Response coupling based nonlinear joint multi-segment shell frequency response function modeling method

Abstract

The application discloses a kind of nonlinear joint surface multi-section shell frequency response function modeling methods based on response coupling.First, the multi-section shell is divided into each sub-cabin section using response coupling substructure method, and the connecting bolt of joint surface is regarded as transmission path, according to the response of target point is the superposition principle of each transmission path response, the response expression of the whole frequency response function of segmented shell is established;After that, on the basis of linear spring-damping connection of segmented joint surface, nonlinear stiffness term is added, and nonlinear joint surface of multi-section shell is constructed;At the same time, according to the actual working environment of multi-section shell, the corresponding frequency response function is obtained by hammering method or finite element analysis method for sub-cabin section;Finally, the parameters between joint surfaces are identified by least square method or artificial intelligence algorithm;So the whole frequency response function of multi-section shell under nonlinear joint surface is obtained.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of vibration control, in particular to a modeling method of frequency response function of multi-section shell with nonlinear joint surface based on response coupling. BACKGROUND

[0002] Stealth performance is one of the key technologies of underwater vehicle, which determines the survival performance of underwater vehicle. However, when the underwater vehicle is subjected to water medium load at a certain frequency, the vibration amplitude of the shell will be excited rapidly, the radiation range of noise will be expanded, and the probability of being discovered by the underwater vehicle will be greatly improved. Therefore, it is urgent to study the vibration reduction and noise reduction of the underwater vehicle to improve its stealth performance. Among many vibration reduction and noise reduction methods, the structural optimization of the shell of the underwater vehicle is the core means to improve its stealth performance, and the accurate overall frequency response function is the necessary condition for the structural optimization. At present, there are three methods to obtain the overall frequency response function of the multi-section shell: 1. hammering experiment method 2. theoretical analysis method 3. overall finite element method. However, the above three methods have certain defects. The experimental method has high precision, but the workload is large; the theoretical analysis method greatly simplifies the structure; the overall finite element method consumes a large amount of machine time.

[0003] The above information disclosed in the background section is only intended to enhance the understanding of the background of the present application, and therefore can contain information that does not constitute the prior art known to those of ordinary skill in the art in the country. SUMMARY

[0004] In view of the characteristics of the multi-section shell, such as multiple joint surfaces, serious nonlinearity between the joint surfaces and complex transmission path, the present application proposes a modeling method of frequency response function of multi-section shell with nonlinear joint surface based on response coupling. The multi-section shell is segmented by the response coupling substructure method, then the nonlinear joint surface is constructed by adding a quadratic stiffness term to the joint surface of the cabin section, and finally the overall frequency response function of the multi-section shell with nonlinear joint surface is modeled by using the transmission path analysis to solve the difficulty of complex path, thereby avoiding the defect of large workload caused by repeated experiments when the parameters of the substructure are changed.

[0005] The purpose of the present application is achieved by the following technical solutions.

[0006] In one aspect of the present application, a modeling method of frequency response function based on response coupling and nonlinear joint surface comprises the following steps:

[0007] In the first step, the multi-section shell is segmented into sub-cabin sections and joint surfaces by using the response coupling substructure method;

[0008] In the second step, according to the transmission path method, the connecting bolts between the joint surfaces are taken as the transmission path, and the response at the target point of the sub-cabin section is the superposition of the responses of each path;

[0009] In the third step, a quadratic nonlinear term is added to the linear spring-damping connection of the joint surface to construct a nonlinear joint surface;

[0010] In the fourth step, hammering or finite element analysis is performed on the sub-cabin section to obtain the corresponding frequency response function;

[0011] In the fifth step, the parameters of the joint surface are identified by the least square method or artificial intelligence algorithm;

[0012] In the sixth step, the identified parameters of the joint surface and the frequency response function are multiplied according to the transfer path method to obtain the overall frequency response function of the multi-section shell.

[0013] In the first step of the method, the multi-section shell is divided into a command cabin, a joint surface and a motor cabin.

[0014] In the second step of the method, the response at the target point of the motor cabin is the superposition of the responses of each path:

[0015]

[0016] wherein T t (w) is the total response at the target point; T s.i (w) is the response of each transmission path in three directions; H si (w) is the transfer function of each transmission path in three directions; F si (w) is the impact force of each transmission path in three directions, n is the total number of connecting bolts of the two cabin sections, and s represents the x, y and z directions.

