Composite vibration response analysis method under combined action of foundation excitation and nodal force excitation

Abstract

The invention discloses a composite vibration response analysis method under the combined action of basic excitation and nodal force excitation, and the method comprises the steps: applying a basic vibration load spectrum to a basic load action position, and carrying out the dynamics calculation of an equipment structure under the basic vibration load spectrum based on a modal superposition method, obtaining a basic excitation response under the basic vibration load spectrum; applying the node force load spectrum to the node force load action node, and carrying out dynamics calculation under the node force load spectrum on the equipment structure based on a modal superposition method to obtain a node force excitation response of the equipment structure under the node force load spectrum; performing superposition calculation on the basic excitation response and the node force excitation response by using a composite response superposition method to obtain a composite vibration response of the equipment structure; reliable composite vibration response of the equipment is obtained through numerical analysis, the reliability of environmental adaptability analysis and evaluation of the airborne precision equipment is improved, and the research and development risk of the precision equipment is effectively reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of structural random composite vibration analysis, and more specifically, it relates to a method for analyzing composite vibration response under the combined action of base excitation and nodal force excitation. Background Art

[0002] The vibration environment load during the service of airborne precision equipment is complex. The equipment structure usually faces the base vibration load excitation brought by the platform and the unsteady aerodynamic force excitation on the part of the structure exposed outside the aircraft. Moreover, in order to meet its physical functions, such precision equipment has extremely high requirements for the random vibration response under complex vibration loads. The displacement and rotation angle responses of key components in the equipment are at the micron or micro-radian level. Therefore, the dynamic design of such precision equipment is one of the key concerns. The main basis in the initial stage of the dynamic design of such equipment is the dynamic calculation and analysis results of the structure. In order to obtain the reliable composite vibration response of the equipment under the base vibration load excitation and nodal force excitation, so as to carry out a credible structural dynamic design for the precision equipment, it is first necessary to establish a method for analyzing the composite vibration response of the precision equipment under the base vibration load excitation and nodal force excitation. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for analyzing composite vibration response under the combined action of base excitation and nodal force excitation to solve the problems existing in the above background art.

[0004] The above technical object of the present invention is achieved through the following technical solutions:

[0005] In a first aspect, the present application provides a method for analyzing composite vibration response under the combined action of base excitation and nodal force excitation, including the following specific steps:

[0006] Establish a dynamic finite element model corresponding to the equipment structure, and determine the base boundary where the base vibration load spectrum is applied and the nodal force positions where the nodal force load spectrum is applied in the dynamic finite element model;

[0007] Based on the boundary constraints of the equipment structure, determine the base load acting position according to the base boundary, and determine the nodal force load acting nodes according to the nodal force positions;

[0008] Apply the base vibration load spectrum to the base load acting position, and carry out dynamic calculation of the equipment structure under the base vibration load spectrum based on the modal superposition method to obtain the base excitation response under the base vibration load spectrum. The base excitation response includes the first displacement response, the first velocity response, and the first root mean square acceleration response;

[0009] Apply the nodal force load spectrum to the nodes where the nodal force load acts, and based on the modal superposition method, conduct dynamic calculations on the equipment structure under the nodal force load spectrum to obtain the nodal force excitation response of the equipment structure under the nodal force load spectrum. The nodal force excitation response includes the second displacement response, the second velocity response, and the second root mean square acceleration response;

[0010] Use the composite response superposition method to superimpose and calculate the base excitation response and the nodal force excitation response to obtain the composite vibration response of the equipment structure. The composite vibration response includes the composite displacement response, the composite velocity response, and the composite root mean square acceleration response.

[0011] Based on the above technical solutions, the present invention can also be improved as follows.

[0012] Furthermore, the above base excitation response is obtained through the following method, specifically:

[0013]

[0014] where M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, represents the base acceleration spectrum excitation vector.

[0015] Furthermore, the above nodal force excitation response is obtained through the following method, specifically:

[0016]

[0017] where M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response, and F represents the nodal force spectrum excitation vector.

