Multi-layer heterogeneous structure guided wave modeling analysis method based on damping introduction and grid optimization

Abstract

The invention discloses a multilayer heterogeneous structure guided wave modeling analysis method based on damping introduction and grid optimization, and belongs to the technical field of aerospace structure health monitoring, and the method comprises the steps: building geometric models of a main bearing-heat insulation tile structure and a piezoelectric element, and defining parameters; defining material parameters of the main bearing-heat insulation tile structure and the piezoelectric element; carrying out multi-physics field coupling setting; a viscous-elastic material is introduced for damping; performing grid division on the structure; and setting a time step for analysis and solution. According to the method, the attenuation effect of related viscous-elastic materials on the guided wave amplitude is considered, grid division is optimized through the sweeping method, the unit freedom degree is remarkably reduced, meanwhile, the grid quality is ensured, and the accuracy of guided wave modeling analysis is further effectively controlled.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace structural health monitoring, and in particular to a multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization. Background Art

[0002] Reusable aircraft are an important development direction in the international aerospace field. Since reusable aircraft will experience harsh aerodynamic heating environments during their service, the thermal protection system is the core of their safe service and reuse. Ceramic insulation tiles are an important solution for the design of large-area thermal insulation structures. Generally, strain isolation pads are used to connect the insulation tiles to the main load-bearing structure, and high-temperature resistant silicone rubber is used for bonding. In this application, this type of multi-layer structure is referred to as the "main load-bearing-insulation tile structure." The health status of the main load-bearing-insulation tile structure is directly related to the safety performance of the reusable aircraft. Conducting guided wave structural health monitoring on it can ensure the reliable operation of the structure, and using modeling and analysis methods to clarify its guided wave propagation mechanism is the basis for targeted damage monitoring.

[0003] Finite element analysis is an efficient and commonly used numerical analysis method. Many mature finite element software have been applied to the numerical modeling and analysis of waveguide structure health monitoring. Finite element analysis has become one of the most commonly used methods for simulating waveguide propagation in structures. Finite element analysis first discretizes the continuum into a finite number of discrete domains that do not overlap and are only connected to each other through nodes. An approximate function that approximates the actual displacement field is assumed in the unit, that is, the shape function. Since the displacement field function is assumed in a small local domain, the difficulty of assuming the displacement field function in the global field is solved. Then, the basic equation of elastic mechanics is used to establish the stiffness equation in the unit, and the total stiffness equation of the structure is formed by assembly, and finally solved using constraints. Finite element analysis is applicable to various complex structures and has the ability to calculate various complex mechanical problems. Its calculation amount is related to the coarseness of the structural mesh division.

[0004] However, for structures such as main bearing-insulation tiles, high temperature resistant silicone rubber and strain isolation pads are viscoelastic materials, which have a significant attenuation effect on guided waves. If the viscoelastic characteristics of the materials are not considered, it is difficult to accurately simulate the propagation of guided waves. Therefore, in order to improve the accuracy of modeling and analysis, it is necessary to study how to select and introduce appropriate damping models. At the same time, the dimensions of this type of structure in the thickness direction are large. When using finite element analysis, conventional meshing methods will greatly increase the calculation cost, reduce the calculation efficiency, and have high requirements on computer hardware. Summary of the invention

[0005] In view of the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a multi-layer heterogeneous structure waveguide modeling and analysis method based on damping introduction and grid optimization, to optimize the existing finite element analysis method so that it can achieve high-precision piezoelectric waveguide modeling and simulation at low cost and quickly, to better describe the propagation characteristics of waveguides in such structures, and to provide support for the subsequent targeted formulation of damage monitoring strategies.

[0006] To achieve the above object, the technical solution of the present invention is:

[0007] A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization includes: step S1, establishing a geometric model of a main bearing-insulation tile structure and a piezoelectric element and defining parameters;

[0008] Step S2, defining the material parameters of the main bearing-insulation tile structure and the piezoelectric element;

[0009] Step S3, multi-physics field coupling setting;

[0010] Step S4, introducing viscoelastic material damping;

[0011] Step S5, meshing the structure;

[0012] Step S6, setting the time step for analysis and solution.

[0013] Furthermore, in the above step S4, the Rayleigh damping model is selected and defined as: C=αM+βK, wherein C is the damping matrix; M is the mass matrix; K is the stiffness matrix; α and β are the mass proportional coefficient and the stiffness proportional coefficient respectively.

