Method suitable for determining vibration response of bolted connection combined structure

Abstract

The embodiment of the invention relates to the technical field of combined structure dynamic analysis, in particular to a method suitable for determining the vibration response of a bolt connection combined structure, and the method comprises the steps: S10, determining the stress distribution of the combination of each bolt and nut; s20, determining the contact load, the normal contact stiffness and the tangential contact stiffness of a connection interface according to the stress distribution of the combination of each bolt and nut determined in the step S10 and the applied external load; s30, determining the strain energy of the connection interface according to the contact load, the normal contact stiffness and the tangential contact stiffness of the connection interface determined in the step S20; s40, according to the strain energy, determined in the step S30, of the connection interface, the first structure and the second structure are combined, the overall strain energy, kinetic energy and external force work of the bolt connection combined structure are established, a system motion equation is established and solved, and the vibration response of the bolt connection combined structure is determined. According to the determination method, the prediction precision and efficiency of the vibration response of the bolted connection combined structure can be improved.

Description

Technical Field

[0001] The embodiments of the present application relate to the technical field of combined structure dynamics analysis, and in particular to a method for determining the vibration response of a bolted combined structure. Background Art

[0002] The statements herein merely provide background information related to the present application and do not necessarily constitute prior art.

[0003] Bolted connection combination structure is currently a common structural connection method for industrial equipment. It has the advantages of simple structure, low cost, easy assembly, strong load-bearing capacity and good geometric adaptability. It is widely used in oil and gas pipeline connections, rocket and missile connections, engine assembly connections, drive shaft docking and other structures.

[0004] Under actual working conditions, bolted composite structures often bear external loads of different forms and magnitudes, and provide connection stiffness and strength for the overall structure through contact and friction loads between the connection interfaces. However, due to the geometric mutations and overall discontinuity of bolted composite structures, problems such as excessive local deformation and stress concentration will occur during the load-bearing process. These problems will weaken the overall structural stiffness of the bolted composite structure and reduce the overall sealing performance and load-bearing capacity of the bolted structure. In particular, due to the existence of the connection interface of the bolted structure, the local stiffness of the connection structure may be weakened and friction damping may be generated, thereby affecting the dynamic behavior of the overall system structure. Summary of the invention

[0005] A brief overview of the present application is provided below in order to provide a basic understanding of certain aspects of the present application. It should be understood that this overview is not an exhaustive overview of the present application. It is not intended to identify the key or important parts of the present application, nor is it intended to limit the scope of the present application. Its purpose is merely to present certain concepts in a simplified form as a prelude to a more detailed description discussed later.

[0006] An embodiment of the present application provides a method for determining the vibration response of a bolted combination structure, wherein the bolted combination structure comprises a first structure, a second structure, a plurality of bolts and a plurality of nuts, the first structure comprises a first edge, the second structure comprises a second edge, the first edge and the second edge are fixed by cooperating with a plurality of bolts and a plurality of nuts, so that the first structure, the second structure, the plurality of bolts and the plurality of nuts form a bolted combination structure, and the first edge and the second edge form a connection interface, and the method comprises the following steps: S10: determining the force distribution of each bolt and nut combination; S20: determining the contact load, normal contact stiffness and tangential contact stiffness of the connection interface according to the force distribution of each bolt and nut combination determined in step S10 and the applied external load; S30: determining the strain energy of the connection interface according to the contact load, normal contact stiffness and tangential contact stiffness of the connection interface determined in step S20; S40: establishing the overall strain energy, kinetic energy and external force work of the bolted combination structure according to the strain energy of the connection interface determined in step S30, in combination with the first structure and the second structure, establishing and solving the system motion equation, and determining the vibration response of the bolted combination structure.

[0007] The method provided in the embodiment of the present application can determine the contact load, normal contact stiffness and tangential contact stiffness of the connection interface according to the force distribution of each bolt and nut combination and the applied external load, thereby determining the strain energy of the connection interface. Then, based on the strain energy of the connection interface and in combination with the first structure and the second structure, the overall strain energy, kinetic energy and external force work of the bolted combination structure can be established, and then the system motion equations can be established and solved to determine the vibration response of the bolted combination structure. This determination method is beneficial to improving the prediction accuracy and efficiency of the vibration response of the bolted combination structure.