[0017] In the third step of the method, a quadratic nonlinear term is added to the linear spring-damping connection of the joint surface, and the elastic force expression in the nonlinear coupling time domain is: F=k non x 2 The quadratic nonlinear term in the time domain is mapped to the frequency domain according to the Laplace transform: The vibration response at the target point of the motor cabin is:

[0018]

[0019] wherein X m，s3 (w) is the acceleration response of the three-direction sensor installed on the motor cabin; F r，s1 (w) is the hammering force in the x, y and z directions at the knocking position of the command cabin; k s2 (w), c s2 (w) and k non，s2 (w) are the connection stiffness, connection damping and quadratic nonlinear connection stiffness of the joint surface in the x, y and z directions, is the force of the s1 direction of the force hammer and the displacement of the s2 direction of the command cabin at the i th bolt position; is the force of the s2 direction of the i th bolt and the displacement of the s3 direction of the motor cabin sensor position; write the target vibration response as a component form:

[0020]

[0021]

[0022]

[0023] Summarize in matrix form:

[0024]

[0025] Wherein,

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] The above formula is the assembly frequency response function containing the connection parameters, wherein, The superscript m of indicates the motor cabin, Including And The superscript f in and indicates the command cabin, Including And k s2 (w) represents the joint surface connection stiffness, k s2 (w) includes k x (w), k y (w) and k z (w); c s2 (w) represents the joint surface connection damping, c s2 (w) includes c x(w) and c y (w) and c z (w) and k non，s2 represents the nonlinear connection stiffness of the joint surface, k non，s2 (w) and k non，x (w) and k non，y (w) and k non，z (w) and k

[0036] In the fourth step of the method, the engineering application is facilitated, and the workload in actual operation is reduced, since the multi-section shell is a cylindrical shell, and the bolts on the 1 / 4 shell are selected as the transmission path, and the frequency response functions at the symmetric bolts are the same.

[0037] In the fifth step (S5) of the method, the command cabin and the motor cabin are connected by 16 bolts, 4 bolts at symmetric positions are selected for analysis, and since the shell has large z-direction stiffness and is not easy to deform, the response contribution of the target point is small, so the connection parameters of the joint surface in the z-direction are ignored.

[0038]

[0039] wherein,

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] wherein, represents the frequency response function from the motor cabin section to the target response point, and the subscript (x, x) represents the response of the x-direction of the target point to the x-direction impact of the bolt point; represents the frequency response function from the command cabin to the bolt point, and the subscript (x, y) represents the response of the x-direction of the bolt point to the y-direction impact of the bolt point, and the meanings and naming rules of the remaining related parameters are similar.

[0047] The parameter identification problem is actually a least square problem, that is, a set of parameters is obtained, so that: is minimum, wherein A is an identification matrix, b is an experimental accurate value, and x is a set of identification parameters.

[0048] In the method, in the fifth step, the identification method adopts a least square algorithm or other artificial intelligence algorithms, such as an ant colony algorithm and a particle swarm optimization algorithm.

[0049] The engineering shell such as the underwater vehicle is a multi-section shell structure, the multi-section shell is divided into substructures by using response coupling substructures, the experimental method and the finite element method are mixedly used for the substructures, and the contradiction between workload and precision is solved. Meanwhile, for the treatment of the connecting surfaces between the substructures, the existing research uses linear spring-damping to fit. However, for the large thin-walled multi-section shell, there is serious nonlinearity between the connecting surfaces, and the current method is obviously not suitable for the frequency response function modeling of the multi-section shell. On the basis of the linear connection of the connecting surfaces, a quadratic nonlinearity stiffness term is added, so as to construct the nonlinear connecting surface, so that the characteristics of the connecting surface of the large thin-walled structure can be better revealed. The frequency response function modeling method of the nonlinear connecting surface multi-section shell based on response coupling provided in the application has great significance for subsequent shell structure optimization and vibration control. The difficulty of the multi-section shell in the aspects of multiple sections, multiple connecting points and complex transmission paths can be effectively solved, meanwhile, when the sub-cabin section structure is changed, the overall frequency response function can be obtained again by combining the existing connecting surface connecting parameters and the frequency response function of the sub-cabin section with unchanged structure, so that a large number of experiments are avoided, and the efficiency of obtaining the overall frequency response function is improved.