[0014] Furthermore, the above step S5 includes:

[0015] Step S51, by Determine the mesh size, where L max is the maximum side length of the finite element; min is the minimum wavelength of the guided wave; n min is the minimum number of intervals between nodes per wavelength;

[0016] Step S52, plane cutting of the upper surface of the main load-bearing structure;

[0017] Step S53, dividing the upper surface of the main load-bearing structure after segmentation into quadrilateral two-dimensional grids, and then translating the quadrilateral two-dimensional grids to different positions of each layer of the main load-bearing structure;

[0018] Step S54, sweeping each layer of two-dimensional grids along the thickness direction of the structure to generate a three-dimensional grid of the geometric model of the entire main load-bearing-insulation tile and piezoelectric element.

[0019] Furthermore, in the above step S6, the time step Δt satisfies:

[0020]

[0021] L min is the minimum side length of the finite element, c pmax is the maximum phase velocity of the guided wave.

[0022] Furthermore, in the above step S1, defining the parameters includes defining the narrow-band sinusoidal modulation excitation signal V a =A a ·[1-cos(2πf c t / N a )]·sin(2πf c t) is used to excite the guided wave, where A a is the amplitude of the excitation signal, f c is the center frequency of the excitation signal; N a is the number of excitation peaks.

[0023] Furthermore, the above step S3 includes imparting electrostatic physics to the piezoelectric element structure, and imparting solid physics to the piezoelectric element structure and the main bearing-insulation tile structure.

[0024] Furthermore, the above-mentioned boundary conditions of solid physics include: linear elastic material, freedom, initial value, piezoelectric material, and low reflection boundary.

[0025] Furthermore, the boundary conditions of the above electrostatic physics include: charge conservation, zero charge and initial value.

[0026] The present invention also provides a device, comprising: one or more processors; a memory for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors execute the above-mentioned multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization.

[0027] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, it implements the above-mentioned multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization.

[0028] Beneficial effect: The multilayer heterogeneous structure guided wave modeling and analysis method proposed in the present invention based on damping introduction and grid optimization takes into account the attenuation effect of the relevant viscoelastic materials on the guided wave amplitude by introducing the Rayleigh damping model. In addition, the mesh division is optimized by the sweeping method, which not only significantly reduces the unit degree of freedom, but also ensures the quality of the mesh, thereby further effectively controlling the accuracy of the guided wave modeling and analysis.

[0029] In order to make the above features and advantages of the invention more obvious and easy to understand, embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 The present invention is a flow chart of a multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization.

[0031] Figure 2 for Figure 1 Flow chart of step S5 in FIG.

[0032] Figure 3 It is a schematic diagram of the main load-bearing-insulation tile structure in a specific embodiment.

[0033] Figure 4 for Figure 3 A partial enlarged view of the middle area 1A.

[0034] Figure 5 It is a schematic diagram of the arrangement of piezoelectric elements on the main load-bearing-insulation tile structure in a specific embodiment.

[0035] Figure 6 It is a schematic diagram of the grid division of the main load-bearing-insulation tile structure in a specific embodiment.

[0036] Figure 7 It is a waveguide signal diagram before adopting the multi-layer heterogeneous structure waveguide modeling and analysis method based on damping introduction and grid optimization of the present invention in a specific embodiment.

[0037] Figure 8 It is a waveguide signal diagram after adopting the multi-layer heterogeneous structure waveguide modeling and analysis method based on damping introduction and grid optimization of the present invention in a specific embodiment. DETAILED DESCRIPTION

[0038] In order to make the purpose and technical solution of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] like Figure 1 As shown, the multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization of the present invention includes the following steps.

[0040] Step S1, establishing the geometric model of the main bearing-insulation tile structure and the piezoelectric element and defining parameters.

[0041] More specifically, the main bearing-insulation tile structure is taken as a research object, and the piezoelectric element is used to excite and sense the guided wave signal.

[0042] Furthermore, the definition parameters in step S1 include defining the narrowband sinusoidal modulation excitation signal V a =A a ·[1-cos(2πf c t / N a )]·sin(2πf c t) is used to excite the guided wave, where A a is the amplitude of the excitation signal, f c is the center frequency of the excitation signal; N a is the number of excitation peaks.

[0043] Furthermore, the definition parameters in step S1 include defining the material properties of the main load-bearing-insulation tile structure, the material properties of the piezoelectric element, etc.

[0044] Step S2, defining the material parameters of the main load-bearing-insulation tile structure and the piezoelectric element.

