Non-linear vibration analysis method, device and equipment for full-composite sandwich plate

Abstract

The invention discloses a nonlinear vibration analysis method, a nonlinear vibration analysis device and nonlinear vibration analysis equipment for a full-composite sandwich plate, and relates to the technical field of mechanical measurement. A nonlinear theoretical model is provided based on a high-order shear deformation theory, a Gibson equivalent theory and a VonKarman large deformation theory; and deducing a vibration equation by using an orthogonal polynomial method and an energy method and solving an energy function to obtain a vibration frequency, introducing a geometric nonlinear correction factor during simulation solving so as to simulate the nonlinear vibration characteristics of the full-composite sandwich plate, continuously representing the complex uncertain deformation in the full-composite sandwich plate, and solving the nonlinear vibration characteristics of the full-composite sandwich plate. Therefore, the accuracy of the predicted nonlinear vibration characteristics is greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical measurement, and in particular to a nonlinear vibration analysis method, device and equipment for a full-composite sandwich plate. Background Art

[0002] As a relatively new material, all-composite sandwich panel ACHCSP has excellent weight reduction, heat insulation, sound insulation and other properties, so it is widely used in construction, aviation, aerospace, military and other fields. Since there are a large number of honeycomb composite sandwich panel structures in actual engineering and they are often subjected to cyclic loads, they may cause fractures and fatigue failures due to vibration during operation. Therefore, it is particularly important to establish a theoretical model of the vibration response of all-composite sandwich panel ACHCSP to predict its vibration response.

[0003] In view of the numerous structural phenomena of the all-composite sandwich panel ACHCSP, some researchers have used homogenization method, finite element method and modal analysis technology to study its vibration characteristics; some researchers have studied the influence of the thickness ratio of honeycomb core and plate and the aspect ratio on the natural frequency; some researchers have used low-order and high-order shear deformation models to study the influence of honeycomb core (transverse shear deformation) on the bending vibration of isotropic face plate thick rectangular sandwich panel; some researchers have used the constitutive model of orthogonal isotropic composite honeycomb sandwich core to solve the vibration characteristics of layered composite honeycomb sandwich core sandwich panel.

[0004] Aiming at the amplitude dependence and strain dependence of the all-composite sandwich panel ACHCSP; some researchers used the homology analysis method, Hamilton's principle and Reddy's principle and introduced the von Karman term to study the geometric nonlinear free vibration problem of symmetrical rectangular honeycomb sandwich panels with four simply supported boundaries and four clamped boundaries; some researchers solved the nonlinear vibration characteristics of honeycomb core-nanocomposite skin sandwich panels based on classical plate theory, von Karman theory and Gibson equivalent theory; some researchers established a high-order finite element model based on Shi's plate theory that only considers geometric nonlinearity but not material nonlinearity to solve the nonlinear static analysis of bidirectional functional gradient sandwich panels under thermal environment.

[0005] At present, in view of the numerous structural phenomena of the all-composite sandwich panel ACHCSP, as well as the amplitude dependence and strain dependence of the all-composite sandwich panel ACHCSP, a targeted nonlinear vibration analysis method is adopted for the all-composite sandwich panel ACHCSP. The research mainly focuses on the linear vibration of honeycomb sandwich panels and the use of first-order shear deformation theory.

[0006] However, the internal structure of the fully composite sandwich panel ACHCSP is relatively complex, and the uncertain deformation during vibration is difficult to predict. Therefore, the method of predicting its nonlinear vibration has low accuracy and reference value. Summary of the invention

[0007] The embodiments of the present invention provide a nonlinear vibration analysis method, device and equipment for a fully composite sandwich panel, which can solve the problem of low accuracy of the current method for predicting its nonlinear vibration in the prior art.

[0008] An embodiment of the present invention provides a nonlinear vibration analysis method for a fully composite sandwich plate, comprising the following steps:

[0009] Vibration test was carried out on the full composite sandwich panel, and based on the high-order shear deformation theory and Von Karman large deformation theory, the nonlinear theoretical model of the full composite sandwich panel was constructed, and the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich panel were obtained;

[0010] Based on the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich plate, the discrete elastic modulus and shear modulus representing the stress and strain in the full composite sandwich plate during the displacement process are extracted, and the discrete elastic modulus and shear modulus are simulated as nonlinear complex elastic modulus and nonlinear complex shear modulus in exponential form.

[0011] According to the nonlinear complex elastic modulus and nonlinear complex shear modulus of the full composite sandwich plate, the Rayleigh-Leeds method is used to obtain the energy of the full composite sandwich plate in the stress-strain process, and the maximum strain energy and maximum kinetic energy of the full composite sandwich plate are obtained.

[0012] According to the maximum strain energy and maximum kinetic energy of the full-composite sandwich plate, the surface displacement of the full-composite sandwich plate under the action of strain energy and kinetic energy is simulated, and the vibration frequency of the full-composite sandwich plate is obtained.