[0050] The above description is only a summary of the technical scheme of the present application, in order to make the technical means of the present application clearer and more understandable, to the extent that the person skilled in the art can implement according to the content of the specification, and in order to make the above and other purposes, characteristics and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application are exemplified below. BRIEF DESCRIPTION OF DRAWINGS

[0051] Various other advantages and benefits of the present application will become apparent to those of ordinary skill in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are included to provide a better understanding of preferred embodiments, and are not to be considered as limiting of the present application. It should be readily understood that the drawings are merely illustrative of the present application and that they, therefore, do not limit the present application, as claimed. Obviously, the drawings described below are only some embodiments of the present application, and other drawings can be obtained from these drawings without creative labor for those of ordinary skill in the art. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0052] In the drawings:

[0053] Figure 1 is a step schematic diagram of the frequency response function modeling method of the nonlinear connecting surface multi-section shell based on response coupling according to an embodiment of the present application;

[0054] Figure 2It is a nonlinear joint schematic diagram based on a response coupling nonlinear joint multi-section shell frequency response function modeling method according to an embodiment of the present application;

[0055] Figure 3 It is an experimental device schematic diagram of the response coupling nonlinear joint multi-section shell frequency response function modeling method according to an embodiment of the present application, wherein the device comprises a data acquisition device, a force hammer and a three-way acceleration sensor;

[0056] Figure 4 It is a response coupling nonlinear joint multi-section shell frequency response function modeling method of a multi-section shell 2-5-8 point middle 8 point response schematic diagram according to an embodiment of the present application;

[0057] Figure 5 It is a time domain and frequency domain diagram in a hammering experiment of the response coupling nonlinear joint multi-section shell frequency response function modeling method according to an embodiment of the present application, and it can be seen that the hammering experiment has sufficient bandwidth in the required frequency domain range, can excite all modes in the frequency band, and proves that the hammering experiment is effective;

[0058] Figure 6 It is a frequency response function schematic diagram of a knocking point on a command cabin section to a certain bolt point of the response coupling nonlinear joint multi-section shell frequency response function modeling method according to an embodiment of the present application, and the example in the present application adopts finite element harmonic response analysis to obtain the frequency response function because the command cabin is convenient to disassemble;

[0059] Figure 7 It is a frequency response function schematic diagram of a knocking point on a motor cabin section to a certain bolt point of the response coupling nonlinear joint multi-section shell frequency response function modeling method according to an embodiment of the present application, and only part of the frequency response function of x-way knocking is listed here, and the frequency response function is obtained by using the hammering method because the motor cabin is inconvenient to disassemble, and the naming rules of the frequency response function are that the right side affects the left side, for example, FRF-y-x represents the frequency response function of x-way knocking and the response of a certain bolt point y;

[0060] Figure 8 It is a nonlinear joint connection parameter frequency domain diagram of the response coupling nonlinear joint multi-section shell frequency response function modeling method according to an embodiment of the present application, and it can be seen that the connection parameter is a function of frequency because the scheme of identifying parameters one by one is adopted;

[0061] Figure 9 It is a comparison diagram of identification results and experimental accurate results of the response coupling nonlinear joint multi-section shell frequency response function modeling method according to an embodiment of the present application;

[0062] Figure 10FIG. 1 is a comparison chart of the 1-4-7 point prediction results of the nonlinear joint surface multi-segment shell frequency response function modeling method based on response coupling according to an embodiment of the present application, the linear joint surface frequency response function modeling method, and the experimental accurate results;

[0063] Figure 11 FIG. 2 is a columnar quantification chart of the 1-4-7 point prediction results of the nonlinear joint surface multi-segment shell frequency response function modeling method based on response coupling according to an embodiment of the present application, the linear joint surface frequency response function modeling method, and the experimental accurate results; wherein the quantification index is the sum of the amplitudes of the inherent frequencies of the frequency response function within the range of 0-500 Hz;

[0064] Figure 12 FIG. 3 is a comparison chart of the 3-6-9 prediction results of the nonlinear joint surface multi-segment shell frequency response function modeling method based on response coupling according to an embodiment of the present application, the linear joint surface frequency response function modeling method, and the experimental accurate results;

[0065] Figure 13 FIG. 4 is a columnar quantification chart of the 3-6-9 nonlinear joint surface prediction results of the nonlinear joint surface multi-segment shell frequency response function modeling method based on response coupling according to an embodiment of the present application, the linear joint surface frequency response function modeling method, wherein the quantification index is the sum of the amplitudes of the inherent frequencies of the frequency response function within the range of 0-500 Hz.