[0018] Furthermore, the above composite vibration response is obtained through the following method, specifically:

[0019]

[0020] where y represents the composite displacement response, represents the composite velocity response, represents the composite root mean square acceleration response, y1 represents the first displacement response, represents the first velocity response, Let \(y_1\) represent the first root mean square acceleration response, and \(y_2\) represent the second displacement response. Let \(v_2\) represent the second velocity response. Let \(a_{rms2}\) represent the second root mean square acceleration response.

[0021] Furthermore, the above method further includes:

[0022] Select the components and parts of concern in the dynamic finite element model, and extract the response results of concern for the components and parts of concern according to the calculation results of the superposition calculation.

[0023] In a second aspect, the present application provides a composite vibration response analysis system under the combined action of base excitation and nodal force excitation, which is applied to the composite vibration response analysis method under the combined action of base excitation and nodal force excitation according to any one of claims 1-5, and includes:

[0024] A first module for establishing a dynamic finite element model corresponding to the equipment structure, and determining the base boundary for applying the base vibration load spectrum and the nodal force position for applying the nodal force load spectrum in the dynamic finite element model;

[0025] A second module for determining the position of the base load acting based on the base boundary according to the boundary constraints of the equipment structure, and determining the nodes of the nodal force load acting according to the nodal force position;

[0026] A third module for applying the base vibration load spectrum to the position of the base load acting, and performing dynamic calculations on the equipment structure under the base vibration load spectrum based on the modal superposition method to obtain the base excitation response under the base vibration load spectrum, where the base excitation response includes the first displacement response, the first velocity response, and the first root mean square acceleration response;

[0027] A fourth module for applying the nodal force load spectrum to the nodes of the nodal force load acting, and performing dynamic calculations on the equipment structure under the nodal force load spectrum based on the modal superposition method to obtain the nodal force excitation response of the equipment structure under the nodal force load spectrum, where the nodal force excitation response includes the second displacement response, the second velocity response, and the second root mean square acceleration response;

[0028] A fifth module for performing superposition calculations on the base excitation response and the nodal force excitation response using the composite response superposition method to obtain the composite vibration response of the equipment structure, where the composite vibration response includes the composite displacement response, the composite velocity response, and the composite root mean square acceleration response.

[0029] Furthermore, in the above third module, the base excitation response is obtained through the following method, specifically:

[0030]

[0031] Wherein, M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, represents the base acceleration spectrum excitation vector;

[0032] In the fourth module, the nodal force excitation response is obtained in the following manner, specifically:

[0033]

[0034] Wherein, M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response, and F represents the nodal force spectrum excitation vector.

[0035] Furthermore, in the above-mentioned fifth module, the composite vibration response is obtained in the following manner, specifically:

[0036]

[0037] Wherein, y represents the composite displacement response, represents the composite velocity response, represents the composite root mean square acceleration response, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response.

[0038] In a third aspect, the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the method according to any one of the first aspect is implemented.

[0039] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method according to any one of the first aspect.

[0040] Compared with the prior art, the present invention has at least the following beneficial effects:

[0041] In this application, the response of the airborne precision equipment under the combined action of the basic excitation and the nodal force excitation is analyzed and evaluated by this method. The reliable composite vibration response of the equipment is obtained through numerical analysis, the reliability of the analysis and evaluation of the environmental adaptability of the airborne precision equipment is improved, and the R & D risk of the precision equipment is effectively reduced. Brief Description of the Drawings

[0042] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0043] Figure 1 is the method flow chart of the analysis method in the embodiment of the present invention;

[0044] Figure 2 is the flow schematic diagram of the analysis method in the embodiment of the present invention;

[0045] Figure 3 is the case schematic diagram of the composite vibration response analysis under the combined action of the basic excitation and the nodal force excitation in the embodiment of the present invention;

[0046] Figure 4 is the connection schematic diagram of the analysis system in the embodiment of the present invention. Detailed Embodiments

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0048] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of the present invention.