[0008] These and other advantages of the present application will become more apparent through the following detailed description of the preferred embodiments of the present application in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to further illustrate the above and other advantages and features of the present application, the specific embodiments of the present application are further described in detail below in conjunction with the accompanying drawings. The accompanying drawings together with the following detailed description are included in this specification and form a part of this specification. Elements with the same function and structure are represented by the same reference numerals. It should be understood that these drawings only describe typical examples of the present application and should not be regarded as limiting the scope of the present application.

[0010] Figure 1 is a structural schematic diagram of a bolt connection assembly structure according to an embodiment of the present application; Figure 2 yes Figure 1 A partial enlarged schematic diagram of a bolted joint assembly structure is shown; Figure 3 is a schematic flow chart of a method for determining a vibration response of a bolted combined structure according to an embodiment of the present application; Figure 4 It is a tangential schematic diagram of mutually contacting micro-protrusions according to an embodiment of the present application.

[0011] It should be noted that the drawings are not necessarily drawn to scale, but are merely shown in a schematic manner that does not affect the reader's understanding.

[0012] Description of reference numerals: 10. Bolt connection combined structure; 101. Connection interface; 1011. Micro-convex body; 11. first structure; 111. first edge; 12. second structure; 121. second edge; 13. Bolts; 14. Nut. DETAILED DESCRIPTION

[0013] Exemplary embodiments of the present application will be described below in conjunction with the accompanying drawings. For the sake of clarity and conciseness, not all features of the actual implementation are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the process of developing any such actual implementation in order to achieve the developer's specific goals, such as meeting those constraints related to the system and business, and these constraints may vary from implementation to implementation. In addition, it should be understood that although the development work may be very complex and time-consuming, it is only a routine task for those skilled in the art who benefit from the content of this application.

[0014] It is also necessary to explain here that, in order to avoid obscuring the present application due to unnecessary details, only the device structure and / or processing steps closely related to the scheme according to the present application are shown in the accompanying drawings, while other details that are not very relevant to the present application are omitted.

[0015] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in this application should have the common meanings understood by persons with ordinary skills in the field to which this application belongs.

[0016] In the description of the embodiments of the present application, “plurality” means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0017] In the current dynamic model of the connection structure, in order to avoid the huge computational cost, the connection structure is often simplified to linear beam connection modeling and calculation. However, the connection structure has a great influence on the dynamic performance of the overall structure due to the interface connection stiffness. At present, there is still a lack of dynamic models that accurately characterize the nonlinear stiffness and damping characteristics of weak stiffness connection structures. In addition, due to the presence of nonlinear factors such as contact and friction on the connection interface, it will bring difficulties to the dynamic modeling of the connection structure. The dynamic models in related technologies often have problems such as insufficient consideration or inability to properly handle nonlinear factors during the modeling process, which will lead to inaccurate analysis results, resulting in large differences between the analysis results and the experimental results, causing great difficulties for subsequent analysis and verification.

[0018] In order to solve the above technical problems, an embodiment of the present application provides a method suitable for determining the vibration response of a bolt-connected composite structure. Figure 1 is a structural schematic diagram of a bolt connection assembly structure according to an embodiment of the present application, Figure 2 yes Figure 1 The enlarged schematic diagram of the bolted joint structure is shown in FIG. Figure 1 and Figure 2 As shown, the bolted connection combination structure 10 includes a first structure 11, a second structure 12, a plurality of bolts 13 and a plurality of nuts 14, the first structure 11 includes a first edge 111, the second structure 12 includes a second edge 121, the first edge 111 and the second edge 121 are fixed by cooperating with the plurality of bolts 13 and the plurality of nuts 14, so that the first structure 11, the second structure 12, the plurality of bolts 13 and the plurality of nuts 14 form the bolted connection combination structure 10, and the first edge 111 and the second edge 121 form a connection interface 101.

[0019] Figure 3 is a schematic flow chart of a method for determining the vibration response of a bolted combined structure according to an embodiment of the present application, such as Figure 3 As shown, the method includes the following steps S10 to S40.

[0020] S10: Determine the force distribution of each combination of the bolt 13 and the nut 14 .

[0021] S20: According to the force distribution of each combination of the bolt 13 and the nut 14 determined in step S10 and the applied external load, the contact load, normal contact stiffness and tangential contact stiffness of the connection interface 101 are determined.