[0045] More specifically, in order to accurately describe the mechanical properties of the structural material, the material parameters of the main bearing-insulation tile structure and the piezoelectric element are defined according to actual needs.

[0046] Step S3, multi-physics field coupling setting.

[0047] More specifically, in order to accurately simulate the excitation and sensing process of the piezoelectric element on the guided wave, a multi-physics field coupling method of solid field and electrostatic field is adopted. Electrostatic physics is assigned to the piezoelectric element structure, and solid physics is assigned to the piezoelectric element and the main bearing-insulation tile structure. As a result, the piezoelectric element structure has both electrostatic properties and solid mechanical properties, successfully realizing electromechanical coupling.

[0048] Furthermore, solid physics includes three boundary conditions by default: linear elastic material, free and initial value. Other boundary conditions that can be included are piezoelectric material and low-reflection boundary.

[0049] The linear elastic material indicates that the material property of the main load-bearing-insulation tile structure defined in step S1 is a linear elastic material, which is assigned to the geometric model of the main load-bearing-insulation tile structure in step S3.

[0050] In this case, freedom is granted to all boundaries of the geometric model of the load-bearing and thermal-insulation tile structure and the piezoelectric element, indicating the freedom of the plate boundary.

[0051] Among them, the initial value is set to 0, indicating that the initial displacement field and velocity field of the geometric model of the main bearing-insulation tile structure and the piezoelectric element are both 0.

[0052] Among them, piezoelectric material represents the material property of the piezoelectric element defined in step S1, which is assigned to the piezoelectric element in step S3. At the same time, considering the damping characteristics of the piezoelectric material, a mechanical damping condition is added, its type is set to Rayleigh damping, and the mass proportional coefficient α and stiffness proportional coefficient β are set to 0 and 2.2×10 -8 .

[0053] Among them, low-reflection boundaries are assigned to the four sides of the geometric model of the main load-bearing-insulation tile structure, which means to suppress the boundary reflection generated during the propagation of guided waves. After application, the set freedom can be covered.

[0054] Furthermore, electrostatic physics includes three boundary conditions by default: charge conservation piezoelectricity, zero charge and initial value. Other boundary conditions that can be included are electric potential and grounding.

[0055] Among them, charge conservation piezoelectricity is assigned to all piezoelectric elements, representing a specific constitutive relationship in the piezoelectric domain.

[0056] Here, zero charge is assigned to the boundaries of all piezoelectric elements, indicating that all boundary charges of the piezoelectric elements are zero.

[0057] Among them, the initial value is set to 0, indicating that the initial potential of the model is 0.

[0058] The potential is set to the narrowband sinusoidal modulation excitation signal V defined in step S1. a , given to the upper surface of the excitation piezoelectric element, indicating the application of a piezoelectric excitation signal.

[0059] Among them, grounding is given to the lower surface of all piezoelectric elements, that is, the connection between the piezoelectric element and the main load-bearing-insulation tile structure, representing the zero potential reference point.

[0060] Step S4, introducing viscoelastic material damping.

[0061] More specifically, considering that among many damping models, the Rayleigh damping model is the most common and easy to implement, the Rayleigh damping model can be used to simulate the damping attenuation of viscoelastic materials. The Rayleigh damping model uses a linear combination of mass and stiffness matrices to describe viscous damping, which is defined as: C = αM + βK. Among them, C is the damping matrix; M is the mass matrix; K is the stiffness matrix; α and β are the mass proportional coefficient and stiffness proportional coefficient respectively.

[0062] Since it is usually impossible to find a perfect combination of mass proportionality coefficient α and stiffness proportionality coefficient β in practice to simultaneously describe A at the same frequency 0 and S 0The attenuation of the two modes can be studied by combining the experimental data and adjusting the specific values ​​of the mass proportional coefficient α and the stiffness proportional coefficient β of the high-temperature resistant silicone rubber and the strain isolation pad to study the attenuation characteristics of different mode guided waves in the main bearing-insulation tile structure.

[0063] Optionally, other damping models may be selected for implementation, but the present invention is not limited thereto.

[0064] Step S5, meshing the structure.

[0065] like Figure 2 As shown, the step S5 further includes the following steps.

[0066] Step S51, by Determine the mesh size.

[0067] Among them, L max is the maximum side length of the finite element; min is the minimum wavelength of the guided wave; n min It is the minimum number of intervals between nodes per wavelength.