[0013] Preferably, the displacement field is obtained by:

[0014]

[0015] w(x,y,z,t)=w0(x,y,t)

[0016] Among them: u, v, w represent the displacement in the x, y, and z directions respectively; u0, v0, w0 represent the displacement in the x, y, and z directions on the clock face respectively.

[0017] Preferably, the displacement-strain relationship and the stress-strain relationship are obtained as follows:

[0018] The displacement-strain relationship of the fully composite sandwich panel is:

[0019]

[0020] Among them: ε1, ε2, ε3, γ4, γ5, γ6 represent the strains in the x, y, and z directions respectively;

[0021] The stress-strain relationship of the fully composite sandwich panel is:

[0022]

[0023] Among them: ε1, ε2, ε3, ε4, ε5, ε6 represent the linear strain and shear strain in the x, y, z directions respectively; represent the strain components respectively.

[0024] Preferably, the acquisition of the nonlinear complex elastic modulus and the nonlinear complex shear modulus of the fiberboard in the full composite sandwich panel includes:

[0025] According to Jones-Nelson nonlinear theory and complex modulus theory, the strain of the fiberboard in the fully composite sandwich panel under uniaxial stress state is simulated to obtain the elastic modulus and shear modulus of the fiberboard representing elastic deformation;

[0026] The elastic modulus and shear modulus of the fiberboard in the full composite sandwich panel are discrete, and under the elastic modulus and shear modulus in this direction, the energy in this direction in the fiberboard is discrete. Then, the discrete elastic modulus and shear modulus are converted into exponential forms, and the nonlinear complex elastic modulus and nonlinear complex shear modulus are:

[0027]

[0028] Where: E nfi represents the nonlinear complex elastic modulus; G nf12 represents the nonlinear complex shear modulus; η1 represents the nonlinear loss factor of the material; A fi , B fi , C fi , D fi Indicates the material nonlinear fitting parameters; U △max represents the maximum strain energy density.

[0029] Preferably, the acquisition of the nonlinear complex elastic modulus and the nonlinear complex shear modulus of the honeycomb layer in the full composite sandwich panel includes:

[0030] According to the Gbsion honeycomb equivalent theory and nonlinear material fitting coefficient, the strain of the honeycomb layer in the full composite sandwich panel under uniaxial stress state is simulated to obtain the elastic modulus and shear modulus of the honeycomb layer representing elastic deformation;

[0031] The elastic modulus and shear modulus of the honeycomb layer in the fully composite sandwich panel are discrete, and under the elastic modulus and shear modulus in this direction, the energy in this direction in the honeycomb layer is discrete. Then, the discrete elastic modulus and shear modulus are converted into exponential forms, and the nonlinear complex elastic modulus and nonlinear complex shear modulus are:

[0032]

[0033]

[0034] Where: E nvi represents the nonlinear complex elastic modulus of the honeycomb layer; E c Represents the original elastic modulus of the honeycomb layer; G nv12 A represents the nonlinear complex shear modulus of the honeycomb layer; vi and B vi Respectively represent the material nonlinear fitting parameters; t c Represents the honeycomb unit wall thickness; l c Represents the length of the honeycomb cell wall.

[0035] Preferably, obtaining the maximum strain energy and maximum kinetic energy of the full composite sandwich plate comprises:

[0036] According to the nonlinear complex elastic modulus and nonlinear complex shear modulus of the fiberboard and honeycomb layer, the strain energy and kinetic energy of the fiberboard and honeycomb layer are obtained based on the Rayleigh-Leeds method:

[0037]

[0038] Among them: U F and T F Respectively represent the strain energy and kinetic energy of the fiber layer; U V and T V represent the strain energy and kinetic energy of the honeycomb layer respectively; ρ F represents the fiber layer density; ρ V represents the honeycomb layer density; h f and h v represent the thickness of the fiber layer and honeycomb layer respectively;

[0039] The strain energy of the fiber layer and the strain energy of the honeycomb layer are superimposed to obtain the maximum strain energy of the full composite sandwich panel; the kinetic energy of the fiber layer and the kinetic energy of the honeycomb layer are superimposed to obtain the maximum kinetic energy of the full composite sandwich panel.

[0040] Preferably, obtaining the vibration frequency of the full composite sandwich panel includes:

[0041] According to the maximum strain energy, maximum kinetic energy and foundation excitation work of the full composite sandwich plate, the Lagrangian energy function is obtained;

[0042] According to the Lagrangian energy function and based on the orthogonal polynomial method, the surface displacement of the fully composite sandwich plate is simulated as follows:

[0043]

[0044]

[0045] Among them: A pq , B pq , C pq , D pq 、E pq represents the unknown parameter; ω represents the natural frequency of the plate; P p (ξ) and P q (η) represents the orthogonal characteristic polynomial;

[0046] Obtain the matrix function (K n +iC-ω 2 M)q=F, and the derivative of the unknown parameters in the matrix function is taken to obtain the vibration frequency of the full composite sandwich plate;

[0047] Where: K n represents the nonlinear stiffness matrix of the composite plate; C represents the nonlinear damping matrix of the composite plate; M represents the mass matrix of the composite plate.

