Method for analyzing dynamic performance degradation of protective coating-composite sheet in thermal vibration environment

Abstract

The invention discloses a method for analyzing dynamic performance degradation of a protective coating-composite sheet in a thermal vibration environment, and belongs to the technical field of high-temperature vibration degradation. After a dynamic degradation model of a protective coating-composite sheet structure in the thermal environment is established, the dynamic elastic modulus of a protective coating and a composite at different temperatures and degradation time is determined; the dynamic response characteristics of the structure are solved based on the first-order shear deformation theory, the Ritz method and the minimum potential energy principle, the dynamic stiffness index for thermal shock degradation resistance quantitative evaluation is provided, and the method has the advantages that the method is suitable for optimizing the thermal shock degradation resistance design of the composite material structure and improving the service life prediction precision.

Description

Technical Field

[0001] The present invention belongs to the technical field of high temperature vibration degradation of structures, and specifically relates to a high temperature vibration performance degradation analysis technology for composite structures, and specifically relates to a method for analyzing the dynamic performance degradation of protective coatings-composite thin plates under thermal vibration environments. Background Art

[0002] Composite thin plates have been widely used in aerospace, shipbuilding and automotive industries due to their light weight, high strength and excellent corrosion resistance. However, in thermal environments, composite thin plates are prone to performance degradation such as thermal oxidation and thermal degradation, which seriously affects their mechanical properties and service life. To address this problem, protective coatings are widely used on the surface of composite thin plates to improve their high temperature resistance and resistance to environmental corrosion.

[0003] Since the protective coating-composite thin plate structure is subjected to high temperature vibration for a long time during actual service, the interface performance between the protective coating and the composite material matrix degrades, which in turn has a significant impact on the overall dynamic performance of the structure. This degradation phenomenon may cause problems such as decreased structural stiffness, changes in vibration characteristics, and shortened fatigue life, which seriously threatens the safety and reliability of the structure. However, there is still a lack of systematic analysis of the dynamic performance degradation mechanism of protective coating-composite thin plates in thermal vibration environments at home and abroad. Therefore, determining the dynamic performance degradation behavior of protective coating-composite thin plate structures in thermal vibration environments is one of the important tasks to improve their service reliability.

[0004] Existing research has certain limitations in the analysis of structural dynamic performance under thermal vibration environment. Experimental research mainly focuses on test devices and methods, while theoretical research focuses more on the single effect of temperature on structural dynamic characteristics, lacking comprehensive consideration of the impact of material performance degradation under thermal vibration environment. For example, patent CN201711057508.5 proposes a method and system for testing nonlinear dynamic parameters of fiber composite plates under thermal vibration environment, which can accurately obtain the nonlinear dynamic parameters of the structure under thermal vibration environment, including nonlinear natural frequency, damping and modal vibration type; patent CN202210373242.X discloses a thermal modal test system and method for thin-walled structures after buckling and large deformation under high temperature environment, realizing continuous vibration excitation of thin-walled structures under high temperature environment; patent CN202410384219.X provides a thermal vibration composite fatigue test device and method suitable for thin-walled structures, which can be used for thermal vibration composite fatigue test of thin-walled structures at the hot end of aircraft engines. However, the above methods are all limited to the scope of experimental testing, lack of in-depth explanation of the test results from the theoretical mechanism level, and it is difficult to reveal the inherent mechanism of structural dynamic performance degradation under thermal vibration environment. Shen Huishen et al. (Comp Mater Sci, 2011, 50(8): 2319-2330), Li Hui et al. (Compos Part B-Eng, 2019, 162:206-218; Mech Syst SignalPr, 2021, 156:107665), Yu Kaiping et al. (Thin Wall Struct, 2024, 205: 112454) conducted theoretical modeling research on the vibration characteristics of composite thin plates and shell structures under thermal vibration environment, and explored the influence of temperature on the inherent characteristics and vibration response of the structure, but generally did not consider the problem of material performance degradation caused by temperature. Patent CN201910446358.X provides a method for analyzing the high-temperature dynamic performance degradation of fiber-reinforced composite plates, but does not consider the influence of protective coatings and lacks quantitative evaluation indicators for performance degradation. Existing research in the field of protective coatings mainly focuses on the development of preparation methods and equipment, represented by patents CN202211416873.1, CN202210348132.8 and CN202411516713.3. Although these studies have achieved innovations in the preparation technology of protective coating materials such as thermal protection and oxidation / ablation, they lack in-depth analysis and evaluation of the structural performance of the coatings.