[0068] Optionally, in order to balance the computational accuracy and computational speed and not exceed the hardware requirements of the computer, n min The value range can be 6 to 10.

[0069] Step S52, plane cutting is performed on the upper surface of the main load-bearing structure.

[0070] More specifically, since the piezoelectric element is circular, the upper surface of the main load-bearing structure is firstly plane-cut to achieve the division of high-quality quadrilateral meshes in the plane.

[0071] Step S53, dividing the upper surface of the segmented main load-bearing structure into quadrilateral two-dimensional grids, and then translating the quadrilateral two-dimensional grids to different positions of each layer of the main load-bearing structure.

[0072] Step S54, sweeping each layer of two-dimensional grids along the thickness direction of the structure to generate a three-dimensional grid of the geometric model of the entire main load-bearing-insulation tile and piezoelectric element.

[0073] Step S6, setting the time step for analysis and solution.

[0074] More specifically, for transient simulations such as piezoelectric guided waves, the time increment of the analysis step becomes unstable when it exceeds a certain limit, so the condition must be met Where Δt is the time step, L min is the minimum side length of the finite element, c pmax is the maximum phase velocity of the guided wave.

[0075] Optionally, the multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization of the present invention also includes step S7, post-processing.

[0076] More specifically, after the modeling analysis is completed, the results of the modeling analysis are stored in a table.

[0077] Optionally, the stress changes of the structure are represented by stress cloud diagrams and deformation diagrams for export analysis.

[0078] The present invention also provides a device, comprising: one or more processors; a memory for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors execute the above-mentioned multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization.

[0079] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the computer program implements the above-mentioned multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization.

[0080] Below Figure 3 The main load-bearing-insulation tile structure in the example is used to introduce the multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization of the present invention. Figure 4 for Figure 3 A partial enlarged view of the middle part IA.

[0081] like Figures 3 to 5 As shown, the size of the main load-bearing-insulating tile structure 1 used in this embodiment is 250mm×250mm×30.8mm, and the main load-bearing-insulating tile structure 1 includes an aluminum plate 11, a first high-temperature resistant silicone rubber layer 12, a strain isolation pad 13, a second high-temperature resistant silicone rubber layer 14 and an insulating tile 15, wherein the thickness of the aluminum plate 11 is 2mm, the thickness of the first high-temperature resistant silicone rubber layer 12 is 0.4mm, the thickness of the strain isolation pad 13 is 3mm, the thickness of the second high-temperature resistant silicone rubber layer 14 is 0.4mm, and the thickness of the insulating tile 15 is a 25mm ceramic tile.

[0082] Optionally, the thermal insulation tile 15 is a ceramic tile.

[0083] Eight piezoelectric elements are arranged on the upper surface of the aluminum plate 11, namely piezoelectric elements PZT1-PZT8. Voltage is applied to one of them to excite waveguides in the structure, and the surface voltages of the remaining piezoelectric elements are collected to sense the waveguides.

[0084] against Figure 3 The main bearing-insulation tile structure in the invention, the specific implementation of the multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization is as follows:

[0085] Establish the geometric model of the main bearing-insulation tile structure and piezoelectric element, such as Figure 3 As shown, a five-peak narrow-band sinusoidal modulation excitation signal is defined, the center frequency is 150kHz, and the excitation amplitude is 70V.

[0086] Define the density, Young's modulus, Poisson's ratio and other parameters of the main bearing-insulation tile structure, and the relative dielectric constant, piezoelectric constant, compliance coefficient and other parameters of the piezoelectric element.

[0087] Electrostatic physics is imparted to the piezoelectric element structure, and solid physics is imparted to the piezoelectric device and the main load-bearing-insulation tile structure. In this way, the piezoelectric element structure can have both electrostatic properties and solid mechanical properties, successfully achieving electromechanical coupling.

[0088] The viscoelastic damping characteristics of the high temperature resistant silicone rubber and the strain isolation pad are described by the Rayleigh damping model. In this specific embodiment, the mass proportional coefficient and stiffness proportional coefficient of the high temperature resistant silicone rubber are α=0, β=9×10 -7 , the mass proportional coefficient and stiffness proportional coefficient of the strain isolation pad are α=0, β=9×10 -6 , used to simulate the decay mode S 0 ; The mass proportional coefficient and stiffness proportional coefficient of high temperature resistant silicone rubber are α=0, β=3×10 -7 , the mass proportional coefficient and stiffness proportional coefficient of the strain isolation pad are α=0, β=9×10 -7 , used to simulate decay mode A 0 .