[0049] It should be noted that: similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0050] Embodiment 1: In order to obtain the reliable composite vibration response of the equipment under the basic vibration load excitation and the nodal force excitation, so as to carry out a credible structural dynamics design for the precision equipment, this embodiment provides a method for analyzing the composite vibration response under the combined action of the basic excitation and the nodal force excitation, as Figure 1 andFigure 2 As shown in the figure, it includes the following specific steps:

[0051] S1. Establish a dynamic finite element model corresponding to the equipment structure, and determine the foundation boundary for applying the foundation vibration load spectrum and the node force positions for applying the node force load spectrum in the dynamic finite element model.

[0052] Among them, when establishing the dynamic finite element model of the equipment structure, the established finite element model of the equipment structure should reflect the actual connection relationships of each component. Assign the material mechanics parameters (including density, elastic modulus, Poisson's ratio, damping factor, etc.) of each component according to the actual situation. The finite element mesh can be generated in the preprocessing module of various commercial finite element software. And determine the load boundary for applying the foundation random excitation load spectrum and the nodes for applying the force load spectrum.

[0053] S2. Based on the boundary constraints of the equipment structure, determine the foundation load acting positions according to the foundation boundary, and determine the node force load acting nodes according to the node force positions.

[0054] Specifically, as Figure 3 shown in the figure, apply the fixed support boundary condition to the foundation load application surface, that is, apply appropriate boundary conditions according to the boundary constraints of the structure and the foundation load application situation.

[0055] Furthermore, conduct modal analysis on the structural dynamic finite element model of the equipment structure. In the modal analysis, the modal analysis cut-off frequency is determined according to the upper limit of the frequency band of concern of the structure. Generally, the highest frequency of the modal analysis is 1.5 times the highest frequency of the load spectrum. And if it is necessary to obtain the structural stress / strain response, the stress / strain calculation switch needs to be turned on in the modal calculation settings. Considering the calculation efficiency, it is recommended to adopt the Block Lanczos method for the modal analysis method.

[0056] S3. Apply the foundation vibration load spectrum to the foundation load acting positions, and conduct dynamic calculations on the equipment structure under the foundation vibration load spectrum based on the modal superposition method to obtain the foundation excitation response under the foundation vibration load spectrum. The foundation excitation response includes the first displacement response, the first velocity response, and the first acceleration root mean square response.

[0057] Among them, apply the foundation vibration load spectrum to the foundation load acting positions as Figure 3 shown in the figure, and solve the first dynamic equation based on the modal superposition method in the random vibration analysis module to conduct the random vibration response analysis of the structure under the foundation excitation load spectrum; it is recommended to unify the unit of the foundation excitation load spectrum to the international unit. The foundation excitation load spectrum in this article is the acceleration load spectrum, and its unit is (m / s 2 ) 2 / Hz.

[0058] Optionally, the basic excitation response is obtained through the above kinetic equation, specifically as follows:

[0059]

[0060] In the formula, M represents the mass matrix of the kinetic finite element model, C represents the damping matrix of the kinetic finite element model, K represents the stiffness matrix of the kinetic finite element model, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, represents the base acceleration spectrum excitation vector.

[0061] S4. Apply the nodal force load spectrum to the nodes where the nodal force load acts, and based on the modal superposition method, conduct the dynamic calculation of the equipment structure under the nodal force load spectrum to obtain the nodal force excitation response of the equipment structure under the nodal force load spectrum. The nodal force excitation response includes the second displacement response, the second velocity response, and the second root mean square acceleration response.

[0062] Among them, apply the nodal force load spectrum to the nodes where the nodal force load acts as shown in Figure 3 and solve the kinetic equation based on the modal superposition method in the random vibration analysis module to conduct the random vibration response analysis of the structure under the nodal force excitation load spectrum; it is recommended that the unit of the nodal force excitation load spectrum be unified as the international unit, and its unit is N 2 / Hz.

[0063] Optionally, the above nodal force excitation response is obtained through the above second kinetic equation, specifically as follows:

[0064]

[0065] In the formula, M represents the mass matrix of the kinetic finite element model, C represents the damping matrix of the kinetic finite element model, K represents the stiffness matrix of the kinetic finite element model, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response, and F represents the nodal force spectrum excitation vector.

[0066] S5. Use the composite response superposition method to superimpose and calculate the basic excitation response and the nodal force excitation response to obtain the composite vibration response of the equipment structure. The composite vibration response includes the composite displacement response, the composite velocity response, and the composite root mean square acceleration response.

