Elastic connection structure quick response calculation method based on main node

Abstract

The invention relates to the technical field of dynamic analysis of large connection structures, and discloses an elastic connection structure rapid response calculation method based on a main node, and the method specifically comprises the following steps: 1, analyzing a molecular structure according to geometric characteristics of a connection system; 2, establishing a substructure and an overall structure finite element model based on thin-layer connection; 3, performing modal analysis on the substructure, and determining a main node of the substructure based on an effective independence method; 4, introducing a boundary displacement coordination condition to connect the substructure main node reduction models to obtain an overall system reduction model; and 5, rapid response calculation is realized based on the overall system main node reduction model, the operation scale of the system reduction model does not depend on the number of degrees of freedom of the overall system any more, but is only related to the number of main nodes and the intercepted modal number, so that the method significantly improves the calculation efficiency, and has extremely high precision.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic analysis of large connection structures, and particularly to a fast response calculation method for an elastic connection structure based on a master node. Background Art

[0002] Excessive vibration of the whole engine is an important cause of aero-engine failures. Almost all the active or in-development aero-engines in China have encountered the problem of excessive vibration of the whole engine. Moreover, with the continuous pursuit of high performance and high thrust-to-weight ratio, the engine rotor and the casing tend to be thinner and lighter, and the rotational speed of the rotor is also increasing continuously. This may make the dynamic influence between the rotor and the casing closer, resulting in more intense or complex coupled vibration problems between the rotor and the casing itself and between the rotor and the casing, forming complex structural dynamic characteristics, and making the vibration problem of the whole engine more prominent. Therefore, the vibration problem of the whole engine system plays a crucial role in the safety and reliability of engine operation. During the development process of the engine, it is very necessary to study the vibration problem of the whole engine system.

[0003] The complex structure of the aero-engine makes it difficult to model the whole engine. The rotor structure of the aero-engine generally includes multi-stage bladed disks, drums, shafts and other structures. The casing structure of the engine is also very complex, mainly including intake casings, intermediate casings, outer casings, load-bearing casings and other casing components. In addition, there are a large number of connection structures in the aero-engine, such as bolt connections between casings and rotor components, spline connections of the rotor, bearings between the casing and the rotor, and between the rotor and the rotor. In order to ensure that the finite element model of the complex structure has sufficient accuracy to reflect the dynamic characteristics of the actual structure for the vibration characteristics analysis of the whole engine, it is necessary to accurately model the complex structure, that is, supermodel modeling. However, due to the high accuracy of the supermodel, the size of the whole engine model is large and the calculation is difficult.

[0004] Therefore, we propose a fast response calculation method for an elastic connection structure based on a master node. Summary of the Invention

[0005] The present invention mainly solves the technical problems existing in the above-mentioned prior art, and provides a fast response calculation method for an elastic connection structure based on a master node.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions. A fast response calculation method for an elastic connection structure based on a master node specifically includes the following steps:

[0007] The first step: dividing sub-structures according to the geometric feature analysis of the connection system;

[0008] The second step: establishing a finite element model of the sub-structure and the overall structure based on thin-layer connection;

[0009] Step 3: Conduct modal analysis on the substructure and determine the main nodes of the substructure based on the effective independence method;

[0010] Step 4: Introduce the boundary displacement coordination condition to connect the reduced model of the main nodes of the substructure to obtain the reduced model of the overall system;

[0011] Step 5: Implement fast response calculation based on the reduced model of the main nodes of the overall system.

[0012] Preferably, the specific method for the first step is as follows: Divide the substructure according to the geometric feature analysis of the connection system, and split the overall structure into individual components according to the connection relationship.

