 f T T through the modal matrix , and the rows occupied by f correspond to the degrees of freedom with interface loads, and the remaining zero parts are internal degrees of freedom.

[0012] In some embodiments, through the division of the mode set, the complete elastic free interface mode set is composed of the retained free interface mode set and the high-frequency mode set that omits the action of the inertial distribution force, that is The subscript represents the high-frequency mode set that omits the action of the inertial distribution force, and the deformation of the elastomer represented by the mode is:

[0013]

[0014] where the high-frequency mode of the quasi-static response only retains the contribution generated by the local interface load, and in the formula​ is the residual modal matrix, which is used to effectively compensate the local static response contribution of the omitted high-frequency modes. represents the block corresponding to the currently loaded interface degrees of freedom in the residual modal matrix Φ, where each column represents a residual mode, which is used to effectively compensate the local quasi-static response caused by the interface concentrated load of the omitted high-frequency modes.

[0015] In some embodiments, for the elastomer discretized by finite elements, the preprocessing depends on finite element calculations. The main characteristic information of the finite element model of the elastomer is included in the mass matrix M 0 and the stiffness matrix K 0 , without applying any constraints, solve the generalized eigenvalue problem defined by the mass matrix and the stiffness matrix, and retain a finite number of free interface principal mode sets Ψ k , and the diagonal matrix composed of the modal eigenvalues of each order is The number of modes retains k-order modes according to the concerned frequency range; each order of stress mode After being calculated by the finite element method, the stress distribution is restored by post-processing, and then the modal mass invariant U is calculated according to the node mass information and the modes of the corresponding nodes i (i = 0 to 8).

[0016] In some embodiments, for the calculation of the attachment modes, according to the connection relationship between the elastomer and the outside in the multi-body system, the degrees of freedom associated with the connection nodes are defined as the interface degrees of freedom, and then any one of the following calculation methods a to c is selected to calculate the attachment modes:

[0017] a. Appropriately select several degrees of freedom of the elastomer and constrain the elastomer not to undergo rigid body motion. Apply a unit force to each interface degree of freedom one by one to obtain the static equilibrium displacement distribution and stress distribution, so as to assemble the attachment modal matrix G b and the attachment stress modal matrix

[0018] b. Assume that the elastomer has N r rigid body degrees of freedom, then arbitrarily select N r degrees of freedom that can restrict rigid body motion to calculate a set of rigid body mode sets, denoted as Φ r , and then calculate the force projection matrix P of inertial release r , obtain the restricted flexibility matrix G according to the selected N r constrained degrees of freedom, and finally transform it into the inertial release attachment mode G = P r G rT G r P r , and select the interface degree of freedom part G bFor the attachment stress mode, it is necessary to obtain the element stress from the element strain matrix and the elastic matrix according to the displacement field of each attachment mode, and then convert it into the nodal stress and assemble it into the attachment stress mode matrix.

[0019] c. Assume that a complete set of elastic modes of the elastic body has been obtained, denoted as Ψ. f And the diagonal matrix composed of the eigenvalues corresponding to each order of modes. A total of N f modes, and in addition, there is also the stress mode matrix composed of each order of modes. Directly obtain the inertial release attachment mode matrix. And the attachment stress mode matrix.

[0020] In some embodiments, when calculating the attachment mode by method a, the remaining modes and the remaining stress mode matrix are obtained according to the retained free interface main modes:

[0021]

[0022] A rigid-flexible coupling multi-body dynamics analysis method based on a new modal flexible body provided by an embodiment of the present disclosure. The new modal flexible body adopted converts this complete free interface mode set into a combination of a few key global main modes and statically equivalent interface remaining modes, which can ensure the completeness and convergence of the modal representation of the moving contact body and achieve a significant reduction in the model scale. Compared with the fixed interface modal synthesis method, the method of the present invention improves the accuracy of contact calculation while introducing a small number of interface degrees of freedom; compared with the finite element method, the method of the present invention significantly reduces the model degrees of freedom.

[0023] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present invention and used together with the specification to explain the principles of the present invention.