[0048] The embodiment of the present invention further provides a nonlinear vibration analysis device for a fully composite sandwich plate, comprising:

[0049] Theoretical simulation module is used to conduct vibration test on the full composite sandwich panel, and to construct the nonlinear theoretical model of the full composite sandwich panel based on the high-order shear deformation theory and Von Karman large deformation theory, and to obtain the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich panel;

[0050] Based on the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich plate, the discrete elastic modulus and shear modulus representing the stress and strain in the full composite sandwich plate during the displacement process are extracted, and the discrete elastic modulus and shear modulus are simulated as nonlinear complex elastic modulus and nonlinear complex shear modulus in exponential form.

[0051] An energy module is used to obtain the energy of the full composite sandwich plate in the stress-strain process according to the nonlinear complex elastic modulus and nonlinear complex shear modulus of the full composite sandwich plate by using the Rayleigh-Leeds method, and to obtain the maximum strain energy and maximum kinetic energy of the full composite sandwich plate;

[0052] The vibration module is used to simulate the surface displacement of the full composite sandwich plate under the action of strain energy and kinetic energy according to the maximum strain energy and maximum kinetic energy of the full composite sandwich plate, and obtain the vibration frequency of the full composite sandwich plate.

[0053] An embodiment of the present invention further provides an electronic device, including a memory and a processor;

[0054] The memory is used to store computer programs;

[0055] The processor is used to implement the steps of the above-mentioned method for nonlinear vibration analysis of a fully composite sandwich panel when executing the computer program stored in the memory.

[0056] The embodiment of the present invention provides a nonlinear vibration analysis method, device and equipment for a fully composite sandwich plate. Compared with the prior art, the beneficial effects thereof are as follows:

[0057] The invention constructs a theoretical model of a full-composite sandwich plate based on a high-order shear deformation theory, and introduces the Von Karman large deformation theory to simulate the displacement field, displacement-strain relationship and stress-strain relationship of the full-composite sandwich plate. Meanwhile, according to the Jones-Nelson nonlinear theory and the Gibson honeycomb equivalent theory, the displacement field and stress-strain of the full-composite sandwich plate in the displacement deformation process are decomposed into discrete stress-strain in a unidirectional state, and the stress-strain in the unidirectional state is fitted into a continuous nonlinear complex elastic modulus and a nonlinear complex shear modulus, and then the vibration frequency of the full-composite sandwich plate is obtained based on an orthogonal polynomial and an energy function. In this process, while constructing a high-order nonlinear theoretical model based on the high-order shear deformation theory, the Gibson equivalent theory and the Von Karman large deformation theory, the invention introduces a geometric nonlinear correction factor representing the deformation state of the model, that is, each discrete stress-strain and energy distribution is fitted into a continuously changing form, and the nonlinear vibration characteristics of the full-composite sandwich plate are obtained thereby, and the complex uncertain deformation in the full-composite sandwich plate is continuously represented, so that the accuracy of the predicted nonlinear vibration characteristics is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic diagram of the overall process of a nonlinear vibration analysis method for a fully composite sandwich plate provided by an embodiment of the present invention;

[0059] Figure 2 A schematic diagram of an ACHCSP theoretical model of a nonlinear vibration analysis method for a fully composite sandwich plate provided in an embodiment of the present invention;

[0060] Figure 3 A schematic diagram of the preparation process of an ACHCSP test piece for a nonlinear vibration analysis method of a fully composite sandwich panel provided in an embodiment of the present invention;

[0061] Figure 4A schematic diagram of ACHCSP vibration response and frequency shift curve under 11.5 Hz excitation amplitude for a nonlinear vibration analysis method of a full composite sandwich panel provided in an embodiment of the present invention;

[0062] Figure 5 A schematic diagram of ACHCSP vibration response and frequency shift curve under 22 Hz excitation amplitude for a nonlinear vibration analysis method of a full composite sandwich panel provided in an embodiment of the present invention;

[0063] Figure 6 A schematic diagram of ACHCSP vibration response and frequency shift curve under 30.4 Hz excitation amplitude for a nonlinear vibration analysis method of a full composite sandwich panel provided in an embodiment of the present invention;

[0064] Figure 7 A schematic diagram of the first three-order nonlinear natural frequencies under different excitation amplitudes of a nonlinear vibration analysis method of a full-composite sandwich plate provided by an embodiment of the present invention;

[0065] Figure 8 A schematic diagram of ACHCSP-related material parameter fitting curves under different excitation amplitudes for a nonlinear vibration analysis method of a full-composite sandwich plate provided in an embodiment of the present invention;

[0066] Fig. 9 A schematic diagram showing a comparison between a first-order ACHCSP experimental result and a theoretical calculation result of a nonlinear vibration analysis method for a fully composite sandwich plate provided by an embodiment of the present invention;

[0067] Fig.10 A schematic diagram showing the comparison between the first-order ACHCSP experimental and theoretical calculation response results of a nonlinear vibration analysis method for a fully composite sandwich plate provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific embodiments disclosed below.