[0066] The present application will be further explained with reference to the drawings and embodiments. DETAILED DESCRIPTION

[0067] The present application will be further explained with reference to the drawings and embodiments. Figures 1 to 13 The specific embodiments of the present application will be described in more detail with reference to the drawings. It should be understood that the present application can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the application to those skilled in the art.

[0068] It should be noted that certain terms have been used throughout the specification and claims which have been used for the purpose of clarity in describing the application. Those skilled in the art will appreciate that the same component can be referred to by different names and that the name given is not intended to limit the component. The present specification and claims are not to be limited by the names of the components. The terms "comprising" or "including" as used throughout the specification and claims are to be interpreted as "including but not limited to." The description that follows is presented by way of example to provide an overall understanding of the principles of the application, and the description is not intended to be complete or exhaustive. The present application is intended to be defined by the claims that follow.

[0069] For the purpose of understanding the embodiments of the present application, further explanation and description will be made below with specific embodiments as examples in conjunction with the accompanying drawings, and each drawing does not constitute a limitation to the embodiments of the present application.

[0070] For a better understanding, Figure 1 The steps of the modeling method of the frequency response function of the multi-segment shell with nonlinear joint surface based on response coupling are shown in Figure 1 The modeling method of the frequency response function of the multi-segment shell with nonlinear joint surface based on response coupling includes the following steps:

[0071] In the first step, the multi-segment shell is segmented by the response coupling method. As described above, the present application adopts the scheme of identifying each joint surface. In order to verify the effectiveness of the proposed method, a two-segment shell assembly is taken as an example, and the substructures are named as the command cabin and the motor cabin, respectively, which are connected by bolts. According to the theory of response coupling method, the segmented assembly can be divided into three parts: the command cabin, the motor cabin and the joint surface.

[0072] In the second step, the coordinate system of the multi-segment shell is established, with the center of the shell structure as the coordinate origin, the ox axis perpendicular to the cross section passing through the origin and perpendicular to the ground, the oy axis perpendicular to the cross section passing through the origin and parallel to the ground, and the oz axis coinciding with the shell axis. According to the transfer path theory, the vibration response at the target point is the superposition of each transfer path, and in the present application, the hammering point-connection bolt-target point is taken as the transfer path. Then, the response at the target point of the motor cabin is:

[0073]

[0074] wherein, T t(w) is the total response at the target point; T si (w) is the response of each transfer path in three directions; H si (w) is the transfer function of each transfer path in three directions; F si (w) is the impact force of each transfer path in three directions, and n is the total number of connection bolts of the two cabin segments.

[0075] In the third step, a quadratic stiffness nonlinear term is constructed between the cabin joint surfaces. The expression of elastic force in nonlinear coupling time domain is: F=k non x 2 . The quadratic nonlinear term in time domain is mapped to frequency domain, and according to Laplace transform, we have: After adding the nonlinear term, the vibration response at the target point of the motor cabin is:

[0076]

[0077] wherein, X m，s3(w) is the acceleration response of the three-direction sensor mounted on the motor compartment; F r，s1 (w) is the hammering force in x, y, z directions at the knocking position of the command cabin; k s2 (w), c s2 (w) and k non，s2 (w) is the connection stiffness, connection damping and quadratic nonlinear connection stiffness in x, y, z directions of the joint surface, is the frequency response function of the force in s1 direction of the force hammer and the displacement in s2 direction of the command cabin at the i th bolt position; is the frequency response function of the force in s2 direction of the i th bolt and the displacement in s3 direction of the motor cabin sensor position; the target vibration response is written as a component form:

[0078]

[0079]

[0080]

[0081] The summary is in the form of a matrix:

[0082]

[0083] wherein,

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] The above formula is the frequency response function of the assembly containing the connection parameters, wherein, the superscript m of indicates the motor cabin, including and the superscript f in and indicates the command cabin, including and k s2 (w) represents the connection stiffness of the joint surface, k s2 (w) includes k x (w), k y (w) and k z (w); c s2 (w) represents the connection damping of the joint surface, c s2 (w) includes c x (w), c y (w) and c z (w); k non，s2 represents the nonlinear connection stiffness of the joint surface, k non，s2 (w) includes k non，x (w), k non，y (w) and k non，z (w).