[0013] Preferably, the specific method for the second step is as follows: Establish a finite element model of the substructure and the overall structure based on thin-layer connection, establish a finite element model of individual components and connect them through elastic connection elements (thin layers) to form a finite element model of the overall structure. The equivalent stiffness of the thin layer can be obtained through the pre-tightening force of the bolt connection. Conduct a static analysis on the tightened bolt connection structure. The parts with relatively large stress are concentrated in the areas where the bolt rod, nut, and the connected parts are in contact. According to the stress received by each part, the connection area can be divided into three parts: (a) the area connected by the screw; (b) the area where the pre-tightening force acts; (c) the area connected by the flange edge. Among them, the axial connection stiffness of the bolt connection structure is mainly determined by (a) and (b). The total stiffness of the bolt part is:

[0014] k s = n(k b + k m )

[0015] where k b is the stiffness of the screw, k m is the combined stiffness of the upper and lower flanges, and n is the total number of bolts. For the bolt area, the expression for the axial stiffness of the screw is:

[0016]

[0017] where A b is the cross-sectional area of the bolt rod, d b is the diameter of the bolt rod, E b is the elastic modulus of the screw, L eq is the equivalent length of the bolt rod, and the expression for L eq is:

[0018]

[0019] Among them, L, β, and ν are the length of the threaded hole, the dimensionless coefficient, and the Poisson's ratio of the screw respectively. For the area affected by the bolt pre-tightening force, the most commonly used analysis method is the "pre-tightening force conical angle method", that is, the stress distribution area of the connected parts is equivalent to a conical area with the top cut off. Outside this area, the stress value is relatively small and is basically a constant value, which can be regarded as not affected by the pre-tightening force. For the connected parts, take the microelement dy within the conical area and integrate the effective load it bears, and the connection stiffness of the connected parts can be obtained as follows:

[0020]

[0021] Among them, E 0i is the elastic modulus of the connected parts, t is the thickness of the flange edge, α is the semi-conical angle, which is related to the magnitude of the bolt pre-tightening force F p , so the axial connection stiffness of the entire bolt pre-tightening force action area is:

[0022]

[0023] Among them, k 01 , k 02 are the stiffnesses of the upper and lower connected parts respectively.

[0024] Preferably, the specific method of the third step is: perform modal analysis on the substructure in ansys, and determine the main nodes of the substructure based on the effective independence method to obtain the reduced model of the main nodes of the substructure. Under the action of unbalanced excitation, the dynamic motion differential equation of the N-degree-of-freedom system is:

[0025]

[0026] Among them, M, K, C, and G are the mass, stiffness, damping, and gyro matrix of the system respectively, u(t) is the response vector at time t, f is the external load, perform modal analysis on the structure, and select the main nodes based on the modal analysis results. First, construct the Fisher information matrix:

[0027] F = Φ T Φ

[0028] Among them, Φ is the mass-normalized vibration mode obtained from modal analysis, F is the Fisher information matrix, and based on the Fisher matrix, construct the effective independent allocation matrix E:

[0029] E = ΦF -1 Φ T

[0030] Among them, the diagonal elements of matrix E represent the contribution degree of degrees of freedom to the mode shape matrix. The values of the diagonal elements are within the range of 0 to 1. The closer the element is to 1, the greater the influence of the corresponding degree of freedom and node on the mode shape matrix. Finally, a threshold T is set, and the nodes corresponding to the diagonal elements greater than T are regarded as master nodes. Based on the selected master nodes, the control equations are divided into a master node matrix and a slave node matrix:

[0031]

[0032] Among them, M mm 、K mm 、C mm 、G mm represent the mass matrix, damping matrix, gyroscopic matrix, and stiffness matrix of the master node degrees of freedom respectively. M ss 、K ss 、C ss 、G ss represent the mass matrix, damping matrix, gyroscopic matrix, and stiffness matrix of the slave node degrees of freedom respectively. M sm 、K sm 、C sm 、G sm 、M ms 、K ms 、C ms 、G ms represent the mass matrix, damping matrix, gyroscopic matrix, and stiffness matrix of the coupled master and slave node degrees of freedom respectively. u m 、u s are the displacement vectors of the master and slave node degrees of freedom respectively. f m is the external force vector corresponding to the master node degrees of freedom. Assume that the responses of all degrees of freedom are linear combinations of fixed-interface normal modes and static constraint modes. The normal modes are the natural mode shapes of the system calculated after constraining the master node degrees of freedom, and their dimension is the number of degrees of freedom plus the number of retained modes. Usually, the higher the order of the retained modes, the higher the accuracy of the dynamic calculation. It can be obtained by solving the characteristic equation and using the mode superposition method. The static constraint modes are the static displacements of the degrees of freedom under the action of boundary forces:

[0033]