[0069] See also Figure 1An embodiment of the present invention provides a nonlinear vibration analysis method for an all-composite sandwich panel. The present invention specifically analyzes the nonlinear vibration of an all-composite honeycomb core sandwich panel (ACHCSP) under different excitation amplitudes. Firstly, a nonlinear theoretical model is proposed based on the high-order shear deformation theory, the Gibson equivalent theory and the Von Karman large deformation theory, and the orthogonal polynomial method and the energy method are used to derive the vibration equation and solve the energy function to obtain the vibration frequency. Meanwhile, in order to ensure the accuracy of the model, the nonlinear related parameters are fitted. Secondly, an ACHCSP test specimen is prepared and frequency sweeping and resonance excitation experiments are performed on it to verify the accuracy of the theoretical model.

[0070] like Figure 2 As shown in the figure, the ACHCSP theoretical model is modeled; first, the xoy coordinate system is established with the middle surface as the reference plane, the plate length is a, the plate width is b, the plate thickness is h, and the fiberboard thickness is h f , the thickness of the honeycomb layer is h c ; The red line 1 represents the fiber direction, 2 represents the perpendicular fiber direction, 3 represents the direction perpendicular to the 1-2 plane, and θ represents the angle between the fiber direction and the x direction; For the honeycomb unit related parameters, l c represents the length of the hexagonal honeycomb cell wall, t c represents the wall thickness of the hexagonal honeycomb unit, α c Indicates the angle of the honeycomb layer unit.

[0071] Based on the high-order shear deformation theory and considering the influence of torsion, the displacement field of the all-composite honeycomb core sandwich panel can be expressed as:

[0072]

[0073] w(x,y,z,t)=w0(x,y,t)

[0074] Among them: u, v, w represent the displacement in the x, y, and z directions respectively; u0, v0, w0 represent the displacement in the x, y, and z directions on the clock face respectively.

[0075] Since the fully composite hexagonal honeycomb core sandwich panel has geometric nonlinearity during large displacement, Von Karman's large deformation theory is introduced, and its strain-displacement relationship is as follows:

[0076]

[0077] Among them: ε1, ε2, ε3, γ4, γ5, γ6 represent the strains in the x, y, and z directions respectively.

[0078] The stress-strain relationship is as follows:

[0079]

[0080] in:

[0081] Based on the Jones-Nelson nonlinear theory and complex modulus theory, the elastic modulus and shear modulus of the upper and lower fiberboards of ACHCSP can be expressed as:

[0082]

[0083] Where: E nfi represents the nonlinear complex elastic modulus; G nf12 represents the nonlinear complex shear modulus; η1 represents the nonlinear loss factor of the material; A fi , B fi , C fi , D fi Represents the material nonlinear fitting parameters.

[0084] Based on the Gbsion honeycomb equivalent theory, the nonlinear material fitting coefficient can be introduced to express the material parameters of the middle honeycomb layer as follows:

[0085]

[0086] Where: E nvi represents the nonlinear complex elastic modulus of the honeycomb layer; E c Represents the original elastic modulus of the honeycomb layer; G nv12 A represents the nonlinear complex shear modulus of the honeycomb layer; vi and B vi Respectively represent the material nonlinear fitting parameters; t c Represents the honeycomb unit wall thickness; l c Represents the length of the honeycomb cell wall.

[0087] Maximum strain energy density U △max for:

[0088]

[0089] Among them: U △ represents strain energy density; U0 represents the strain energy density; △ A dimensionless constant.

[0090] The ACHCSP stress-strain relationship is:

[0091]

[0092] Where: i Represents the stress in all directions; ε i They correspond to strains in different directions.

[0093] The stiffness coefficient of the upper and lower fiberboards is:

[0094]

[0095] The stiffness coefficient of the honeycomb layer is:

[0096]

[0097] Q 44 =G nv23 ,Q 66 =G nv12 ,Q 55 =G nv13

[0098] Since there is a certain angle between the fiber cortex and the x-axis in the ACHCSP fiberboard, its eccentric stiffness matrix is:

[0099]

[0100] in: represents the eccentric stiffness coefficient; specifically:

[0101]

[0102]

[0103] Based on the Rayleigh-Leeds method, the kinetic energy of the fiber layer and the honeycomb layer in ACHCSP can be expressed as:

[0104]

[0105] Among them: U F and T F Respectively represent the strain energy and kinetic energy of the fiber layer; U V and T V represent the strain energy and kinetic energy of the honeycomb layer respectively; ρ F represents the fiber layer density; ρ V represents the honeycomb layer density; h f and h v Represent the thickness of the fiber layer and the honeycomb layer respectively.