[0005] Existing research mainly focuses on the degradation of static properties of composite materials and their structures in high temperature environments. For example, patent CN 202211571574.5 provides a life prediction method for fiber-reinforced composite materials taking into account high temperature degradation, which is used to predict the fatigue life of composite materials; patent CN 202310461910.9 discloses a performance degradation prediction method for continuous carbon fiber reinforced ceramic matrix composite materials, which simulates the damage process of this composite material in a high temperature environment through finite element software; patent CN202410968125.7 provides a finite element macro-micro model based on composite material performance parameters, which can perform progressive failure analysis and is suitable for failure simulation under tension, bending, torsion and composite loads; but the above results are not suitable for dynamic performance degradation analysis of structures under high temperature vibration environments. Chung et al. (Compos Part A, 2000, 31(9):945-957) and Fan Wei et al. (Journal of Composite Materials, 2015, 32(5):1260-1270) studied the performance changes of composite materials after aging under temperature environment. They analyzed the effect of temperature on the degradation of static properties of materials by aging weight loss, bending test and SEM, but did not consider its effect on the degradation of dynamic properties.

[0006] In summary, although the above patents and literature have conducted different degrees of research on the dynamic performance of composite structures under thermal vibration environments through experimental and theoretical analysis, the existing theoretical models generally only consider the direct impact of temperature on the dynamic performance of the structure, and fail to fully consider the material performance degradation effect caused by temperature, making it difficult to accurately reveal the dynamic performance degradation mechanism of the structure under thermal vibration environments. In particular, there are no reports on the research of protective coating-composite sheet structures considering the impact of material degradation, and there is a lack of corresponding analytical models and analysis methods. Therefore, providing a method for analyzing the dynamic performance degradation of protective coating-composite sheet metal under thermal vibration environments and establishing corresponding performance degradation evaluation indicators have important theoretical significance and engineering application value for in-depth revelation of the performance degradation mechanism under thermal vibration, optimizing the design of structural resistance to thermal vibration degradation, and improving the accuracy of life prediction. Summary of the invention

[0007] The present invention provides a method for analyzing the degradation of dynamic properties of a protective coating-composite thin plate under a thermal vibration environment. The method establishes a structural dynamic analytical model by comprehensively considering the influence of ambient temperature and degradation time on material properties, and corrects the model in combination with high-temperature vibration degradation test data. The temperature-time dependence of the dynamic elastic modulus of the material is constructed based on a particle swarm optimization algorithm, and then the structural dynamic properties under different temperatures and degradation times are predicted. A dynamic stiffness evaluation index is proposed to quantitatively characterize the thermal vibration degradation resistance of the structure, and the method has high prediction accuracy.

[0008] The technical solution of the present invention is as follows:

[0009] The method for analyzing the degradation of dynamic performance of protective coating-composite thin plate under thermal vibration environment includes the following steps:

[0010] Step 1: Select fiber-reinforced composite sheet specimens, prepare protective coating and coating-composite sheet specimens, and determine the geometry and material parameters of the sheet and coating;

[0011] Step 2: Establish a theoretical dynamic model of protective coating-composite sheet considering the effects of temperature and degradation time;

[0012] Step 3: Build a thermal vibration degradation test system to measure the dynamic response characteristics of the sample at room temperature and different degradation times under multi-temperature conditions;

[0013] Step 4: Combining the theoretical model with the structural dynamic response parameters obtained from the experiment, the geometric and material parameters of the specimen are corrected using a multi-level method;

[0014] Step 5: Based on the test data under multiple temperature conditions, the dynamic elastic modulus of the composite and coating materials is determined by combining the theoretical model with the particle swarm optimization algorithm;

[0015] Step 6: Establish the quantitative relationship between the dynamic elastic modulus of composite and coating materials and temperature and degradation time;

[0016] Step 7: Propose a dynamic stiffness index for quantitative evaluation of thermal vibration degradation resistance;

[0017] Step 8: Study the degradation mechanism of dynamic performance of protective coating-composite thin plate under thermal vibration environment.