[0094] In the preferred embodiment of the method, in the fourth step S4, the multi-section shell is a cylindrical shell, and the bolts on the 1 / 4 shell are selected as the transmission path, and the frequency response functions at the symmetric bolts are the same.

[0095] In the preferred embodiment of the method, in the fifth step S5, the command cabin and the motor cabin are connected by 16 bolts, 4 bolts at symmetric positions are selected for analysis, and the frequency response functions at the symmetric positions are the same; and since the shell has large z-direction stiffness and is not easy to deform, the response contribution to the target point is small, so the connection parameters of the joint surface in the z-direction are ignored. Then, the transverse and longitudinal connection parameters are calculated as follows:

[0096]

[0097] wherein,

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] wherein, represents the frequency response function from a bolt on the motor cabin section to the target response point, and the subscript (x, x) represents the response of the x-direction of the target point to the x-direction impact at the bolt point; H (x, y) represents the frequency response function from the point of hammering on the command cabin to a certain bolt point, the subscript (x, y) represents the response of the bolt point in the y direction to the impact at the bolt point in the x direction, the meanings of the remaining related parameters and the naming rules are similar, and the naming rules are that the right side affects the left side.

[0105] It can be seen that the parameter identification problem is actually a least square problem, that is, a set of parameters is obtained so that: is minimum. Wherein, A is an identification matrix, b is an experimental accurate value, and x is a set of identification parameters.

[0106] In the sixth step, the connection parameters and the segmented frequency response function obtained in the above steps are multiplied according to the TPA theory, so that the overall frequency response function of the assembled body is obtained.

[0107] In order to further illustrate the method of the present application, Figure 1 is a step schematic diagram of the method for modeling the multi-segment shell frequency response function based on the response coupling nonlinear joint surface. First, the multi-segment shell is divided into each cabin segment by using the response coupling substructure; then the joint surface connecting bolt is regarded as a transfer path by using the transfer path method, and the response expression of the overall frequency response function is established according to the superposition principle of the responses of each transfer path; there are two types of unknown data in the expression: the frequency response function of the cabin segment and the connection parameters of the joint surface. First, the corresponding frequency response function is obtained by hammering method or finite element analysis method for the cabin segment, and the nonlinear stiffness term is added on the basis of the linear spring-damping connection between the segments to construct the nonlinear joint surface; then the parameters between the joint surfaces are identified by the least square method or artificial intelligence algorithm; and thus the overall frequency response function of the multi-segment shell under the nonlinear joint surface is obtained.

[0108] Figure 2 is a nonlinear joint surface schematic diagram of the method for modeling the multi-segment shell frequency response function based on the response coupling nonlinear joint surface according to an embodiment of the present application, and the nonlinear stiffness term is added on the basis of the linear connection. The linear stiffness, linear damping and nonlinear stiffness are simulated by three directions.

[0109] Figure 3 is an experimental device of the method for modeling the multi-segment shell frequency response function based on the response coupling nonlinear joint surface according to an embodiment of the present application; as shown in Figure 2 the entire experimental device is composed of a multi-segment shell, a data acquisition system, a three-direction acceleration sensor and a force hammer. The first two segments of the shell are labeled as points 1-9, wherein points 2-5-8 are used for identification experiments; points 1-4-7 and points 3-6-9 are used for prediction experiments. Specifically, points 1-3 are used to apply x-direction excitation, and points 4-6 are used to apply y-direction excitation. Points 7-9 are response points for placing sensors. The relationship between identification and prediction is similar to the training set and test set in machine learning. At the same time, the center of the shell is taken as the coordinate origin to mark the coordinate system used in the present application.

[0110] Figure 4 is a schematic diagram of the response of the target point of the multi-segment shell based on the response-coupled nonlinear joint surface multi-segment shell frequency response function modeling method according to an embodiment of the application, wherein the response of the target point in the parameter identification stage 2-5-8 points is listed. The naming rule of the frequency response function is that the right side affects the left side, for example: FRF-x-y represents the frequency response function obtained by the y-direction excitation and the x-direction response.