[0025] Figure 1 is a diagram showing the composition of the mode set of the new modal flexible body in an embodiment of the present invention;

[0026] Figure 2 is a schematic flow chart of the implementation of the method for processing the new modal flexible body in an embodiment of the present invention;

[0027] Figure 3 is a graph of the Mises stress curve of the root node of the large gear and the axial displacement curves of the root node and the tooth surface node of the large gear in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the present invention, rather than limiting the present invention. In addition, it should be noted that for the convenience of description, only the parts related to the present invention rather than all the structures are shown in the drawings.

[0029] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flowcharts. Although the flowcharts describe the steps as sequential processes, many of the steps can be implemented in parallel, concurrently, or simultaneously. In addition, the order of the steps can be rearranged. The process can be terminated when its operations are completed, but it can also have additional steps not included in the drawings. The process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0030] When the fixed interface modal synthesis method is used in multi-body dynamics to characterize a moving contact flexible body, the moving contact elastic body is accompanied by changes in the contact interface during large-range motion. For example, at three different moments, the object has three different contact states, and its current contact interfaces are Γ 1 , Γ 2 and Γ 3 . When the fixed interface modal synthesis method is used to characterize an elastic body, it is necessary to retain the constraint modes and fixed interface main modes corresponding to different contact interfaces to ensure the completeness and convergence of the modal characterization of the elastic body.

[0031] However, it is difficult to complete the calculation and re-orthogonalization of the modal set of the fixed interface modal synthesis method in the pre-processing process of the dynamic simulation, and it is difficult to recalculate and switch the modal set during the dynamic simulation. The contradiction between the time-varying nature of the moving contact interface and the invariance of the modal representation set is difficult to overcome. Therefore, this method is more suitable for the case where the external connection interface of the elastic body is fixed during the entire dynamic simulation process. To avoid the recalculation and switching of the modal set, this method has to regard the global potential contact area of the moving contact body as the interface connected to the outside and retain the corresponding constraint modes and fixed interface main modes to achieve the modal reduction of the deformation response under any contact state. However, the large-range potential contact interface will greatly increase the scale of the modal model. This results in the fixed interface modal method being unable to efficiently ensure the completeness and convergence of the modal characterization of the moving contact elastic body.

[0032] The large-scale rigid body motion of the moving contact elastic body can be effectively separated by the floating coordinate description method, and the deformation response relative to the floating coordinate system is the result of the combined action of the moving contact load and the inertial distributed load, and can be decomposed into a superposition of a set of complete elastic free interface modal responses. This modal characterization is complete and convergent, but fails to achieve model scale reduction. The method of the embodiment of the present invention includes the large-scale rigid body motion of the moving contact elastic body being effectively separated by the floating coordinate description method, and the deformation response relative to the floating coordinate system is the result of the combined action of the moving contact load and the inertial distributed load, and can be decomposed into a superposition of a set of complete elastic free interface modal responses, and this set of complete elastic free interface modal sets is converted into a combination of a few key global main modes and statically equivalent interface residual modes, so as to ensure the completeness and convergence of the modal characterization of the moving contact elastic body. And a significant reduction in model scale is achieved.

[0033] In the state of static equilibrium, the local contact load makes the elastic body show a local response characteristic that gradually weakens from the local contact interface to the global, especially the response at the stress level. Under the superposition characterization of the complete elastic free interface main mode, the response superposition of each order mode near the local contact interface is enhanced, while the response at a distance cancels each other, thereby realizing the modal restoration of local characteristics. In the dynamic process, the time-varying moving load may also dynamically excite some low-frequency free interface main modes, which manifest as a global dynamic response with equivalent deformation everywhere in the elastic body. In addition, the inertial distributed force generated by the movement of the floating coordinate system may also have a high degree of coupling with some global modes and produce a non-negligible contribution. In summary, when a set of complete modal sets is used to characterize the response of the elastic body, generally only a few key main modes in the global response produce the main contribution. Therefore, by retaining a few key free interface main modes, the convergence of the global response can be guaranteed. However, the local response caused by local loads can only be manifested through the superposition of a large number of main modes, and it is impossible to find the main modes that produce the main contribution of certain orders. Therefore, the key to achieving modal model reduction is to convert the local response contribution of the complete modal set into an equivalent representation by a few local static modes, thereby greatly reducing the scale of the modal model while ensuring the completeness and convergence of the modal representation.