[0018] The step 2 comprises the following steps:

[0019] Step 2.1: Establish the protective coating-composite sheet structure coordinate system;

[0020] Step 2.2: Define the structure and material related parameters;

[0021] Step 2.3: Propose the relationship between the dynamic elastic modulus and loss factor of composite materials and coatings considering the influence of temperature and degradation time;

[0022] Step 2.4: Determine the displacement expression of the protective coating-composite sheet structure;

[0023] Step 2.5: Determine the constitutive relationship of the protective coating-composite sheet considering the thermal degradation effect;

[0024] Step 2.6: Determine the resultant internal force and moment of the protective coating-composite sheet;

[0025] Step 2.7: Determine the natural frequencies and mode shapes of the protective coating-composite sheet;

[0026] Step 2.8: Determine the frequency vibration response of the protective coating-composite sheet under foundation excitation;

[0027] Step 2.9: Determine the time domain vibration response of the protective coating-composite sheet under impulse excitation.

[0028] The step 3 comprises the following steps:

[0029] Step 3.1: Establish a protective coating-composite sheet dynamic performance degradation test system under basic excitation in a thermal vibration environment;

[0030] Step 3.2: Build a protective coating-composite sheet dynamic performance degradation test system under impact excitation in a thermal vibration environment.

[0031] The step 4 comprises the following steps:

[0032] Step 4.1: Correct the dimensional parameters of the protective coating-composite sheet based on the first level;

[0033] Step 4.2: Correct the elastic modulus and Poisson's ratio of the protective coating-composite sheet based on the second level;

[0034] Step 4.3: Correct the loss factor of the protective coating-composite sheet based on the third level.

[0035] The step 5 comprises the following steps:

[0036] Step 5.1: Obtain multiple sets of test data of protective coating-composite sheet at different temperatures and degradation times;

[0037] Step 5.2: Determine the thermal dynamic elastic modulus of the composite and protective coating materials.

[0038] The step 6 considers the influence of temperature and degradation time on the fiber reinforced composite material, and uses the exponential function method to establish the relationship between the dynamic elastic modulus and loss factor of the fiber reinforced composite material in each direction and the temperature and degradation time: the material parameter expression of the protective coating-composite sheet degradation model is fitted using CFtool in Matlab to obtain the fitting coefficient related to the degradation time and temperature.

[0039] Based on the time domain expression of the known pulse vibration response, the exciting force and vibration response of the protective coating-composite sheet are transformed by fast Fourier transform to obtain the dynamic stiffness of the structure, and this index is used to evaluate the thermal vibration degradation resistance of the system.

[0040] Step 5.1 combines the theoretical model with the particle swarm optimization algorithm to determine the dynamic elastic modulus of the composite material and protective coating under different temperature conditions and degradation time.

[0041] Step 3.1 and step 3.2 obtain the time domain and frequency dynamic response characteristics of the structure.

[0042] Step 8 obtains the influence of degradation time, the presence or absence of protective coating and coating parameters on the degradation of dynamic properties of protective coating-composite thin plate under thermal vibration environment.

[0043] The beneficial effects of the present invention are as follows: a protective coating-composite sheet dynamic degradation model considering the influence of material temperature and degradation time is established, and the dynamic elastic modulus of composite and coating materials at different temperatures and degradation times is determined by comparing theoretical and test results; the dynamic response characteristics of the structure are solved based on the first-order shear deformation theory, Ritz method and minimum potential energy principle, and a dynamic stiffness index for quantitative evaluation of thermal vibration resistance degradation performance is proposed. This method is simple to calculate and has high accuracy, and is suitable for optimizing the thermal vibration resistance design of the structure and improving the accuracy of life prediction, and has high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of the method for analyzing the degradation of dynamic properties of protective coating-composite thin plates under thermal vibration environment;

[0045] Figure 2 Schematic diagram of the theoretical model of the dynamics of protective coating-composite thin plate under thermal vibration environment;

[0046] Figure 3 Thermal vibration degradation test system: (a) schematic diagram and physical picture of basic excitation system, (b) physical picture of pulse excitation system;

[0047] Figure 4 This is the flow chart of reverse identification of material parameters based on particle swarm optimization algorithm;

[0048] Figure 5 Dynamic elastic modulus obtained for identification: (a)-(c) composite sheet, (d) protective coating;

[0049] Figure 6 Dynamic response test results: (a) pulse excitation time domain signal, (b) comparison of theoretical prediction and experimental test time domain vibration response;