[0067] Among them, perform the superposition operation according to the SRSS method to obtain the composite vibration response of the structure under the combined action of the base excitation load spectrum and the nodal force excitation load spectrum. The above composite vibration response is obtained through the following method, specifically as follows:

[0068]

[0069] In the formula, y represents the composite displacement response, represents the composite velocity response, represents the composite root mean square acceleration response, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response.

[0070] Specifically, the above method further includes:

[0071] Select the components and parts of interest in the dynamic finite element model, and extract the response results of the components and parts of interest according to the calculation results of the superposition calculation.

[0072] Among them, this method analyzes and evaluates the response of the airborne precision equipment to the combined random vibration under the joint action of the base excitation and the nodal force excitation, obtains the reliable combined vibration response of the equipment through numerical analysis, improves the reliability of the analysis and evaluation of the environmental adaptability of the airborne precision equipment, and effectively reduces the R & D risk of the precision equipment.

[0073] Embodiment 2: The embodiment of the present application provides a combined vibration response analysis system under the joint action of the base excitation and the nodal force excitation, which is applied to the combined vibration response analysis method under the joint action of the base excitation and the nodal force excitation in Embodiment 1, as Figure 4 shown, including:

[0074] The first module is used to establish a dynamic finite element model corresponding to the equipment structure, and determine the base boundary where the base vibration load spectrum is applied and the nodal force position where the nodal force load spectrum is applied in the dynamic finite element model.

[0075] The second module is used to determine the position where the base load acts according to the base boundary based on the boundary constraints of the equipment structure, and determine the nodes where the nodal force load acts according to the nodal force position.

[0076] The third module is used to apply the base vibration load spectrum to the position where the base load acts, and carry out dynamic calculation of the equipment structure under the base vibration load spectrum based on the modal superposition method to obtain the base excitation response under the base vibration load spectrum. The base excitation response includes the first displacement response, the first velocity response and the first root mean square acceleration response; in the above third module, the base excitation response is obtained through the following method, specifically:

[0077]

[0078] Wherein, M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, represents the base acceleration spectrum excitation vector.

[0079] The fourth module is used to apply the node force load spectrum to the nodes where the node force load acts, and perform dynamic calculations on the equipment structure under the node force load spectrum based on the mode superposition method to obtain the node force excitation response of the equipment structure under the node force load spectrum. The node force excitation response includes the second displacement response, the second velocity response, and the second root mean square acceleration response; in the fourth module, the node force excitation response is obtained through the following method, specifically:

[0080]

[0081] Wherein, M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response, and F represents the node force spectrum excitation vector.

[0082] The fifth module is used to perform superposition calculation on the base excitation response and the node force excitation response by using the composite response superposition method to obtain the composite vibration response of the equipment structure. The composite vibration response includes the composite displacement response, the composite velocity response, and the composite root mean square acceleration response.

[0083] Optionally, in the above fifth module, the composite vibration response is obtained through the following method, specifically:

[0084]

[0085] Wherein, y represents the composite displacement response, represents the composite velocity response, represents the composite root mean square acceleration response, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response.

[0086] Embodiment 3: An embodiment of the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the method in Embodiment 1 is implemented.

[0087] Embodiment 4: An embodiment of the present application provides a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method in Embodiment 1.

[0088] The specific embodiments described above further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. Analysis method for composite vibration response under the combined action of basic excitation and node force excitation, characterized in that It includes the following specific steps: Establish a dynamic finite element model corresponding to the device structure, and determine the base boundary for applying the base vibration load spectrum and the node force positions for applying the node force load spectrum in the dynamic finite element model; Based on the boundary constraints of the device structure, determine the base load acting positions according to the base boundary, and determine the node force load acting nodes according to the node force positions; Apply the base vibration load spectrum to the base load acting positions, and carry out dynamic calculations on the device structure under the base vibration load spectrum based on the mode superposition method to obtain the base excitation response under the base vibration load spectrum, where the base excitation response includes the first displacement response, the first velocity response, and the first root mean square acceleration response; Apply the node force load spectrum to the node force load acting nodes, and carry out dynamic calculations on the device structure under the node force load spectrum based on the mode superposition method to obtain the node force excitation response of the device structure under the node force load spectrum, where the node force excitation response includes the second displacement response, the second velocity response, and the second root mean square acceleration response; Use the composite response superposition method to perform superposition calculations on the base excitation response and the node force excitation response to obtain the composite vibration response of the device structure, where the composite vibration response includes the composite displacement response, the composite velocity response, and the composite root mean square acceleration response.