[0034] The free interface modal synthesis method adopted in the embodiment is as follows: Figure 1 The figure shows the modal set composition of the free interface modal synthesis method. First, the elastic body response is decomposed into low-frequency and high-frequency modal parts according to the system excitation frequency, and then the global and local response superposition representation is used to efficiently ensure the completeness and convergence of the modal representation of the moving contact body. The global response is represented by retaining a few key main modes, and the local quasi-static contribution caused by the contact interface force is compensated by introducing the static equivalent current interface residual mode.

[0035] like Figure 1As shown, the floating coordinate description method effectively separates the rigid body motion from the deformation response. A complete set of elastic free interface principal modes can accurately characterize the deformation of the elastic body, and the modal responses of each order are decoupled single-degree-of-freedom vibration equations. Among them, the low-frequency modes generate dynamic responses while the high-frequency modes generate quasi-static responses. To ensure the global response convergence, it is necessary to retain the low-frequency modes to accurately characterize the global dynamic response of the elastic body. In addition, when the form of the inertial force distribution is very similar to some high-frequency modes, the high coupling between the inertial force and these high-frequency modes will generate a non-negligible global quasi-static response.

[0036] Assume that the m-th order mode of the elastic body is The inertial force generated by the main motion form of the elastic body is denoted as f i , then the degree of coupling between the inertial force and the mode can be determined by the dot product value of the mode and the inertial force. In the free interface modal synthesis method, according to the main motion form of the elastic body under specific working conditions, some key high-frequency modes can be retained and combined with the low-frequency modes to form a set of retained free interface modal sets, denoted as where the subscript represents the set of high-frequency modes that cannot ignore the action of the inertial force, and l represents the set of low-frequency modes. This set of retained modes can ensure the convergence of the global response of the elastic body, and its global response mode is as shown in (a) of Figure 1 .

[0037] In the decoupled single-degree-of-freedom modal equation, the modal generalized force is divided into two parts: the local interface force and the inertial distribution force. The local response of the elastic body is mainly generated by the action of the local interface force, and the contribution of the inertial distribution force is small. Therefore, ignoring the contribution of the distributed inertial force in the quasi-static response of the high-frequency modes does not affect the convergence of the local response. Among them, the modal generalized force generated by the local interface force is converted from the interface node load vector F b = [0 f T T through the modal matrix , and the rows occupied by f correspond to the degrees of freedom with interface loads, and the remaining zero parts are internal degrees of freedom. f is the interface part node load vector, and f T is the transpose of the interface part node load vector.

[0038] After re-dividing the modal set, the complete free interface modal set is composed of the retained modes and the high-frequency modes that omit the contribution of the distributed force, that is The deformation of the elastic body characterized by this set of modes is:

[0039]

[0040] η k represents the retained modal coordinates, represents the high-order modal coordinates, denotes the inverse matrix of the high-order modal coordinate eigenvalue matrix, denotes the modal matrix of the transpose, denotes the transpose of the interface block of the high-order modal matrix, which can ensure the completeness and convergence of modal representation. Among them, the high-frequency modes of the quasi-static response only need to retain the contributions generated by local interface loads, which is crucial for the convergence of the local response of the elastic body. In the formula is the residual modal (also known as the residual attachment modal) matrix, which can effectively compensate for the local static response contributions of the omitted high-frequency modes, denotes the corresponding block of the currently loaded interface degrees of freedom in the residual modal matrix Φ, where each column represents a residual mode, such as Figure 1 (b) shows that they have significant local response characteristics, so they can effectively compensate for the local quasi-static response caused by the interface concentrated load of the omitted high-frequency modes. Through the above static equivalence conversion of the main modes and residual modes, a large number of high-frequency modal responses are cleverly represented as the superposition of the contributions of a few currently effective interface loads. The interface node loads are regarded as the generalized coordinates describing the deformation state of the elastic body, called the interface force coordinates and denoted as f, thus realizing the conversion between most modal coordinates and a few effective interface force coordinates. This is the key to reducing the scale of the modal model of the moving contact elastic body. In this way, the elastic degrees of freedom can be reduced from N of the original model f to k + b, where k represents the number of free interface modes retained, and b represents the number of degrees of freedom of the current interface effective load. The retained free interface modes represent the global response of the elastic body, while the residual modes efficiently compensate for the local quasi-static response caused by the omitted high-frequency modes due to interface loads.