[0034] Among them, q is the modal coordinate, Φ C is the static constraint mode, Φ N is the fixed-interface normal mode, and the expressions of Φ C and Φ N are respectively:

[0035]

[0036] Wherein, φ is the vibration mode, and n is the lowest order mode number to be retained. Then, the transformation matrix T is constructed as follows:

[0037]

[0038] Based on the transformation matrix T, a master node reduction model is constructed:

[0039]

[0040] Finally, based on the master node reduction model, the time-domain control equation is constructed, and the dynamic response calculation can be carried out:

[0041]

[0042] Preferably, the specific method of the fourth step is as follows: the boundary displacement coordination condition is introduced to connect the substructure master node reduction models to obtain the overall system reduction model. Assume that the substructure P and the substructure Q are connected by the connecting structure thin layer C. The mass matrix M and the stiffness matrix K of the overall structure are obtained in the following forms respectively:

[0043]

[0044] Wherein, is the constraint mode of the connecting substructure C. The degree-of-freedom division of the overall structure and the overall displacement vector are:

[0045]

[0046] Wherein, is the internal degree of freedom, is the boundary degree of freedom. The interface displacement coordination condition is introduced as:

[0047]

[0048] Wherein, L P and L Q are the coordinate rotation transformation matrices. By constructing the transformation matrix T2, the form after the assembly of the substructures can be obtained as follows:

[0049]

[0050] Using T2 for the second transformation, the connection of the substructures is realized:

[0051]

[0052] Finally, the reduced dynamic equation of the system is obtained as:

[0053]

[0054] Preferably, the specific method for the fifth step is as follows: based on the overall system master node reduction model, rapid response calculation is realized, and the operation scale of the system reduction model no longer depends on the degrees of freedom of the overall system, but only on the number of master nodes and the number of intercepted modes.

[0055] Beneficial effects

[0056] The present invention provides a rapid response calculation method for an elastic connection structure based on master nodes, having the following beneficial effects:

[0057] 1. For the rapid response calculation method for an elastic connection structure based on master nodes, the operation scale of the system reduction model no longer depends on the degrees of freedom of the overall system, but only on the number of master nodes and the number of intercepted modes. Therefore, this method significantly improves the calculation efficiency and has extremely high accuracy at the same time.

[0058] 2. For the rapid response calculation method for an elastic connection structure based on master nodes, based on the master node reduction model, sufficient accuracy is retained, and at the same time, the calculation efficiency is greatly improved, and the effectiveness and superiority of the method have been preliminarily verified. Description of the drawings

[0059] Figure 1 It is the stress nephogram of the bolt connection structure under the pre-tightening force of the present invention;

[0060] Figure 2 It is the regional diagram of the bolt connection structure of the present invention;

[0061] Figure 3 It is the geometric model diagram of the connecting casing of the present invention;

[0062] Figure 4 It is the finite element model diagram of the connecting casing of the present invention;

[0063] Figure 5 It is the master node reduction model diagram of the intermediate casing of the present invention;

[0064] Figure 6 It is the master node reduction model diagram of the outer casing of the present invention;

[0065] Figure 7 It is the master node reduction model diagram of the connecting casing of the present invention;

[0066] Figure 8 It is the comparison diagram of the main modal vibration modes of the original model and the modal of the master node model of the present invention. Detailed implementation manners

[0067] Example 1: A rapid response calculation method for an elastic connection structure based on master nodes, as Figure 1 - Figure 2 shown, specifically includes the following steps:

[0068] Step 1: Divide the sub-structures according to the geometric feature analysis of the connection system;

[0069] Step 2: Establish the finite element models of the sub-structures and the overall structure based on thin-layer connections;

[0070] Step 3: Conduct modal analysis on the sub-structures and determine the main nodes of the sub-structures based on the effective independence method;

[0071] Step 4: Introduce the boundary displacement coordination conditions to connect the reduced models of the main nodes of the sub-structures to obtain the reduced model of the overall system;