[0106] From this, the maximum strain energy and maximum kinetic energy of ACHCSP can be obtained as:

[0107] U max =U F +U V

[0108] T max =T F +T V

[0109] Apply basic excitation to ACHCSP, the excitation amplitude is:

[0110] p(t)=ρhω 2 Ye iωt

[0111] Where: Y represents the excitation amplitude; ω represents the excitation frequency.

[0112] The basic excitation applied can be equivalent to the work done by the uniformly distributed inertial force, and the uniformly distributed inertial force is:

[0113] p(t)=ρhω 2 Ye iωt

[0114] Therefore, the maximum value of the work done by the uniformly distributed inertial force is:

[0115] W max =ρhω 2 Y∫∫ A WlqA

[0116] According to the maximum strain energy, maximum kinetic energy and basic excitation work, the Lagrangian energy function is obtained as follows:

[0117] L=T max +W max -U max

[0118] Based on the orthogonal polynomial method, it can be assumed that the ACHCSP mid-surface displacement is:

[0119] w0(x,y,t)=e iωt W(ξ,η)

[0120] The ACHCSP mid-surface displacement is expressed by the undetermined parameters as:

[0121]

[0122] Among them: A pq , B pq , C pq , D pq 、E pq represents the unknown parameter; ω represents the natural frequency of the plate; P p (ξ) and P q (η) represents the orthogonal characteristic polynomial; specifically:

[0123]

[0124] P2(ζ)=(ζ-B2)P1(ζ),ζ=ξ,η,k>2

[0125] P k (ζ)=(ζ-Bk ) k-1 (ζ)-C k P k-2 (ζ)

[0126] Among them: B k and P k represents the coefficient parameter; and Represents the characteristic polynomial of orthogonality; specifically:

[0127]

[0128] ζ=ξ,η, ξ=x / a, η=y / b

[0129] Where: W(ξ) represents the weight function coefficient.

[0130] Derivative the unknown coefficients of the above formula and solve its eigenvalues ​​to obtain:

[0131] (K n +iC-ω 2 M)q=F

[0132] Where: K n represents the nonlinear stiffness matrix of the composite plate; C represents the nonlinear damping matrix of the composite plate; M represents the mass matrix of the composite plate.

[0133] According to the above formula, the nonlinear natural frequency of ACHCSP under the basic excitation amplitude can be obtained.

[0134] The specific implementation experiment is:

[0135] 1. ACHCSP test specimens.

[0136] ACHCSP is mainly composed of upper and lower TC300 carbon fiber plates and a middle hexagonal honeycomb layer. The laying angle of the carbon fiber plates is [0° / 90°], and the middle honeycomb layer is mainly cast by resin-based carbon nanotube solution.

[0137] like Figure 3 As shown in the figure, the specific production process of the ACHCSP test piece is as follows: the carbon fiber plate is made of 21 layers of orthotropic carbon fiber layers glued together by epoxy resin; the specific production process of the intermediate honeycomb layer is as follows: first, IN2 flow-conducting resin of the volume of the honeycomb layer and 10% of TX-10 emulsifier by mass are mixed evenly in a beaker, and the beaker is placed in a 40°C water bath heating pot and stirred at a speed of 400 rad / min for 30 minutes until the bubbles in the mixed solution are completely stirred out.

[0138] Use an electronic balance to take 0.5% by mass of carbon nanotubes and CR17 glass fibers and add them to the solution, and continue stirring for 30 minutes to fully mix the resin with the carbon nanotubes and glass fibers. Take 30% by mass of AT30 slow curing agent and add it to the mixed solution and continue stirring for 5 minutes.

[0139] The stirred resin-based carbon nanotube solution was placed in a preheated vacuum drying oven for degassing. The vacuum degree was 10 -4 Pa, the drying oven temperature is 80°C; finally, the resin-based carbon nanotube solution after defoaming treatment is added into the prepared silicone mold and left to stand for 15-24 hours for demoulding.

[0140] After the fiberboard and the hexagonal honeycomb layer are made, they are bonded with epoxy film. Before bonding, ensure that there is no condensed water on the surface and cut and bond according to the size of the honeycomb layer; after bonding, place it in a hot box at 150°C for 30 minutes to get ACHCSP. The materials and geometric parameters of the prepared ACHCSP fiberboard and the middle hexagonal honeycomb layer are shown in Table 1.

[0141] Table 1 Geometric parameters and material parameters of ACHCSP fiberboard and honeycomb layer

[0142]

[0143] 2. Experimental testing and experimental process.

[0144] In the construction of the experimental test system, it is mainly composed of a vibration console, LMS SCADAS data acquisition instrument, LMSTest.lab mobile workstation, fixture, vibration table, and PCB 353B15 acceleration sensor.