[0041] For a moving contact elastic body, the large-range motion characteristics result in a very large potential contact area on the surface of the contact body, while there is only a local small-range contact force at the current moment. The free interface modal synthesis method is very suitable for the characterization of such elastic bodies with moving contact characteristics. Retaining a few key free interface main modes can ensure the convergence of the global response of the elastic body. These free main modes of the contact interface are applicable to any contact state in the moving contact of the elastic body, without the need to switch according to the contact interface in the dynamic simulation. In addition, the residual modes of the current contact interface can compensate for the local quasi-static response caused by the omitted high-frequency modes due to the contact interface force, greatly reducing the model solution scale while ensuring the completeness and convergence of the modal representation of the moving contact elastic body.

[0042] Modal data calculation steps based on the finite element model

[0043] such as Figure 2As shown in the figure, the main difference between the new modal flexible body modeling method and the traditional fixed interface modal synthesis method for flexible bodies lies in the calculation and processing of modal data. The application object of the modal synthesis method is the elastic body discretized by finite elements. Therefore, its preprocessing depends on finite element calculation. The main characteristic information of the elastic body finite element model is contained in the mass matrix M 0 and the stiffness matrix K 0 . Without applying any constraints, solve the generalized eigenvalue problem defined by the mass matrix and the stiffness matrix, and retain a finite number of free interface main modal sets Ψ k , and the diagonal matrix composed of the modal eigenvalues of each order is represents the eigenvalue of the k-th order mode. The number of modes can be determined according to the frequency range of interest. Assume that k modes are retained. In addition, each order of stress mode can also be calculated by the finite element method and the stress distribution can be restored by post-processing. s represents the stress mode. Then, according to the node mass information and the corresponding node modes, the modal mass invariant U i (i = 0 to 8, representing nine invariants U0, U1, U2,..., U8) can be calculated.

[0044] In the calculation of the attachment mode, first, according to the connection relationship between the elastic body and the outside in the multi-body system, the degrees of freedom associated with the connection nodes are defined as the interface degrees of freedom, and then any one of the following calculation methods a to c can be selected according to the specific problem to calculate the attachment mode::

[0045] a. Appropriately select several degrees of freedom of the elastic body and constrain the elastic body not to undergo rigid body motion. Apply a unit force to each interface degree of freedom one by one to obtain the static equilibrium displacement distribution and stress distribution, so as to assemble the attachment mode matrix G b and the attachment stress mode matrix

[0046] b. Assume that the elastic body has N r rigid body degrees of freedom, then arbitrarily select N r degrees of freedom that can restrict rigid body motion to calculate a set of rigid body mode sets, denoted as Φ r , and then calculate the force projection matrix P r of inertial release. Obtain the restricted flexibility matrix G r according to the selected N r constrained degrees of freedom, and finally convert it into the inertial release attachment mode G = P rT G r P r , and select the part G b of the interface degrees of freedom among them. For the attachment stress mode, it is necessary to obtain the element stress from the element strain matrix and the elastic matrix according to the displacement field of each attachment mode, and then convert it into the node stress of each node and assemble it into the attachment stress mode matrix

[0047] c. Assume that a complete set of elastic modes of the elastomer has been obtained, denoted as Ψ f and a diagonal matrix composed of the eigenvalues corresponding to each order of modes There are a total of N f modes. In addition, there is also a stress mode matrix composed of each order of modes Then the inertia release attachment mode matrix can be directly obtained and the attachment stress mode matrix The application object of this calculation method is generally a modal reduction elastomer. Through the free modal synthesis method, the model can be reduced in order again while ensuring the same convergence as the original modal reduction elastomer. Since all the elastic modes of the modal reduction elastomer have been obtained, it is more convenient to calculate the remaining modes according to the definition formula.