[0022] S30: Determine the strain energy of the connection interface 101 according to the contact load, normal contact stiffness and tangential contact stiffness of the connection interface 101 determined in step S20.

[0023] S40: Based on the strain energy of the connection interface 101 determined in step S30, in combination with the first structure 11 and the second structure 12, the overall strain energy, kinetic energy and external force work of the bolted combined structure 10 are established, the system motion equation is established and solved, and the vibration response of the bolted combined structure 10 is determined.

[0024] The method provided in the embodiment of the present application can determine the contact load, normal contact stiffness and tangential contact stiffness of the connection interface 101 according to the force distribution of the combination of each bolt 13 and nut 14 and the applied external load, thereby determining the strain energy of the connection interface 101, and then based on the strain energy of the connection interface 101, combined with the first structure 11 and the second structure 12, the overall strain energy, kinetic energy and external force work of the bolted combination structure 10 can be established, and then the system motion equation is established and solved to determine the vibration response of the bolted combination structure 10. This determination method is beneficial to improving the prediction accuracy and efficiency of the vibration response of the bolted combination structure 10.

[0025] In some embodiments, step S10 also includes the following steps: S11: Slice the position where the bolt 13 and the nut 14 contact the first edge 111 and the second edge 121; obtain multiple slices, and mesh the multiple slices; S12: Based on the division, establish a finite element model for the object obtained by the division; S13: Determine the boundary conditions of the finite element model; S14: Determine the preload force between the bolt 13 and the nut 14 and the first edge 111 and the second edge 121; S15: Determine the force distribution based on the preload force.

[0026] The method provided in the embodiment of the present application slices and divides the position where the bolt 13 and the nut 14 contact the first edge 111 and the second edge 121, and then establishes a finite element model for the divided object, so as to use the finite element model to determine the preload force between the bolt 13 and the nut 14 and the first edge 111 and the second edge 121, thereby determining the force distribution. This method can improve the efficiency of numerical calculation, and can also avoid the influence of the pressure at the contact position of the first edge 111 and the second edge 121 on the final force distribution result, so as to ensure the accuracy of the determined force distribution.

[0027] In some embodiments, step S11 also includes: S111: simulating the bolt 13 and the nut 14 into a solid cylinder and a hollow cylinder; S112: simulating the area where the first edge 111 and the second edge 121 contact the bolt 13 and the nut 14 into a hollow disk including a screw hole; S113: using two mutually perpendicular virtual planes to divide the area where the bolt 13, the nut 14 and the first edge 111 and the second edge 121 cooperate; S114: dividing the area where the first edge 111, the second edge 121 cooperate with the bolt 13 and the nut 14.

[0028] The method provided in the embodiment of the present application first simulates the bolt 13 and the nut 14 into a solid cylinder and a hollow cylinder, and simulates the area where the first edge 111 and the second edge 121 contact the bolt 13 and the nut 14 into a hollow disk including a screw hole, and then uses two mutually perpendicular virtual planes to divide the area where the bolt 13, the nut 14 and the first edge 111 and the second edge 121 cooperate, which is conducive to generating a polyhedral mesh with high quality and relatively regular shape, thereby facilitating obtaining more accurate contact pressure distribution calculation results, making the simulation results more precise.

[0029] In some embodiments, the bolt 13 may be simulated as having a diameter of The nut 14 is simulated as a solid cylinder with a diameter of of a hollow cylinder. represents the contact diameter between the first structure 11 and the bolt 13 .

[0030] In such an embodiment, since the strain of the thread has little effect on the contact pressure at the connection interface 101 under the action of the preload force, the threads on the bolt 13 and the nut 14 can be ignored, and since the length and width of the first structure 11 and the second structure 12 are large enough, the influence of the first edge 111 and the second edge 121 on the pressure distribution of the connection interface 101 can be ignored.

[0031] In some embodiments, in step S113 , the intersection of the two virtual planes is the center line of the bolt 13 . Then, the bolt connection assembly structure 10 is divided into four parts symmetrical around the center line of the bolt 13 .

[0032] In some embodiments, in step S20, the force applied to a point on the connection interface 101 is determined based on the preload and the position of the point from the bolt 13, and the force distribution of the connection interface 101 under the preload condition is determined based on the forces of all points on the connection interface 101, so as to ensure the accuracy and reliability of the determined force distribution of the connection interface 101 under the preload condition.