[0072] Step 5: Realize the fast response calculation based on the reduced model of the main nodes of the overall system. The specific method of Step 1 is: divide the sub-structures according to the geometric feature analysis of the connection system, and split the overall structure into individual components according to the connection relationship. The specific method of Step 2 is: establish the finite element models of the sub-structures and the overall structure based on thin-layer connections, establish the finite element model of an individual component and form the finite element model of the overall structure through elastic connection elements (thin layers). The equivalent stiffness of the thin layer can be obtained from the pre-tightening force of the bolt connection. Conduct static analysis on the tightened bolt connection structure. The parts with larger stress are concentrated in the areas where the bolt rod, nut and the connected parts are in contact. According to the stress received by each part, the connection area can be divided into three parts: (a) the area connected by the screw; (b) the area where the pre-tightening force acts; (c) the area connected by the flange edge. The axial connection stiffness of the bolt connection structure is mainly determined by (a) and (b). The total stiffness of the bolt part is:

[0073] k s =n(k b +k m )

[0074] where k b is the stiffness of the screw, k m is the combined stiffness of the upper and lower flanges, and n is the total number of bolts. For the bolt area, the expression of the axial stiffness of the screw is:

[0075]

[0076] where A b is the cross-sectional area of the bolt rod, d b is the diameter of the bolt rod, E b is the elastic modulus of the screw, L eq is the equivalent length of the bolt rod, and the expression of L eq is:

[0077]

[0078] Among them, L, β, and ν are the length of the screw hole, the dimensionless coefficient, and the Poisson's ratio of the screw rod, respectively. For the area affected by the bolt pre-tightening force, the most commonly used analysis method is the "pre-tightening force conical angle method", that is, the stress distribution area of the connected parts is equivalent to a conical area with the top cut off as shown in Figure 1 . Outside this area, the stress value is relatively small and is basically a constant value, which can be regarded as not affected by the pre-tightening force. For the connected parts, take the microelement dy in the conical area and integrate the effective load it receives to obtain the connection stiffness of the connected parts as:

[0079]

[0080] Among them, E 0i is the elastic modulus of the connected parts, t is the thickness of the flange edge, α is the semi-conical angle, which is related to the magnitude of the bolt pre-tightening force F p . Therefore, the axial connection stiffness of the entire bolt pre-tightening force action area is:

[0081]

[0082] Among them, k 01 , k 02 are the stiffnesses of the upper and lower connected parts, respectively. The specific method for the third step is: perform modal analysis on the substructure in ansys, and determine the main nodes of the substructure based on the effective independence method to obtain the reduced model of the main nodes of the substructure. Under the action of unbalanced excitation, the dynamic motion differential equation of the N-degree-of-freedom system is:

[0083]

[0084] Among them, M, K, C, and G are the mass, stiffness, damping, and gyro matrix of the system respectively, u(t) is the response vector at time t, f is the external load, perform modal analysis on the structure, and select the main nodes based on the modal analysis results. First, construct the Fisher information matrix:

[0085] F = Φ T Φ

[0086] Among them, Φ is the mass-normalized vibration mode obtained from modal analysis, F is the Fisher information matrix, and based on the Fisher matrix, construct the effective independent distribution matrix E:

[0087] E = ΦF -1 Φ T

[0088] Among them, the diagonal elements of matrix E represent the contribution degree of degrees of freedom to the mode shape matrix. The values of the diagonal elements are within the range of 0 to 1. The closer the element is to 1, the greater the influence of the corresponding degree of freedom and node on the mode shape matrix. Finally, a threshold T is set, and the nodes corresponding to the diagonal elements greater than T are regarded as master nodes. Based on the selected master nodes, the governing equations are divided into a master node matrix and a slave node matrix:

[0089]

[0090] Among them, M mm 、K mm 、C mm 、G mm represent the mass matrix, damping matrix, gyroscopic matrix, and stiffness matrix of the master node degrees of freedom respectively. M ss 、K ss 、C ss 、G ss represent the mass matrix, damping matrix, gyroscopic matrix, and stiffness matrix of the slave node degrees of freedom respectively. M sm 、K sm 、C sm 、G sm 、M ms 、K ms 、C ms 、G ms represent the mass matrix, damping matrix, gyroscopic matrix, and stiffness matrix of the coupled master and slave node degrees of freedom respectively. u m 、u s are the displacement vectors of the master and slave node degrees of freedom respectively. f m is the external force vector corresponding to the master node degrees of freedom. Assume that the responses of all degrees of freedom are linear combinations of fixed-interface normal modes and static constraint modes. The normal mode is the natural mode shape of the system calculated after constraining the master node degrees of freedom. Its dimension is the number of degrees of freedom plus the number of retained modes. Generally, the higher the order of the retained modes, the higher the accuracy of the dynamic calculation. It can be obtained by solving the characteristic equation and using the mode superposition method. The static constraint mode is the static displacement of the degrees of freedom under the action of boundary forces:

[0091]

[0092] Among them, q is the modal coordinate, Φ C is the static constraint mode, Φ N is the fixed-interface normal mode, and the expressions of Φ C and Φ N are respectively:

[0093]

[0094] Among them, φ is the vibration mode, and n is the lowest order mode number to be retained. Then, the transformation matrix T is constructed as follows:

[0095]

[0096] Based on the transformation matrix T, a reduced master node model is constructed:

[0097]

[0098] Finally, based on the reduced master node model, the time-domain control equation is constructed, and the dynamic response calculation can be carried out:

[0099]

[0100] The specific method of the fourth step is as follows: The boundary displacement coordination condition is introduced to connect the reduced master node models of the substructures to obtain the reduced model of the overall system. Assume that the substructure P and the substructure Q are connected by the connecting structure thin layer C as Figure 2 shown. The mass matrix M and the stiffness matrix K of the overall structure are in the following forms respectively:

[0101]

[0102] Among them, is the constraint mode connecting the substructure C. The degree-of-freedom division of the overall structure and the overall displacement vector are:

[0103]

[0104] Among them, is the internal degree of freedom, is the boundary degree of freedom. The interface displacement coordination condition is introduced as:

[0105]

[0106] Among them, L P and L Q are the coordinate rotation transformation matrices. By constructing the transformation matrix T2, the form after the assembly of the substructures can be obtained as follows:

[0107]

[0108] Using T2 for the second transformation, the connection of the substructures is realized:

[0109]

[0110] Finally, the reduced dynamic equation of the system is obtained as:

[0111]

[0112] The specific method for the fifth step is as follows: Based on the overall system master node reduction model, rapid response calculation is realized. The operation scale of the system reduction model no longer depends on the degrees of freedom of the overall system, but only on the number of master nodes and the number of intercepted modes. Since the operation scale of the system reduction model no longer depends on the degrees of freedom of the overall system, but only on the number of master nodes and the number of intercepted modes, this method significantly improves the calculation efficiency and has extremely high accuracy at the same time.

[0113] Example 2: On the basis of Example 1, as Figure 3 - Figure 7 shown, the connecting casing geometric model is as Figure 3 shown. The front end is the outer casing, the rear end is the intermediate casing, and the flange is connected by 60 bolts with a tightening torque of 22 N·m. According to the thin layer connection modeling theory, a thin layer is used to replace the bolt connection, the calculated layer stiffness is 3561 Mpa, and the MPC connection is used between the thin layer and the casing. The finite element model of the connecting casing is established as Figure 4 shown. Modal analysis is carried out on the substructure. Based on the modal analysis results, the effective independent method is adopted to select the master nodes. Considering the vibration modes within 6 pitches of the casing, at least 12 nodes are required per circle to reflect the vibration characteristics of each pitch, and 24 nodes can more clearly reflect the vibration characteristics of 6 pitches and can reflect the vibration characteristics of up to 12 pitches at most. According to the specific situation of the intermediate casing, to ensure the model accuracy and improve the calculation efficiency, finally 32 nodes are selected circumferentially in the outer circle and 3 circles axially; 24 nodes are selected circumferentially in the inner circle and 2 circles axially; plus the nodes on the support plate, there are a total of 208 master nodes; according to the specific situation of the outer casing, 32 nodes are selected circumferentially in the outer circle and 3 circles axially, with a total of 96 master nodes. Therefore, there are a total of 304 master nodes in the connecting casing. Compared with the 20,000 nodes of the simplified model, the model reduction rate is 99%. The master node reduction models of the intermediate casing and the outer casing are as Figure 5 、 Figure 6 shown. The boundary displacement coordination condition is introduced to connect the master node reduction models of the substructures to obtain the connecting casing system reduction model, as Figure 7 shown. Response calculations are carried out on the original model and the master node reduction model of the connecting casing. The comparison of the main modal vibration modes of the original model and the modal of the master node model is as Figure 8 shown. The comparison of the calculation results is shown in Table 1. It can be seen that the MAC values of each order modal vibration modes within 1000 HZ are all greater than 0.95, and the modal frequency differences are all within 0.6%. The comparison of the response calculation time is shown in Table 2. Before reduction, the modal response calculation time is 4.5 s. After reduction, the time is 0.6 s. Compared with before reduction, the efficiency of the master node reduction response calculation is increased by 86%. In summary, based on the master node reduction model, sufficient accuracy is retained, and at the same time, the calculation efficiency is greatly improved. The effectiveness and superiority of the method have been preliminarily verified.