[0111] Figure 5 is a time domain and frequency domain diagram in a hammering experiment of the frequency response function modeling method of the nonlinear joint surface multi-segment shell based on the response coupling according to an embodiment of the application. It can be seen that the hammering experiment has sufficient bandwidth in the required frequency domain range, and can excite all modes in the frequency band, proving that the hammering experiment is effective.

[0112] Figure 6 is a frequency response function from a knocking point on the command cabin segment to a certain bolt point of the frequency response function modeling method of the nonlinear joint surface multi-segment shell based on the response coupling according to an embodiment of the application. In the example in the application, the command cabin is easy to disassemble, and the frequency response function is obtained by using finite element harmonic response analysis.

[0113] Figure 7 is a frequency response function from a knocking point on the motor cabin segment to a certain bolt point of the frequency response function modeling method of the nonlinear joint surface multi-segment shell based on the response coupling according to an embodiment of the application. Here, only part of the frequency response function of the x-direction knocking is listed. In the example in the application, the motor cabin is not easy to disassemble, and the frequency response function is obtained by using the hammering method. The naming rule of the frequency response function is that the right side affects the left side, for example: FRF-y-x represents the frequency response function of the x-direction knocking and the y-direction response of a certain bolt point.

[0114] Figure 8 is a frequency domain diagram of the connection parameter of the frequency response function modeling method of the nonlinear joint surface multi-segment shell based on the response coupling according to an embodiment of the application. As the scheme of identifying the parameters one by one is adopted, it can be seen that the connection parameter is a function of the frequency.

[0115] Figure 9 is a comparison diagram of the identification result and the experimental accurate result of the frequency response function modeling method of the nonlinear joint surface multi-segment shell based on the response coupling according to an embodiment of the application.

[0116] Figure 10 is a comparison diagram of the prediction result of the 1-4-7 points and the linear joint surface frequency response function modeling method and the experimental accurate result of the frequency response function modeling method of the nonlinear joint surface multi-segment shell based on the response coupling according to an embodiment of the application.

[0117] Figure 11Figure 6 is a columnar quantification chart of the 1-4-7 point prediction results of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling according to an embodiment of the present application compared with the linear joint surface frequency response function modeling method and the experimental accurate results, wherein the quantification index is the sum of the amplitudes of the inherent frequencies of the frequency response function within the range of 0-500 Hz.

[0118] Figure 12 Figure 7 is a comparison chart of the 3-6-9 prediction results of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling according to an embodiment of the present application compared with the linear joint surface frequency response function modeling method and the experimental accurate results.

[0119] Figure 13 Figure 8 is a columnar quantification chart of the 3-6-9 nonlinear joint surface prediction results of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling according to an embodiment of the present application compared with the linear joint surface frequency response function modeling method, wherein the quantification index is the sum of the amplitudes of the inherent frequencies of the frequency response function within the range of 0-500 Hz.

[0120] In the preferred embodiment of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling of the present application, in the first step S1, the multi-section shell is segmented by using the response coupling substructure method. Taking the scaled-down model used in the present application as an example, the two substructures are named as the command cabin and the motor cabin, and the two cabin sections are connected by bolts. The segmented assembly can be divided into three parts: the command cabin, the motor cabin and the joint surface.

[0121] In the preferred embodiment of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling of the present application, in the first step S2, the response at the target point of the motor cabin is obtained according to the transfer path method.

[0122] In the preferred embodiment of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling of the present application, in the first step S3, a nonlinear stiffness term is added to the linear spring-damping connection between the segments on the basis of the joint surface, and taking the quadratic nonlinear term as an example, the expression of the elastic force in the nonlinear coupling time domain is F=k non x 2 . The quadratic nonlinear term in the time domain is mapped to the frequency domain, and according to the Laplace transform, the following equation can be obtained: The quadratic nonlinear term is added to the response of the target point to obtain the response of the target point under the nonlinear joint surface. It is written in the component form and then summarized in the matrix form, so as to obtain the overall frequency response function of the target point after the segmentation of the two-section shell.