[0033] In some embodiments, in step S20, the following steps are also included: S21: discretize the connection interface 101 into multiple contact units; S22: determine the contact state of multiple contact units; S23: use fractal geometry method and determine the normal contact stiffness and damping of the connection interface 101 according to the contact state; S24: establish a finite element model of the connection interface 101; S25: determine the overall contact load, normal contact stiffness and tangential contact stiffness of the interface according to the normal contact stiffness and damping of the connection interface 101 determined in step S23 and the finite element model of the connection interface 101 established in step S24.

[0034] The method provided in the embodiment of the present application discretizes the connection interface 101 into multiple contact units and determines the contact state of the multiple contact units, then uses the fractal geometry method and according to the contact state to determine the normal contact stiffness and damping of the connection interface 101, and establishes a finite element model of the connection interface 101 to determine the overall contact load, normal contact stiffness and tangential contact stiffness of the interface. This determination method discretizes the connection interface 101 into multiple contact units, which is beneficial to improving its calculation efficiency and the accuracy of the calculation results, thereby ensuring the accuracy and reliability of the ultimately determined overall contact load, normal contact stiffness and tangential contact stiffness of the interface.

[0035] In some embodiments, a dynamic theory model of the connection interface 101 of the bolt 13 is established, and when simulating the bolt-connected composite structure 10 , a micro-slip model can be used to simulate the friction contact behavior in the actual bolt 13 connection.

[0036] In some embodiments, the connection interface 101 is discretized into a plurality of contact units, and each contact unit is characterized by a group of contact pairs to characterize the contact state of the contact unit.

[0037] In some embodiments, the friction force on the contact surface of the contact unit and the relative displacement of the contact point are determined using the normal contact stiffness, tangential contact stiffness and friction coefficient of the contact pair.

[0038] In some embodiments, step S22 also includes: S221: determining the tangential force and normal force of multiple contact units; S222: determining the contact state based on the tangential force and the normal force, which has a relatively high reliability.

[0039] In some embodiments, the contact unit transmits tangential force and normal force between the two contact surfaces, thereby establishing a relative motion relationship between the two contact surfaces.

[0040] In some embodiments, the contact state includes: sticking, slipping and separation. The normal force and the normal relative displacement of the contact unit satisfy the following expression (1): (1).

[0041] in, represents the normal force; max represents the maximum value; represents the normal stiffness; Represents normal relative displacement.

[0042] The tangential force and the tangential relative displacement of the contact element satisfy the following expression (2): (2).

[0043] in, represents the tangential force; represents the tangential stiffness; represents the tangential relative displacement; sgn represents the sign function; represents the first derivative of the tangential relative displacement; represents the absolute tangential displacement; Represents the friction coefficient.

[0044] The embodiment of the present application can determine the contact status of multiple contact units relatively accurately and quickly through the above expressions (1) and (2), with high efficiency.

[0045] In some embodiments, when the tangential force is less than the critical friction stress, no relative movement occurs between the two contact surfaces of the contact unit, and at this time, it can be determined that the contact state is sticky.

[0046] In some embodiments, when the tangential force is greater than the critical friction stress, relative movement occurs between the two contact surfaces of the contact unit, and at this time, it can be determined that the contact state is separation.

[0047] In some embodiments, when the tangential force is equal to the critical friction stress, there begins to be a tendency for relative movement between the two contact surfaces of the contact unit. At this time, it can be determined that the contact state is slip.

[0048] In some embodiments, in step S25, the interface overall contact load satisfies the following expression (3):

[0049] (3).

[0051] in, represents the overall contact load of the interface; It represents the normal contact load of the micro-asperity. The connection interface in the bolted joint structure is a rough surface composed of micro-asperities of different scales. represents the normal contact load during elastic deformation; Represents the normal contact load during elastic-plastic deformation; , Represents the normal contact load at different elastic-plastic deformations; represents the normal contact load at full plastic deformation; represents the contact area of ​​the asperity; represents the effective contact area of ​​the micro-asperity; represents the elastic-plastic contact area of ​​the asperity; represents the overall contact area of ​​the asperity; represents the maximum contact cross-sectional area of ​​the micro-convex body; represents the cross-sectional area density function of the micro-convex body, which satisfies the following expression (4): (4).

[0052] in, represents a three-dimensional fractal function; Indicates about The force function.

[0053] In some embodiments, the normal contact stiffness satisfies the following expression (5): (5).