[0114] Table 1 Correlation between Simplified Model of Connecting Casing and Main Node Model

[0115]

[0116]

[0117] Table 2 Comparison of Response Calculation Time

[0118]

[0119] Working principle of the present invention: In practical applications, this method can effectively handle the rapid response calculation problems of large-scale complex structures, especially suitable for structural design and analysis in fields such as aerospace, automotive manufacturing, and ship engineering. By reducing the degrees of freedom of calculation, this method not only shortens the calculation time but also reduces the demand for computing resources, enabling engineers to perform structural design and optimization more efficiently. In addition, while ensuring the calculation accuracy, this method can also flexibly adapt to different types of structures and connection methods, providing greater flexibility and reliability for engineering design.

[0120] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A fast response calculation method for elastic connection structure based on master node, characterized in that: The specific steps include: Step 1: Analyze and divide the substructure according to the geometric characteristics of the connection system; Step 2: Establish the finite element model of the substructure and the overall structure based on thin layer connection; Step 3: Perform modal analysis on the substructure and determine the main nodes of the substructure based on the effective independent method; Step 4: Introduce boundary displacement coordination conditions to connect the substructure main node reduction models to obtain the overall system reduction model; Step 5: Implement fast response calculation based on the overall system master node reduction model.

2. The method for calculating the rapid response of the elastic connection structure based on the master node according to claim 1, characterized in that: The specific method of the first step is: dividing the substructure according to the geometric characteristics of the connection system, and splitting the overall structure into individual components according to the connection relationship.

3. The method for rapid response calculation of elastic connection structure based on master node according to claim 1, characterized in that: The specific method of the second step is: establish a substructure and an overall structural finite element model based on thin layer connection, establish a single component finite element model and connect it through an elastic connection unit (thin layer) to form an overall structural finite element model, wherein the equivalent stiffness of the thin layer can be obtained by the bolt connection preload, and perform static analysis on the bolt connection structure. The part with greater stress is concentrated in the contact area between the bolt rod, nut and the connected parts. According to the stress of each part, the connection area can be divided into three parts: (a) the area of ​​screw connection; (b) the area of ​​preload; (c) the area of ​​flange edge connection, wherein the axial connection stiffness of the bolt connection structure is mainly determined by (a) and (b), and the total stiffness of the bolt part is: k s =n(k b +k m ) Among them, k b is the screw stiffness, k m is the joint stiffness of the upper and lower flanges, n is the total number of bolts, and for the bolt area, the axial stiffness expression of the screw is: Among them, A b is the cross-sectional area of ​​the bolt shank, d b is the diameter of the bolt shank, E b is the elastic modulus of the screw, L eq is the equivalent length of the bolt rod, L eq The expression is: Among them, L, β and ν are the length of the screw hole, the dimensionless coefficient and the Poisson's ratio of the screw respectively. For the bolt preload area, the most commonly used analysis method is the "preload cone angle method", which is to make the stress distribution area of ​​the connected part equivalent to the cone area with the top cut off. Outside this area, the stress value is relatively small and is basically a constant value, which can be regarded as unaffected by the preload. For the connected part, take the microelement dy in the cone area and integrate the effective load it receives, and the connection stiffness of the connected part can be obtained as: Among them, E 0i is the elastic modulus of the connected parts, t is the flange thickness, α is the semi-cone angle, and the bolt preload F p The size is related, so the axial connection stiffness of the entire bolt preload area is: Among them, k 01 , k 02 are the stiffness of the upper and lower connected parts respectively.