[0089] The structure is meshed. In order to ensure the accuracy of the waveguide simulation results and reduce the calculation cost and improve the calculation efficiency, in terms of mesh size, in this specific embodiment, the maximum mesh size is 1.3mm. In terms of meshing method, the model is first divided. The shape of the piezoelectric element is cut out on the upper surface of the main load-bearing structure. At the same time, a square area is cut out with the center of the circle as the center, and the area is divided. At the same time, other parts of the upper surface of the main load-bearing structure are divided; then a two-dimensional mesh is drawn, including the inside of the piezoelectric element, the transition area and other areas of the main load-bearing structure. The meshing result is as follows: Figure 6 As shown in the figure, it can be seen that the quadrilateral mesh has good quality and the nodes are continuous. At the same time, the two-dimensional mesh is translated to different positions of each layer of the structure, and finally the two-dimensional meshes of each layer are swept along the thickness direction of the structure to generate the three-dimensional mesh of the entire main load-bearing-insulation tile. The final generated mesh is as follows Figure 6 shown.

[0090] Set the relevant parameters of the piezoelectric guided wave transient solver. In this specific embodiment, the time step is 10 -7 .

[0091] The calculation results are exported and analyzed. The signal diagrams before and after the multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization of the present invention are respectively Figure 7 , Figure 8 The error and unit freedom of finite element modeling analysis are shown in Table 1. It can be seen that the multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization proposed in the present invention improves the simulation accuracy and reduces the calculation cost.

[0092] Table 1

[0093]

[0094] Although the present invention has been disclosed as above by way of embodiments, it is not intended to limit the present invention. Any person having ordinary knowledge in the technical field may make some changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be determined by the scope of the attached patent application.

Claims

1. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization, characterized in that: include, Step S1, establishing a geometric model of the main bearing-insulation tile structure and the piezoelectric element and defining parameters; Step S2, defining the material parameters of the main bearing-insulation tile structure and the piezoelectric element; Step S3, multi-physics field coupling setting; Step S4, introducing viscoelastic material damping; Step S5, meshing the structure; Step S6, setting the time step for analysis and solution.

2. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as claimed in claim 1, characterized in that: In the step S4, the Rayleigh damping model is selected and defined as: C=αM+βK, wherein C is the damping matrix; M is the mass matrix; K is the stiffness matrix; α and β are the mass proportional coefficient and the stiffness proportional coefficient respectively.

3. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as claimed in claim 2, characterized in that: The step S5 comprises: Step S51, by Determine the mesh size, where L max is the maximum side length of the finite element; min is the minimum wavelength of the guided wave; n min is the minimum number of intervals between nodes per wavelength; Step S52, plane cutting of the upper surface of the main load-bearing structure; Step S53, dividing the upper surface of the main load-bearing structure after segmentation into quadrilateral two-dimensional grids, and then translating the quadrilateral two-dimensional grids to different positions of each layer of the main load-bearing structure; Step S54, sweeping each layer of two-dimensional grids along the thickness direction of the structure to generate a three-dimensional grid of the geometric model of the entire main load-bearing-insulation tile and piezoelectric element.

4. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as claimed in claim 1, characterized in that: In step S6, the time step Δt satisfies: L min is the minimum side length of the finite element, c pmax is the maximum phase velocity of the guided wave.

5. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as claimed in claim 1, characterized in that: In step S1, defining parameters includes defining a narrow-band sinusoidal modulation excitation signal V a =A a ·[1-cos(2πf c t / N a )]·sin(2πf c t) is used to excite the waveguide, where A a is the amplitude of the excitation signal, f c is the center frequency of the excitation signal; N a is the number of excitation peaks.

6. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as claimed in claim 1, characterized in that: The step S3 includes imparting electrostatic physics to the piezoelectric element structure, and imparting solid physics to the piezoelectric element structure and the main bearing-insulation tile structure.

7. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as claimed in claim 6, characterized in that: The boundary conditions of solid physics include: linear elastic material, freedom, initial value, piezoelectric material, and low reflection boundary.

8. A multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as claimed in claim 6, characterized in that: The boundary conditions of electrostatic physics include: charge conservation, zero charge and initial value.

9. A device, characterized in that: The device includes: one or more processors; a memory for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors execute a multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements a multi-layer heterogeneous structure guided wave modeling and analysis method based on damping introduction and grid optimization as described in any one of claims 1 to 8.

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