2. The composite vibration response analysis method under the combined action of basic excitation and nodal force excitation according to claim 1, wherein The base excitation response is obtained in the following manner, specifically: where M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, represents the base acceleration spectrum excitation vector.

3. The composite vibration response analysis method under the combined action of basic excitation and nodal force excitation according to claim 1, characterized in that, The node force excitation response is obtained in the following manner, specifically: Wherein, M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response, and F represents the nodal force spectrum excitation vector.

4. The compound vibration response analysis method under the combined action of basic excitation and node force excitation according to claim 1, characterized in that, The composite vibration response is obtained in the following manner, specifically: where y represents the composite displacement response, represents the composite velocity response, represents the composite root mean square acceleration response, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response.

5. The compound vibration response analysis method under the combined action of basic excitation and node force excitation according to claim 1, characterized in that The method further includes: Select the concerned components and parts in the dynamic finite element model, and extract the concerned response results of the concerned components and parts according to the calculation results of the superposition calculation.

6. A composite vibration response analysis system under the combined action of base excitation and nodal force excitation, which is applied to the composite vibration response analysis method under the combined action of base excitation and nodal force excitation according to any one of claims 1-5, characterized in that, It includes: The first module is used to establish a dynamic finite element model corresponding to the device structure, and determine the base boundary for applying the base vibration load spectrum and the node force positions for applying the node force load spectrum in the dynamic finite element model; The second module is used to determine the base load acting positions according to the base boundary based on the boundary constraints of the device structure, and determine the node force load acting nodes according to the node force positions; The third module is used to apply the base vibration load spectrum to the base load acting positions, and carry out dynamic calculations on the device structure under the base vibration load spectrum based on the mode superposition method to obtain the base excitation response under the base vibration load spectrum, where the base excitation response includes the first displacement response, the first velocity response, and the first root mean square acceleration response; The fourth module is used to apply the node force load spectrum to the node force load acting nodes, and carry out dynamic calculations on the device structure under the node force load spectrum based on the mode superposition method to obtain the node force excitation response of the device structure under the node force load spectrum, where the node force excitation response includes the second displacement response, the second velocity response, and the second root mean square acceleration response; The fifth module is used to perform superposition calculation on the basic excitation response and the nodal force excitation response by using the composite response superposition method to obtain the composite vibration response of the device structure, where the composite vibration response includes a composite displacement response, a composite velocity response, and a composite acceleration root mean square response.

7. The composite vibration response analysis system under the combined action of basic excitation and node force excitation according to claim 6, characterized in that In the third module, the basic excitation response is obtained in the following manner, specifically: In the formula, M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, represents the base acceleration spectrum excitation vector; In the fourth module, the nodal force excitation response is obtained in the following manner, specifically: where M represents the mass matrix of the dynamic finite element model, C represents the damping matrix of the dynamic finite element model, K represents the stiffness matrix of the dynamic finite element model, y2 represents the second displacement response, represents the second velocity response, represents the second acceleration root mean square response, and F represents the nodal force spectral excitation vector.

8. The compound vibration response analysis system under the combined action of basic excitation and node force excitation according to claim 6, characterized in that In the fifth module, the composite vibration response is obtained in the following manner, specifically: where y represents the composite displacement response, represents the composite velocity response, represents the composite root mean square acceleration response, y1 represents the first displacement response, represents the first velocity response, represents the first root mean square acceleration response, y2 represents the second displacement response, represents the second velocity response, represents the second root mean square acceleration response.

9. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the method described in any one of claims 1-5 is implemented.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to execute the method described in any one of claims 1-5.

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