[0145] In the vibration test, the upper and lower fiberboards and the middle honeycomb layer of ACHCSP were struck with a PCB 086C01 modal hammer to obtain their approximate natural frequency range, and the frequency range containing their natural frequencies was taken to perform nonlinear vibration sweep tests with different excitation amplitudes to determine their nonlinear vibration responses under different excitation amplitudes; the experimental parameters were set as follows: the test bandwidth was set to 0-3000Hz, the resolution was set to 0.5Hz, and the added window function was set to Hanning window.

[0146] After determining the experimental procedure or test setup, the tested ACHCSP board is fixed in the cantilever structure with a clamping length of 20 mm. During the vibration test, the ACHCSP test piece is fixed on the vibration table by a fixture, and the PCB acceleration sensor is attached to the ACHCSP 1 / 3 away from the fixed end by 3M adhesive. At the same time, the PCB sensor needs to avoid the node line position. After multiple experiments, the nonlinear vibration response and natural frequency shift degree of ACHCSP under different excitation amplitudes are determined. Finally, the geometric nonlinear fitting parameters of ACHCSP are determined by combining the theoretical and experimental results.

[0147] 3. Experimental results.

[0148] 1. Specific experimental results.

[0149] The above experimental results are analyzed to verify whether ACHCSP has geometric nonlinearity under different excitation amplitudes; Figure 4 , Figure 5 and Figure 6 The resonance response curves and frequency deflection of ACHCSP under different excitation amplitudes are given. Figure 4 At 11.5Hz, Figure 5 At 22Hz, Figure 6 is at 30.4Hz; Figure 7 The figure shows the changes of the first three-order nonlinear natural frequencies of ACHCSP under different excitation amplitudes.

[0150] Since the high-order vibration displacement of ACHCSP is not obvious, the first three-order vibration of ACHCSP is taken as an example to study its geometric nonlinear phenomenon; Figure 4 , Figure 5 and Figure 6 It can be seen that ACHCSP has geometric nonlinearity, and the frequency offset amplitude of ACHCSP under different excitation amplitudes gradually decreases; taking the first-order natural frequency as an example, the natural frequency decreases by 13.4Hz, 7.9Hz, 5.9Hz, and 3.8Hz when the excitation amplitude increases from 2g to 10g, and it can be seen that the frequency decrease value is getting smaller and smaller; at the same time, it can be found that with the continuous increase of the excitation amplitude, its natural frequency has a tendency to rotate. This is because when the excitation amplitude continues to increase, the amplitude of ACHCSP becomes larger and larger, and the composite material will have geometric nonlinearity at this time; the reason is that the geometric nonlinearity of the composite material will cause stiffness hardening at a large amplitude, which is opposite to the stiffness softening caused by the material nonlinearity, so the resonant frequency decrease value will become smaller and smaller. When the excitation amplitude increases to a certain value, the stiffness hardening caused by geometric nonlinearity will dominate and increase its resonant frequency.

[0151] In this experiment, the main reason why the resonance frequency of ACHCSP did not show a reverse increase under a large excitation amplitude is that the stiffness of ACHCSP is relatively large. Secondly, due to the limitation of the experimental equipment, the experiment can only increase the excitation amplitude to 10g. In order to verify whether the theoretical model can accurately predict the nonlinear vibration phenomenon of ACHCSP, the theoretical results are combined with the experimental results to fit the nonlinear parameters of ACHCSP.

[0152] 2. Fitting parameters.

[0153] From the experimental results above, it can be seen that ACHCSP has geometric nonlinearity as the excitation amplitude increases. Therefore, the nonlinearity-related fitting parameters of ACHCSP are determined based on the experimental data. The fitting parameters are determined by importing the maximum strain energy density of ACHCSP under different excitation amplitudes and the identified material parameters into the environmental curve fitting tool of MATLAB software, and fitting the geometric nonlinear fitting parameters of ACHCSP through this tool. Figure 8 As shown, the results of fitting the relevant material parameters of ACHCSP under different excitation amplitudes are shown; as shown in Tables 2 and 3, the nonlinear material parameters of the ACHCSP fiber layer and the honeycomb layer under different excitation amplitudes and the maximum strain energy density of ACHCSP under different excitation amplitudes are shown.

[0154] Table 2 Nonlinear material parameters under different excitation amplitudes

[0155]

[0156]

[0157] Table 3 Maximum strain energy density under different excitation amplitudes

[0158] Excitationrange / g 2 4 6 8 10 <![CDATA[MaximumstrainenergydensityU △ ]]> 27.44 109.78 247.01 439.13 686.15

[0159] The specific values ​​of the ACHCSP nonlinear fitting parameters can be obtained from the above table and the material fitting parameter picture; as shown in Tables 4 and 5, they are the nonlinear fitting coefficients of the ACHCSP fiberboard and the honeycomb layer.