[0050] Figure 7 Comparison diagram between theoretical solution and experimental results of the first four natural frequencies of the specimen under different temperature conditions and degradation time: (a) 100℃, (b) 200℃;

[0051] Figure 8 Comparison diagram of the theoretical solution and experimental results of the first two-order resonance response of the specimen under different temperature conditions and degradation time: (a) 100℃, (b) 200℃;

[0052] Fig. 9 The analysis diagrams of the coating effect with and without coating at different degradation times: (a) 100℃, (b) the first three natural frequencies of the specimen at 200℃;

[0053] Fig.10 The analysis diagrams of coating effect with and without coating at different degradation times: (a) 100℃, (b) the first three-order resonance responses of the specimen at 200℃;

[0054] Fig.11 This is a diagram showing the effect of the thickness ratio of the protective coating on the first three-order resonance responses of the structure;

[0055] Fig.12 The first four-order dynamic stiffness curves of protective coating-composite thin plate under different temperature conditions: (a) 20℃, (b) 100℃, (c) 200℃. DETAILED DESCRIPTION

[0056] The method for analyzing the degradation of dynamic performance of protective coating-composite thin plate under thermal vibration environment includes the following steps:

[0057] Step 1: Select fiber-reinforced composite sheet specimens, prepare protective coating and coating-composite sheet specimens, and determine the geometry and material parameters of the sheet and coating;

[0058] Step 1.1: Determine the size parameters of the fiber composite sheet in combination with the manufacturer's production conditions and process standards, and the manufacturer provides material parameters;

[0059] Step 1.2: Select the 380 series ceramic coating produced by Jiangsu Junyuan New Materials Co., Ltd., and use the atomization deposition process to prepare a protective coating on the surface of the composite sheet. The coating material parameters are provided by the manufacturer.

[0060] Step 2: Establish a theoretical dynamic model of protective coating-composite sheet considering the effects of temperature and degradation time;

[0061] Step 2.1: Establish the protective coating-composite sheet structure coordinate system;

[0062] Assuming that the protective coating is evenly coated on both sides of the composite sheet structure, a global coordinate system o-xyz is defined on the midplane of the sheet structure, along the length, width and thickness of the sheet; a local coordinate system o-123 is defined on the fiber material, which are the three main axis directions of the fiber material; θ k is the angle between the direction of the k-th layer of fiber material 1 and the x-axis;

[0063] Step 2.2: Define the structure and material related parameters;

[0064] The total length of the plate is a, the total width is b, and the total thickness is h f , the thickness of the protective coating is h c ; The number of fiber layers is n, and each layer is located on the lower surface h of the z coordinate axis n and higher surface h n+1and the thickness is the same; the elastic modulus and thermal expansion coefficient along the fiber direction and perpendicular to the fiber direction in the fiber / resin layer are E 1 、E 2 , α 1 , α 2 , the shear modulus is G 12 ; The elastic modulus and thermal expansion coefficient of the protective coating are E c , α c ; The Poisson's ratio of the strains in the 1st and 2nd directions of the fiber caused by the stress in the 1st direction is ν 12 , the Poisson's ratio of the strain in the 1st and 2nd directions of the fiber caused by the stress in the 2nd direction is ν 21 ; Poisson's ratio ν of protective coating c ; The densities of the fiber reinforcement layer and the protective coating are ρ f and ρ c ;

[0065] Step 2.3: Propose the relationship between the dynamic elastic modulus and loss factor of composite materials and coatings considering the influence of temperature and degradation time;

[0066] It is assumed that the performance degradation of fiber reinforced composites and homogeneous protective coating materials caused by thermal effects is the main reason for the macroscopic dynamic degradation of coating-composite thin plates. Considering the influence of temperature and degradation time on fiber reinforced composites, the exponential function method is used to establish the relationship between the dynamic elastic modulus and loss factor of fiber reinforced composites in all directions and the changes with temperature and degradation time:

[0067] (1)

[0068] In the formula, , , , , , A represents the elastic modulus and loss factor of fiber reinforced composites at room temperature. i and F i (i=1, 2, 12) represents the adjusted fitting coefficient, B i and H i represents the degradation fitting coefficient, C i and L i represents the time fitting coefficient, and t represent temperature and degradation time respectively.