[0123] In the preferred embodiment of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling of the application, in the first step S4: according to the actual service environment of the shell, the corresponding frequency response function is obtained by hammering method or finite element analysis method. For the scaled model in the application, the command cabin is easy to disassemble, and the frequency response function is obtained by using finite element harmonic response; the motor cabin is not easy to disassemble, and the frequency response function is obtained by using hammering experiment.

[0124] In the preferred embodiment of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling of the application, in the first step S5: since the connection parameter is identified by frequency in the application, and the shell is cylindrical and has stiffness characteristics in the z direction, the parameter identification formula can be obtained from step S3.

[0125] In the preferred embodiment of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling of the application, in the first step S6: the connection parameters and the segmented frequency response functions identified in the above steps are multiplied according to the TPA theory, and the overall frequency response function of the assembled body can be obtained.

[0126] In one embodiment, as shown in Figure 4 is the response of the target point 8 when x-direction excitation is applied to point 2 and y-direction excitation is applied to point 5 among points 2-5-8. Figure 5 is a time domain and frequency domain graph according to a hammering experiment in the application. It can be seen that the hammering experiment has sufficient bandwidth in the required frequency domain range, and can excite all modes in the frequency band, proving that the hammering experiment is effective. Figure 6 is a frequency response function of a command cabin according to the application, which is obtained by using finite element harmonic response method. Figure 7 is a frequency response function of a motor cabin according to the application, which is obtained by using hammering experiment. Figure 8 is a frequency domain graph of a nonlinear joint surface connection parameter according to the application. Since the parameter identification scheme is by frequency, it can be seen that the connection parameter is a function of frequency. Figure 9 is a comparison graph of the nonlinear joint surface frequency response function modeling method and the experimental accurate result according to the application. It can be seen that for FRF with large amplitude, the identified connection parameter can be well fitted with the experimental FRF; and for FRF with small amplitude, the fitting accuracy is relatively poor due to the interference of environmental factors such as noise, but it is still within the acceptable range of engineering. Figure 10is a comparison chart of the prediction results of one 1-4-7 point according to the present application and the linear joint surface frequency response function modeling method and the experimental accurate results. It can be seen that, in some frequency bands, compared with the joint surface parameters with nonlinear terms, the frequency response function identified by the linear method is obviously higher than the experimental value, in some experimental value smoothing frequency bands, the linear method will identify additional peak values, and the identification method with nonlinear terms is smoother and closer to the experimental value. Figure 11 is a columnar quantification chart of one 1-4-7 nonlinear joint surface prediction results and the linear joint surface frequency response function modeling method according to the present application, wherein the quantification index is the sum of the amplitudes of the inherent frequencies of the frequency response function in the range of 0-500Hz. It can be seen that the sum of the errors of the frequency response functions identified by the nonlinear identification in the x-direction response and the y-direction response at the inherent frequencies is less than that of the frequency response functions identified by the linear identification, and the accuracy of the FRF identified by the nonlinear identification is increased by 46%, 49%, 3% and 2% respectively for x-direction knocking, x-direction response, y-direction knocking, x-direction response, x-direction knocking, y-direction response and y-direction knocking, y-direction response. Figure 12 is a comparison chart of the prediction results of one 3-6-9 point according to the present application and the linear joint surface frequency response function modeling method and the experimental accurate results. Similarly, its prediction results are similar to the prediction results of 1-4-7 points. Figure 13 is a columnar quantification chart of one 3-6-9 nonlinear joint surface prediction results and the linear joint surface frequency response function modeling method according to the present application. It can be seen that the sum of the errors of the frequency response functions identified by the nonlinear identification in the x-direction response and the y-direction response at the inherent frequencies is less than that of the FRF identified by the linear identification, and the accuracy of the FRF identified by the nonlinear identification is increased by 39%, 53%, 59% and 17% respectively for x-direction knocking, x-direction response, y-direction knocking, x-direction response, x-direction knocking, y-direction response and y-direction knocking, y-direction response. Figures 9 to 13 The verification results and the prediction results of can fully prove the effectiveness and superiority of the nonlinear joint surface multi-section shell frequency response function modeling method based on response coupling proposed in the present paper.