[0160] Table 4 Nonlinear fitting coefficients of ACHCSP fiberboard

[0161]

[0162] Table 5 Nonlinear fitting coefficients of ACHCSP honeycomb layer

[0163]

[0164] The determination of the above fitting parameters can enable the model to more accurately predict the nonlinear vibration characteristics of ACHCSP under different excitation amplitudes.

[0165] 4. Comparison between theory and experiment.

[0166] The experimental results are compared with the theoretical calculation results, as shown in Table 6. Fig. 9 , Table 7 and Fig.10 , which are comparison diagrams of experimental results with theoretical calculation results considering both material nonlinearity and geometric nonlinearity, and comparison diagrams of theoretical calculation results considering only material nonlinearity.

[0167] Table 6 Comparison of experimental and theoretical calculation results of 1st-order ACHCSP

[0168]

[0169]

[0170] Table 7 Comparison of experimental and theoretical calculation response results of 1st-order ACHCSP

[0171]

[0172] Through Table 6 and Fig. 9 It can be seen that when only the material amplitude dependence is considered, the maximum error between the experimental results and the theoretical calculation results is 3.94%, which is still not accurate enough; when the geometric nonlinear material fitting parameters are added, the maximum error between the calculation results and the experimental test results is only 1.75%. Compared with the calculation results that only consider the material nonlinearity, the error is reduced by 2.19%; when only the influence of material nonlinearity is considered, the vibration response is slightly larger, with a maximum error of 9.16% and a minimum error of 3.30%. After adding the influence of geometric nonlinearity, the maximum error is reduced from 9.16% to 5.64%, and the minimum error is reduced to 1.68%. This shows that the model designed by the present invention can accurately predict the nonlinear vibration of ACHCSP, and the addition of the geometric nonlinear consideration can make the theoretical model calculate the structure more accurately.

[0173] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A nonlinear vibration analysis method for a fully composite sandwich panel, characterized in that: The following steps are involved: Vibration test was carried out on the full composite sandwich panel, and based on the high-order shear deformation theory and Von Karman large deformation theory, the nonlinear theoretical model of the full composite sandwich panel was constructed, and the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich panel were obtained; Based on the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich plate, the discrete elastic modulus and shear modulus representing the stress and strain in the full composite sandwich plate during the displacement process are extracted, and the discrete elastic modulus and shear modulus are simulated as nonlinear complex elastic modulus and nonlinear complex shear modulus in exponential form. According to the nonlinear complex elastic modulus and nonlinear complex shear modulus of the full composite sandwich plate, the Rayleigh-Leeds method is used to obtain the energy of the full composite sandwich plate in the stress-strain process, and the maximum strain energy and maximum kinetic energy of the full composite sandwich plate are obtained. According to the maximum strain energy and maximum kinetic energy of the full-composite sandwich plate, the surface displacement of the full-composite sandwich plate under the action of strain energy and kinetic energy is simulated, and the vibration frequency of the full-composite sandwich plate is obtained.

2. The nonlinear vibration analysis method of a fully composite sandwich panel according to claim 1, characterized in that: The displacement field is obtained as follows: w(x,y,z,t)=w0(x,y,t) Among them: u, v, w represent the displacement in the x, y, and z directions respectively; u0, v0, w0 represent the displacement in the x, y, and z directions on the clock face respectively.

3. The nonlinear vibration analysis method of a fully composite sandwich panel according to claim 1, characterized in that: The displacement-strain relationship and the stress-strain relationship are obtained as follows: The displacement-strain relationship of the fully composite sandwich panel is: Among them: ε1, ε2, ε3, γ4, γ5, γ6 represent the strains in the x, y, and z directions respectively; The stress-strain relationship of the fully composite sandwich panel is: Among them: ε1, ε2, ε3, ε4, ε5, ε6 represent the linear strain and shear strain in the x, y, z directions respectively; ε i 0 , ε i 1 , represent the strain components respectively.

4. The nonlinear vibration analysis method of a fully composite sandwich panel according to claim 1, characterized in that: The acquisition of the nonlinear complex elastic modulus and the nonlinear complex shear modulus of the fiberboard in the full composite sandwich panel includes: According to Jones-Nelson nonlinear theory and complex modulus theory, the strain of the fiberboard in the fully composite sandwich panel under uniaxial stress state is simulated to obtain the elastic modulus and shear modulus of the fiberboard representing elastic deformation; The elastic modulus and shear modulus of the fiberboard in the full composite sandwich panel are discrete, and under the elastic modulus and shear modulus in this direction, the energy in this direction in the fiberboard is discrete. Then, the discrete elastic modulus and shear modulus are converted into exponential forms, and the nonlinear complex elastic modulus and nonlinear complex shear modulus are: Where: E nfi represents the nonlinear complex elastic modulus; G nf12 represents the nonlinear complex shear modulus; η1 represents the nonlinear loss factor of the material; A fi , B fi , C fi , D fi Indicates the material nonlinear fitting parameters; U △max represents the maximum strain energy density.