[0069] Similarly, assuming that the dynamic elastic modulus of the homogeneous protective coating is and loss factor for:

[0070] (2)

[0071] In the formula, , A represents the Young's modulus and loss factor of the protective coating at room temperature. c , B c , C c, F c , H c and L c represents the corresponding fitting coefficients.

[0072] In order to consider the influence of material damping, the elastic modulus of fiber reinforced composite sheets and protective coatings in thermal environments are expressed as complex modulus:

[0073] (3)

[0074] In the formula, * indicates plural number. (i=1, 2, 12, c) represent the complex elastic modulus of the fiber reinforced composite sheet and the protective coating, respectively.

[0075] Step 2.4: Determine the displacement expression of the protective coating-composite sheet structure;

[0076] In order to consider the influence of shear deformation, based on the first-order shear deformation theory, the displacement expression of the protective coating-composite sheet structure can be obtained as follows:

[0077] (4)

[0078] Where u, v, and w represent the displacement of any point on the structure; u 0 , v 0 , w 0 is the displacement of a point in the mid-plane in the x, y, and z directions; , is the rotation angle around the x and y axes, and t is the time.

[0079] Step 2.5: Determine the constitutive relationship of the protective coating-composite sheet considering the thermal degradation effect;

[0080] Due to the symmetry of the protective coating-composite sheet structure, the bending motion is not coupled with the stretching motion. 0 and v 0 can be ignored. Non-zero positive strain , and in-plane shear strain , , for:

[0081] (5)

[0082] Based on the generalized Duhamel-Neumann form of Hooke's law, plane stress is expressed in a shorthand notation: (6)

[0083] In the formula, stress ,strain It is also defined in a similar way. represents thermal strain; S ij The softness component.

[0084] The stress-strain relationship in any direction is as follows:

[0085] (7)

[0086] In the formula, is the eccentric stiffness coefficient.

[0087] The constitutive relationship expression of the protective coating is:

[0088] (8)

[0089] In the formula,

[0090] , , (9)

[0091] For the stress-strain relationship of the kth layer of the composite plate:

[0092] (10)

[0093] In the formula,

[0094] (11)

[0095] The thermal strain of composite thin plates at uniform temperature is:

[0096] (12)

[0097] , , They represent the thermal expansion coefficient of the composite sheet along their respective directions, and the specific expressions are:

[0098] (13)

[0099] Step 2.6: Determine the resultant internal force and moment of the protective coating-composite sheet;

[0100] By integrating the stress of each layer along the thickness direction of the thin plate, the resultant internal force and moment of the protective coating-composite thin plate under thermal environment varying with temperature and degradation time are obtained:

[0101] (14)

[0102] (15)

[0103] (16)

[0104] Where N x , N y , N xy and M x , M y , M xy are the resultant values ​​of the internal force and moment respectively; Q x and Q y is the corresponding resultant lateral shear force; , , and , , are the resultant values ​​of the internal forces and moments on the thermal surface, respectively. The assumed shear correction factor =5 / 6; where A ij , B ij and D ij are the tensile, tensile-bending coupling, and bending stiffness, respectively expressed as:

[0105] (17)

[0106] Step 2.7: Determine the natural frequencies and mode shapes of the protective coating-composite sheet;

[0107] Considering the influence of thermal environment and degradation time, based on the dynamic performance degradation model of protective coating-composite thin plate, the minimum potential energy principle and Ritz method are used to solve the natural frequency and vibration mode of the structure.

[0108] The kinetic energy T of the upper and lower protective coatings and the composite sheet c1 , T c2 , T f , the strain energy U of the system caused at room temperature 0 , the strain energy U of the system caused by thermal stress T It is expressed as:

[0109] (18)

[0110] (19)

[0111] The displacement w(x, y, ΔT, t) of the composite sheet in a thermal environment is assumed to be:

[0112] (20)

[0113] In the formula, is the circular frequency of the composite plate vibration, which is the same as the excitation frequency, is the vibration mode function, which has the following form:

[0114] (twenty one)

[0115] Where M and N are the maximum cutoff coefficients. are the coefficients to be solved, (i=1,2…,M), (j=1,2…,N) is a series of orthogonal polynomials that satisfy the boundary conditions.