[0054] in, represents the normal contact stiffness; represents the elastic critical contact area of ​​the asperity; represents the plastic critical contact area of ​​the asperity; represents the elastic contact stiffness; Represents the elastic-plastic contact stiffness.

[0055] In some embodiments, the tangential contact stiffness satisfies the following expression (6): (6).

[0056] in, represents the tangential contact stiffness of the asperity; It represents the tangential contact stiffness when the asperity undergoes elastic deformation; It represents the tangential contact stiffness when the micro-convex body undergoes elastic-plastic deformation; It represents the tangential contact stiffness of the asperity when plastic deformation occurs. It is used to describe the relationship between the tangential force and displacement between the asperity and the contact surface under plastic deformation conditions.

[0057] The method provided in the embodiment of the present application can ensure the calculation efficiency of the overall contact load, normal contact stiffness and tangential contact stiffness of the interface through the above expressions (3) to (6).

[0058] Figure 4 is a tangential schematic diagram of mutually contacting micro-convex bodies according to an embodiment of the present application, such as Figure 4 As shown, the stiffness characteristics of the contact surface are derived from the elastic deformation and elastoplastic deformation process of the micro-asperities 1011. The micro-asperities 1011 in the elastic deformation state store elastic strain energy, and the micro-asperities 1011 in the elastoplastic deformation state store elastoplastic strain energy. Elasticity and elastoplastic strain energy are the two main distribution forms of interface contact stiffness.

[0059] In some embodiments, the stiffness of the micro-protrusion 1011 when elastically deformed satisfies the following expression (7): (7).

[0060] in, represents the stiffness of the micro-convex body 1011 when elastic deformation occurs; represents the normal deformation of the micro-convex body 1011; represents the normal contact load during elastic deformation; Represents the derivative symbol.

[0061] In some embodiments, the stiffness of the micro-protrusion 1011 when undergoing elastic-plastic deformation satisfies the following expression (8): (8).

[0062] in, represents the stiffness of the micro-convex body 1011 when elastic-plastic deformation occurs; represents the normal deformation of the micro-convex body 1011; Represents the normal contact load during elastic-plastic deformation; Represents the derivative symbol.

[0063] In some embodiments, the contour features of the connection interface 101 are combined with the contact mechanics of the micro-protrusions 1011 using a three-dimensional fractal function. According to the different deformation states of the micro-protrusions 1011, the loads of different types of micro-protrusions 1011 are integrated and summed to determine the overall contact load, normal contact stiffness and tangential contact stiffness of the interface.

[0064] In some embodiments, in step S30, an expression for the strain energy of the connection interface 101 is established based on the contact load, normal contact stiffness, and tangential contact stiffness determined in step S20, which has high reliability.

[0065] In some embodiments, step S40 also includes: S41: based on the expression of the strain energy of the connection interface 101 determined in S30, combined with the first structure 11 and the second structure 12, the overall strain energy, kinetic energy and external force work of the bolted combination structure 10 are established; S42: based on the overall strain energy, kinetic energy and external force work established in S41, the motion equation of the bolted combination structure 10 is determined; S43: based on the motion equation, the Rayleigh-Ritz method and the mode superposition method are used to determine the free and forced vibration responses of the bolted combination structure 10.

[0066] The method provided in the embodiment of the present application establishes the overall strain energy, kinetic energy and external work done by the bolted combination structure 10 based on the expression of the strain energy of the connection interface 101, in combination with the first structure 11 and the second structure 12, so as to determine the motion equation of the bolted combination structure 10, and then uses the Rayleigh-Ritz method and the mode superposition method to determine the free and forced vibration responses of the bolted combination structure 10, so that the accuracy of the determined free and forced vibration responses of the bolted combination structure 10 is higher.

[0067] In some embodiments, the Rayleigh-Ritz method is used to derive the equation of motion, which satisfies the following expression (9): (9).

[0068] in, represents the mass matrix; represents the damping matrix of the connection interface 101; represents the equivalent stiffness of the connection interface 101; represents the tangential relative displacement; represents the first derivative of the tangential relative displacement; represents the second derivative of the tangential relative position; Indicates the force.

[0069] In some embodiments, for the interface contact problem, the contact force of the interface satisfies the following expression (10): (10).

[0070] in, represents the contact force; represents the effective contact stiffness; Represents the tangential relative displacement.