5. The nonlinear vibration analysis method of a fully composite sandwich panel according to claim 1, characterized in that: The acquisition of the nonlinear complex elastic modulus and the nonlinear complex shear modulus of the honeycomb layer in the full composite sandwich panel includes: According to the Gbsion honeycomb equivalent theory and nonlinear material fitting coefficient, the strain of the honeycomb layer in the full composite sandwich panel under uniaxial stress state is simulated to obtain the elastic modulus and shear modulus of the honeycomb layer representing elastic deformation; The elastic modulus and shear modulus of the honeycomb layer in the fully composite sandwich panel are discrete, and under the elastic modulus and shear modulus in this direction, the energy in this direction in the honeycomb layer is discrete. Then, the discrete elastic modulus and shear modulus are converted into exponential forms, and the nonlinear complex elastic modulus and nonlinear complex shear modulus are: Where: E nvi represents the nonlinear complex elastic modulus of the honeycomb layer; E c Represents the original elastic modulus of the honeycomb layer; G nv12 A represents the nonlinear complex shear modulus of the honeycomb layer; vi and B vi Respectively represent the material nonlinear fitting parameters; t c Represents the honeycomb unit wall thickness; l c Represents the length of the honeycomb cell wall.

6. The nonlinear vibration analysis method of a fully composite sandwich panel according to claim 1, characterized in that: The method of obtaining the maximum strain energy and the maximum kinetic energy of the fully composite sandwich plate comprises: According to the nonlinear complex elastic modulus and nonlinear complex shear modulus of the fiberboard and honeycomb layer, the strain energy and kinetic energy of the fiberboard and honeycomb layer are obtained based on the Rayleigh-Leeds method: Among them: U F and T F Respectively represent the strain energy and kinetic energy of the fiber layer; U V and T V represent the strain energy and kinetic energy of the honeycomb layer respectively; ρ F represents the fiber layer density; ρ V represents the honeycomb layer density; h f and h v represent the thickness of the fiber layer and honeycomb layer respectively; The strain energy of the fiber layer and the strain energy of the honeycomb layer are superimposed to obtain the maximum strain energy of the full composite sandwich panel; the kinetic energy of the fiber layer and the kinetic energy of the honeycomb layer are superimposed to obtain the maximum kinetic energy of the full composite sandwich panel.

7. The nonlinear vibration analysis method of a fully composite sandwich panel according to claim 1, characterized in that: The step of obtaining the vibration frequency of the full composite sandwich panel comprises: According to the maximum strain energy, maximum kinetic energy and foundation excitation work of the full composite sandwich plate, the Lagrangian energy function is obtained; According to the Lagrangian energy function and based on the orthogonal polynomial method, the surface displacement of the fully composite sandwich plate is simulated as follows: Among them: A pq , B pq , C pq , D pq 、E pq represents the unknown parameter; ω represents the natural frequency of the plate; P p (ξ) and P q (η) represents the orthogonal characteristic polynomial; Obtain the matrix function (K n +iC-ω 2 M)q=F, and the derivative of the unknown parameters in the matrix function is taken to obtain the vibration frequency of the full composite sandwich plate; Where: K n represents the nonlinear stiffness matrix of the composite plate; C represents the nonlinear damping matrix of the composite plate; M represents the mass matrix of the composite plate.

8. A nonlinear vibration analysis device for a fully composite sandwich panel, characterized in that: include: Theoretical simulation module is used to conduct vibration test on the full composite sandwich panel, and to construct the nonlinear theoretical model of the full composite sandwich panel based on the high-order shear deformation theory and Von Karman large deformation theory, and to obtain the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich panel; Based on the displacement field, displacement-strain relationship and stress-strain relationship of the full composite sandwich plate, the discrete elastic modulus and shear modulus representing the stress and strain in the full composite sandwich plate during the displacement process are extracted, and the discrete elastic modulus and shear modulus are simulated as nonlinear complex elastic modulus and nonlinear complex shear modulus in exponential form. An energy module is used to obtain the energy of the full composite sandwich plate in the stress-strain process according to the nonlinear complex elastic modulus and nonlinear complex shear modulus of the full composite sandwich plate by using the Rayleigh-Leeds method, and to obtain the maximum strain energy and maximum kinetic energy of the full composite sandwich plate; The vibration module is used to simulate the surface displacement of the full composite sandwich plate under the action of strain energy and kinetic energy according to the maximum strain energy and maximum kinetic energy of the full composite sandwich plate, and obtain the vibration frequency of the full composite sandwich plate.

9. An electronic device, characterized in that: include: Memory and processor; The memory is used to store computer programs; The processor is used to implement the steps of the nonlinear vibration analysis method of a full-composite sandwich panel as claimed in any one of claims 1 to 7 when executing the computer program stored in the memory.

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