[0048] Generally, the first method a is used to calculate the attachment modes, and then the remaining modes and the remaining stress mode matrix are obtained according to the retained free interface main modes

[0049]

[0050] In a specific embodiment, a calculation example of a pair of gear contacts. A rotational speed constraint Ns = 500 RPM is applied to the center of the large gear, and a torque M = 10 Nm is applied to the center of the small gear. The simulation time is 0.15 s, among which the first 0.03 s is the rotational speed increase and torque application stage, and the rotational speed and torque are smoothly transitioned from zero to the target values through the STEP smoothing transition function. The subsequent 0.12 s is the uniform rotation stage of the large gear, and the large gear rotates about 1 circle during this time period. Figure 3 It is the Mises stress curve of the root node of the large gear and the axial displacement curve graph of the root node and the tooth surface node of the large gear. The Mises stress represents the von Mises stress, where the dashed line is the calculation result of this article and fits well with the finite element method.

[0051] Based on the above embodiments, a rigid-flexible coupling multi-body dynamics analysis method based on a new modal flexible body is provided. The new modal flexible body adopted in this method converts this complete free interface modal set into a synthesis of a few key global main modes and statically equivalent interface remaining modes, which can ensure the completeness and convergence of the modal representation of the moving contact body and realize a significant reduction in the model scale. Compared with the fixed interface modal synthesis method, the method of the present invention improves the accuracy of contact calculation when introducing a small number of interface degrees of freedom; compared with the finite element method, the method of the present invention significantly reduces the model degrees of freedom.

[0052] In this article, the terms "including", "comprising" or any other variants thereof are intended to cover non-exclusive inclusion, so that a step or method including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent in such a step or method.

[0053] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A rigid-flexible coupling multi-body dynamics analysis method based on a new modal flexible body, characterized in that: The method includes the following steps: effectively separating the large-scale rigid body motion of the moving contact elastic body by a floating coordinate description method; the deformation response relative to the floating coordinate system is the result of the combined action of the moving contact load and the inertial distributed load, and can be decomposed into a superposition of a set of complete elastic free interface modal responses; and converting this set of complete elastic free interface modal sets into a combination of a few key global main modes and statically equivalent interface residual modes, so as to ensure the completeness and convergence of the modal representation of the moving contact elastic body.

2. The method according to claim 1, characterized in that: The deformation response of the elastic body is decomposed into low-frequency modes and high-frequency modes according to the system excitation frequency. Then the global response and local response are superimposed to ensure the completeness and convergence of the modal representation of the moving contact body. The global response is represented by retaining a few key main modes, and the local quasi-static contribution caused by the contact interface force is compensated by introducing the statically equivalent current interface residual mode.

3. The method according to claim 2, characterized in that: Each modal response is a decoupled single-degree-of-freedom vibration equation, in which the low-frequency mode produces a dynamic response and the high-frequency mode produces a quasi-static response.

4. The method according to claim 3, characterized in that: When the distribution form of the inertial force is similar to that of the high-frequency mode, the high coupling between the inertial force and the high-frequency mode will produce a global quasi-static response.

5. The method according to claim 4, characterized in that: Assume that the mth mode of the moving contact elastic body is φ m The inertial force generated by the main form of motion is recorded as f i , then the degree of coupling between the inertial force and the mode is determined by the dot product value φ of the mode and the inertial force m ·f i Judgment; According to the main motion form of the elastic body under specific working conditions, some key high-frequency modes are retained and low-frequency modes are combined to form a set of retained free interface modes, which is recorded as The subscript represents the high-frequency mode set where the inertial distributed force cannot be ignored, and l represents the low-frequency mode set. This set of free interface mode sets ensures the convergence of the global response of the elastic body.