Claims

1. A method for modeling the frequency response function of a multi-segment shell with a nonlinear interface based on response coupling, characterized in that, The method includes the following steps: In the first step (S1), the response coupling substructure method is used to divide the multi-segment shell into sub-compartment segments and joint surfaces; In the second step (S2), according to the transmission path method, the connecting bolts between the mating surfaces are taken as the transmission path, and the response at the target point of the sub-compartment is the superposition of the responses of each path. In the third step (S3), a quadratic nonlinear term is added to the linear spring-damped connection of the joint surface to construct a nonlinear joint surface of the multi-segment shell; In the fourth step (S4), the sub-section is subjected to impact testing or finite element analysis to obtain the corresponding frequency response function; In the fifth step (S5), the parameters of the bonding surface are identified using the least squares method or artificial intelligence algorithms; In the sixth step (S6), the parameters of the identified mating surface and the frequency response function are multiplied according to the transfer path method to obtain the overall frequency response function of the multi-segment shell under the nonlinear mating surface.

2. The method according to claim 1, characterized in that, Multi-section hulls include those for underwater vehicles and spacecraft.

3. The method according to claim 1, characterized in that, In the first step (S1), the multi-section shell is divided into a command compartment, a joint surface, and an engine compartment.

4. The method according to claim 3, characterized in that, In the second step (S2), the response at the target point in the engine room is the superposition of the responses from each path: ， in, This represents the total response at the target point. For the response in each of the three directions of the transmission path; For each transmission path, there are three transfer functions in each direction; The impact force in each transmission path is in three directions, n is the total number of connecting bolts between the two sections, and s represents the x, y, and z directions.

5. The method according to claim 4, characterized in that, In the third step (S3), a quadratic nonlinear term is added to the linear spring-damped connection at the joint surface. The expression for the elastic force in the nonlinear coupling time domain is as follows: Mapping the quadratic nonlinear term in the time domain to the frequency domain, according to the Laplace transform, we get: Then, under the nonlinear interface, the vibration response at the target point of the motor compartment is: ， in, It is the acceleration response of the three-dimensional sensor installed in the motor compartment; The hammering force in the x, y, and z directions at the impact point of the command module; , and It refers to the connection stiffness, connection damping, and second-order nonlinear connection stiffness in the x, y, and z directions of the interface. It is the frequency response function of the force in the s1 direction of the hammer and the command cabin in the s2 direction at the position of the i-th bolt; It is the force on the i-th bolt in the s2 direction and the frequency response function of the sensor position in the motor compartment in the s3 direction; the target vibration response is written in component form: ， ， ， Summarized in matrix form: ， in, ， ， ， ， ， ， ， ， ， The above formula is the frequency response function of the assembly including connection parameters, where, The superscript 'm' indicates the motor compartment. include , and ; The superscript 'f' in the text indicates the command module. include , and ; Indicates the connection stiffness of the mating surface. include , and ; Indicates the damping of the mating surface connection. include , and ; This indicates the nonlinear connection stiffness of the mating surface. include , and .

6. The method according to claim 5, characterized in that, In the fourth step (S4), the multi-segment shell is a cylindrical shell, and the bolts on 1 / 4 of the shell are selected as the transmission path. The frequency response functions at the symmetrical bolts are the same.

7. The method according to claim 5, characterized in that, In step five (S5), the command compartment and the motor compartment are connected by 16 bolts. Four bolts at symmetrical positions are selected for analysis. Since the shell has high stiffness in the z-direction and is not easily deformed, its contribution to the response at the target point is small. Therefore, the connection parameters in the z-direction of the mating surface are ignored. The transverse and longitudinal connection parameters are calculated as follows: ， in, ， ， ， ， ， ， in, This represents the frequency response function from a bolt on the motor compartment to the target response point, where the subscript (x, x) indicates the x-direction response of the impact at the bolt point to the target point. This represents the frequency response function from the impact point on the command module to a certain bolt point. The subscript (x, y) indicates the response of the bolt point in the x direction to the impact in the y direction. The other parameters follow the same logic. The parameter identification problem is actually a least squares problem, that is, to find a set of parameters such that: Minimum, of which For identification matrix, Let x be the experimental accuracy value, and let x be the set of identification parameters.

8. The method according to claim 5, characterized in that, In the fifth step (S5), the identification method adopts ant colony algorithm, particle swarm optimization algorithm or neural network algorithm.

Images