[0071] In some embodiments, vibration analysis may be performed in combination with Hooke's law, D'Alembert's principle, elasticity theory, and the like.

[0072] First, based on the analysis of the end face rotation angle relationship, end face tension, end face bending moment, and end face shear force, and applying Hooke's law, D'Alembert principle, and elastic mechanics principles, it can be determined that the elastic vibration differential equation satisfies the following expression (11): (11).

[0073] in, represents partial derivative; Indicates coordinate value; Indicates time; express Young's modulus of elasticity at ; express The end moment of inertia at Representing coordinates and time Function of express The mass per unit length at ; Representing coordinates and time The second derivative of Representing coordinates and time The external force function.

[0074] In some embodiments, let the right side of expression (11) is equal to zero, it can be determined that the elastic vibration free vibration equation satisfies the following expression (12): (12).

[0075] In some embodiments, , and substituting it into the above expression (12), we can obtain the following expression (13): (13).

[0076] in, represents the derivative symbol; The system elastic vibration mode function representing the connection structure of the bolt 13; express Young's modulus of elasticity at ; express The end moment of inertia at express The mass per unit length at ; represents the generalized coordinates of elastic vibration.

[0077] In some embodiments, in the above expression (13), the right side of the equation depends on the variable , the left side of the equation depends on the variable , by transforming the above expression (13), we can obtain the following expressions (14) and (15): (14); (15).

[0078] in, The system elastic vibration mode function representing the connection structure of the bolt 13; express Young's modulus of elasticity at ; express The end moment of inertia at express The mass per unit length at ; represents the generalized coordinates of elastic vibration; Represents the natural frequency of elastic vibration.

[0079] In some embodiments, from the above expressions (14) and (15), the free vibration solution of the equation satisfies the following expression (16): (16).

[0080] in, Indicates Secondary vibration mode; Indicates The modal function of the secondary vibration mode is used to describe the displacement distribution of each point in the system during free vibration; Indicates The time function of the secondary vibration mode is used to reflect the change of the vibration amplitude of this vibration mode over time.

[0081] For forced vibration, substituting it into expression (11), we can obtain the following expression (17): (17).

[0082] Then, multiply both sides of expression (17) by , and integrated along the bolted joint structure, the following expression (18) can be obtained after simplification: (18).

[0083] in, Indicates Secondary vibration mode; Indicates The natural frequency of the secondary vibration mode; Indicates The modal function of the sub-vibration mode, which is used to describe the displacement distribution of the system during free vibration; The scope of the structure representing the integral.

[0084] In some embodiments, The forced vibration equation of the elastic vibration of the secondary vibration mode satisfies the following expression (19): (19).

[0085] in, Indicates The generalized force of the sub-mode, ; Indicates The generalized mass of the submode, .

[0086] Regarding the embodiments of the present application, it should also be noted that, in the absence of conflict, the embodiments of the present application and the features therein can be combined with each other to obtain new embodiments.

[0087] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. The protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for determining the vibration response of a bolted composite structure, characterized in that: The bolt connection assembly structure comprises a first structure, a second structure, a plurality of bolts and a plurality of nuts, the first structure comprises a first edge, the second structure comprises a second edge, the first edge and the second edge are fixed by the plurality of bolts and the plurality of nuts, so that the first structure, the second structure, the plurality of bolts and the plurality of nuts form the bolt connection assembly structure, the first edge and the second edge form a connection interface, and the method comprises the following steps: S10: Determine the force distribution of each bolt and nut combination; S20: determining the contact load, normal contact stiffness and tangential contact stiffness of the connection interface according to the force distribution of each combination of the bolt and the nut determined in step S10 and the applied external load; S30: determining the strain energy of the connection interface according to the contact load, normal contact stiffness and tangential contact stiffness of the connection interface determined in step S20; S40: Based on the strain energy of the connection interface determined in step S30, in combination with the first structure and the second structure, the overall strain energy, kinetic energy and external force work of the bolted combined structure are established, the system motion equation is established and solved, and the vibration response of the bolted combined structure is determined.

2. The method according to claim 1, characterized in that In step S10, the following steps are also included: S11: Slice the positions where the bolt and the nut contact the first edge and the second edge; obtain a plurality of slices, and divide the plurality of slices into grids; S12: according to the division, establishing a finite element model for the object obtained by the division; S13: Determine the boundary conditions of the finite element model; S14: determining a pre-tightening force between the bolt and the nut and the first edge and the second edge; S15: Determine the force distribution according to the preload force.