6. The method according to claim 5, characterized in that: In the decoupled single-degree-of-freedom modal equation, the modal generalized force is divided into local interface force and inertial distributed force, where the modal generalized force generated by the local interface force is represented by the interface node load vector F b =0f T ] T Through the modal matrix The rows occupied by f correspond to the degrees of freedom with interface loads, and the remaining zeros are internal degrees of freedom. f is the node load vector of the interface part, and f T is the transpose of the load vector of some nodes on the interface.

7. The method according to claim 6, characterized in that: By dividing the modal set, the complete elastic free interface modal set is composed of the free interface modal set and the high-frequency modal set with the inertial distributed force ignored, that is, Subscript Represents the high-frequency mode set ignoring the inertial distributed force, and the elastic deformation represented by the mode is: The high-frequency modes of the quasi-static response only retain the contribution caused by the local interface load, η k represents the retained modal coordinates, represents the higher-order modal coordinates, represents the inverse matrix of the eigenvalue matrix of the higher-order modal coordinates, Represents the modal matrix The transpose of represents the transpose of the interface block of the higher-order modal matrix, is the residual mode matrix, which is used to effectively compensate for the local static response contribution of the neglected high-frequency mode. It represents the block corresponding to the degree of freedom of the currently loaded interface in the residual mode matrix Φ, where each column represents a residual mode, which is used to effectively compensate for the local quasi-static response of the omitted high-frequency mode caused by the concentrated load on the interface.

8. The method according to claim 1, characterized in that: For the elastic body discretized by finite element, the pre-processing depends on finite element calculation. The main characteristic information of the finite element model of the elastic body is contained in the mass matrix M0 and the stiffness matrix K0. Without imposing any constraints, the generalized eigenvalue problem defined by the mass matrix and the stiffness matrix is ​​solved, and a finite number of free interface main mode sets Ψ are retained. k , the diagonal matrix composed of the eigenvalues ​​of each order mode is Represents the eigenvalue of the k-th mode. The number of modes is based on the frequency range of interest. The k-th mode is retained; each stress mode After the finite element method is used to calculate, the stress distribution is restored, and then the modal mass invariant U is calculated based on the node mass information and the mode of the corresponding node. i , i takes an integer between 0 and 8, and s represents the stress mode.

9. The method according to claim 8, characterized in that: For the calculation of the attachment mode, the degrees of freedom associated with the connection nodes are defined as interface degrees of freedom according to the connection relationship between the elastic body and the outside in the multi-body system, and then any of the following calculation methods a to c is selected to calculate the attachment mode: a. Appropriately select several degrees of freedom of the elastic body and constrain the elastic body to not undergo rigid body motion. Apply unit force to each degree of freedom of the interface one by one to obtain the static equilibrium displacement distribution and stress distribution, thereby assembling the adhesion mode matrix G b and the adhesion stress modal matrix b. Assume that the elastic body has N r rigid body degrees of freedom, then any selection that can restrict the rigid body motion N r The degrees of freedom are calculated based on a set of rigid body modes, denoted as Φ r , and then calculate the force projection matrix P of inertial release r , according to the selected N r The constrained degrees of freedom are obtained by the constrained flexibility matrix G r , and finally transformed into the inertial release adhesion mode G = P rT G r P r , select the interface degree of freedom part G b For the attachment stress mode, it is necessary to obtain the unit stress from the unit strain matrix and the elastic matrix according to the displacement field of each attachment mode, and then convert it into the stress of each node and assemble it into the attachment stress mode matrix. c. Assume that the complete elastic mode set of the elastic body has been obtained, denoted as Ψ f And the diagonal matrix composed of the eigenvalues ​​corresponding to each mode Total N f modes, and also the stress modal matrix composed of each mode Directly obtain the inertial release adhesion mode matrix And the adhesion stress modal matrix 10. The method according to claim 9, characterized in that: When the attachment mode is calculated using method a, the residual mode and residual stress mode matrix are obtained based on the retained free interface main mode:

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