4. The method for calculating the rapid response of the elastic connection structure based on the master node according to claim 1, characterized in that: The specific method of the third step is: perform modal analysis on the substructure in ANSYS, determine the main nodes of the substructure based on the effective independence method, and obtain the main node reduction model of the substructure. Under the action of unbalanced excitation, the dynamic motion differential equation of the N-degree-of-freedom system is: Mu(t)+(C+ΩG)u(t)+Ku(t)=f(Ω,t) Among them, M, K, C, and G are the mass, stiffness, damping, and gyro matrix of the system, respectively. u(t) is the response vector at time t, and f is the external load. The modal analysis of the structure is performed. Based on the modal analysis results, the effective independent method is adopted to select the main nodes. First, the Fisher information matrix is ​​constructed: F=Φ T F Among them, Φ is the mass normalized vibration shape obtained by modal analysis, F is the Fisher information matrix, and based on the Fisher matrix, the effective independent allocation matrix E is constructed: E=ΦF -1 Φ T Among them, the diagonal elements of matrix E represent the contribution of degrees of freedom to the vibration matrix. The values ​​of diagonal elements are in the range of 0 to 1. The closer the elements are to 1, the greater the influence of the corresponding degrees of freedom and nodes on the vibration matrix. Finally, a threshold T is set, and the nodes corresponding to the diagonal elements greater than T are regarded as master nodes. Based on the selected master nodes, the control equations are divided into master node matrices and slave node matrices: Among them, M mm , K mm , C mm , G mm Represent the mass matrix, damping matrix, gyro matrix and stiffness matrix of the master node degrees of freedom respectively, M ss , K ss , C ss , G ss The mass matrix, damping matrix, gyro matrix and stiffness matrix represent the slave node degrees of freedom respectively, M sm , K sm , C sm , G sm 、M ms , K ms , C ms , G ms Represent the mass matrix, damping matrix, gyro matrix and stiffness matrix of the master and slave node degrees of freedom coupling, u m 、u s are the displacement vectors of the master and slave node degrees of freedom, respectively, m The external force vector corresponding to the main node degree of freedom is assumed to be a linear combination of the fixed-interface normal mode and the static constraint mode. The normal mode is the natural mode vibration shape of the system calculated after constraining the main node degree of freedom. Its dimension is the number of degrees of freedom plus the number of retained modes. Generally, the higher the number of retained modes, the higher the accuracy of dynamic calculation. It can be obtained by solving the characteristic equation and using the modal superposition method. The static constraint mode is the static displacement of the degree of freedom under the action of the boundary force: Where q is the modal coordinate, Φ C is the statically constrained mode, Φ N is the fixed interface normal mode, Φ C and Φ N The expressions are: Among them, φ is the vibration mode, n is the lowest order mode number retained, then the transformation matrix T is constructed: Construct the main node reduction model based on the transformation matrix T: Finally, the time domain control equation is constructed based on the master node reduction model to carry out the dynamic response calculation:

5. The method for rapid response calculation of elastic connection structure based on master node according to claim 1, characterized in that: The specific method of the fourth step is: introduce boundary displacement coordination conditions to connect the reduced models of the main nodes of the substructures to obtain the reduced model of the overall system, assuming that the substructure P and the substructure Q are connected by a connecting structure thin layer C, and obtain the mass matrix M and stiffness matrix K of the overall structure in the following forms: in, To connect the constraint modes of substructure C, the degree of freedom division and overall displacement vector of the overall structure are: in, is the internal degree of freedom, is the boundary degree of freedom, and the interface displacement coordination condition is introduced as follows: Among them, L P and L Q is the coordinate rotation transformation matrix, constructing the transformation matrix T2, and the assembled substructure is as follows: Using T2 for the second conversion, the substructures are connected: Finally, the reduced dynamic equation of the system is: Mq+Cq+Kq=f(t) 6. The method for calculating the rapid response of the elastic connection structure based on the master node according to claim 1, characterized in that: The specific method of the fifth step is: fast response calculation is realized based on the main node reduction model of the overall system. The operation scale of the system reduction model no longer depends on the number of degrees of freedom of the overall system, but is only related to the number of main nodes and the number of intercepted modes.

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