3. The method according to claim 2, characterized in that In step S11, it also includes: S111: simulating the bolt and the nut into a solid cylinder and a hollow cylinder; S112: simulating the areas where the first edge and the second edge contact the bolt and the nut as a hollow disk including a screw hole; S113: using two mutually perpendicular virtual planes to divide the area where the bolt, the nut, and the first edge and the second edge match; S114: Divide the area where the first edge, the second edge, the bolt, and the nut cooperate.

4. The method according to claim 2, characterized in that: In step S20, the force applied to the point on the connection interface is determined based on the preload force and the distance between the point on the connection interface and the bolt, and the force distribution of the connection interface under the preload force condition is determined based on the forces of all points on the connection interface.

5. The method according to claim 1, characterized in that In step S20, the following steps are also included: S21: discretizing the connection interface into a plurality of contact units; S22: Determine the contact status of the plurality of contact units; S23: using a fractal geometry method and according to the contact state, determining the normal contact stiffness and damping of the connection interface; S24: establishing a finite element model of the connection interface; S25: According to the normal contact stiffness and damping of the connection interface determined in step S23 and the finite element model of the connection interface established in step S24, determine the overall contact load, normal contact stiffness and tangential contact stiffness of the interface.

6. The method according to claim 5, characterized in that In step S22, it also includes: S221: Determine the tangential force and the normal force of the plurality of contact units; S222: Determine the contact state according to the tangential force and the normal force.

7. The method according to claim 6, characterized in that The contact states include: sticking, slipping and separation; The normal force, the tangential force and the normal relative displacement of the contact unit satisfy the following expression: ； ； in, represents the normal force; max represents the maximum value; represents the normal stiffness; represents the normal relative displacement; represents the tangential force; represents the tangential stiffness; represents the tangential relative displacement; sgn represents the sign function; represents the first derivative of the tangential relative displacement; represents the absolute tangential displacement; Represents the friction coefficient.

8. The method according to claim 5, characterized in that In step S25, The overall contact load of the interface satisfies the following expression: ； in, represents the overall contact load of the interface; represents the normal contact load of the micro-protrusion, and the connection interface in the bolt connection assembly structure is a rough surface composed of the micro-protrusions of different scales; represents the normal contact load during elastic deformation; Represents the normal contact load during elastic-plastic deformation; , Represents the normal contact load at different elastic-plastic deformations; represents the normal contact load at full plastic deformation; represents the contact area of ​​the micro-protrusion; represents the effective contact area of ​​the micro-convex body; represents the elastic-plastic contact area of ​​the micro-asperity; represents the overall contact area of ​​the asperities; represents the maximum contact cross-sectional area of ​​the micro-convex body; represents the cross-sectional area density function of the micro-convex body, which satisfies the following expression: ； in, represents a three-dimensional fractal function; Indicates about The force function of The normal contact stiffness satisfies the following expression: ； in, represents the normal contact stiffness; represents the elastic critical contact area of ​​the micro-asperity; represents the plastic critical contact area of ​​the micro-asperity; represents the elastic contact stiffness; represents the elastic-plastic contact stiffness; The tangential contact stiffness satisfies the following expression: ； in, represents the tangential contact stiffness of the asperity; represents the tangential contact stiffness when the micro-convex body undergoes elastic deformation; represents the tangential contact stiffness when the micro-convex body undergoes elastic-plastic deformation; It represents the tangential contact stiffness of the micro-protrusion when plastic deformation occurs.

9. The method according to claim 1, characterized in that: In step S30, an expression for the strain energy of the connection interface is established according to the contact load, normal contact stiffness and tangential contact stiffness determined in step S20.

10. The method according to claim 9, characterized in that In step S40, the method further includes: S41: Establishing the overall strain energy, kinetic energy and external force work of the bolted combined structure according to the expression of the strain energy of the connection interface determined in S30 and combining the first structure and the second structure; S42: determining the motion equation of the bolted combined structure according to the overall strain energy, kinetic energy and external force work established in S41; S43: According to the motion equation, the Rayleigh-Ritz method and the mode superposition method are used to determine the free and forced vibration responses of the bolt-connected composite structure.

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