[0116] Orthogonalize the polynomial functions that meet the boundary conditions to obtain a series of orthogonal polynomials:

[0117] (twenty two)

[0118] In the formula, H i and V i is the coefficient function, and its expressions are:

[0119] (twenty three)

[0120] In the formula, the weight function W Usually taken as 1; and is a polynomial function that satisfies the boundary conditions:

[0121] (twenty four)

[0122] Since the structure of interest is in a cantilever state, , , , .

[0123] According to the Ritz method, the harmonic component e is ignored. iwt The influence of , the energy function L is expressed as:

[0124] L = U 0 +U T -(T c1 +T c2 +T f ) (25)

[0125] Based on the principle of minimum potential energy, the inherent characteristics of the protective coating-composite sheet under thermal environment are solved, that is, the undetermined parameters that make the functional L take the minimum value are solved. The expression is as follows:

[0126] (26)

[0127] We get M×N homogeneous linear algebraic equations and express them in matrix form:

[0128] (27)

[0129] In the formula, the complex modulus stiffness , K and C are the stiffness and damping matrices, and M is the mass matrix.

[0130] The above formula is used to obtain a certain order natural frequency of the protective coating-composite sheet in the thermal environment, and the corresponding eigenvector is substituted into the vibration mode function , and obtain the mode shape of this order; repeat the above steps to obtain all the vibration shapes of interest.

[0131] Step 2.8: Determine the frequency vibration response of the protective coating-composite sheet under foundation excitation;

[0132] Assuming that the clamping end of the protective coating-composite sheet has a basic excitation as a resonant excitation, the expression y(t) is:

[0133] (28)

[0134] Where Y is the amplitude of the basic excitation and ω is the angular frequency of the basic excitation.

[0135] The total displacement λ at any point x, y on the structure can be expressed as:

[0136] λ(x, y, t)= y(t)+w(x, y, t) (29)

[0137] Where w(x, y, t) is the deflection of a certain point of the protective coating-composite sheet.

[0138] The foundation excitation y(t) of the structure is equivalent to the uniformly distributed inertia force load q(t), and its expression is:

[0139] (30)

[0140] The work done by the uniformly distributed inertial force on the structure is obtained as W q for:

[0141] (31)

[0142] Based on the Ritz method, the harmonic component e is ignored. iwtThe influence of , the energy function L is expressed as:

[0143] L = U 0 +U T -W q -(T c1 +T c2 +T f ) (32)

[0144] Let the partial derivative of the energy function L with respect to the coefficient a be zero and express it in matrix form:

[0145] (33)

[0146] In the formula, a represents the response vector, F e Represents the exciting force vector.

[0147] Substituting the response vector a at the specified excitation frequency into equation (29) can obtain the vibration response of any point on the protective coating-composite sheet under the base excitation.

[0148] Step 2.9: Determine the time domain vibration response of the protective coating-composite sheet under impulse excitation;

[0149] Assume that the structure is at point R e (x 0 , y 0 ) is subjected to pulse excitation F(t), f(t) is the composite sheet at point R r (x 1 ,y 1 ), the vibration response at , is expressed as:

[0150] (34)

[0151] In the formula, f 0 is the excitation amplitude, ω is the excitation angular frequency, t 1 is the time of the incentive effect, x 0 and 0 is the coordinate value of the excitation point.

[0152] Based on the inherent characteristics of protective coating-composite thin plate under thermal environment, the mode superposition method is used to solve the time domain vibration response X(t) of the composite thin plate under pulse excitation load, and its mathematical expression is:

[0153] (35)

[0154] Where W mn (x, y) is the mode shape, T mn are the components of each vibration mode.

[0155] Under the assumption of small damping, the damped generalized vibration differential equation can be expressed as:

[0156] (36)

[0157] (37)

[0158] In the formula, and are the (m, n)th order generalized force and generalized mass respectively, is the r-th modal damping ratio of the composite plate.

[0159] Under zero initial conditions, the solution of the above equation can be expressed by Duhamel integration as:

[0160] (38)

[0161] In the formula, ω d is the angular frequency of the damped system, and its expression is .

[0162] The Simpson numerical integration method is used to solve the above equation and substitute it into equation (35) to obtain the time domain vibration response X(t) of the protective coating-composite sheet under the action of pulse excitation F(t).

[0163] Step 3: Build a thermal vibration degradation test system to measure the dynamic response characteristics of the sample at room temperature and different degradation times under multi-temperature conditions;

[0164] Step 3.1: Establish a protective coating-composite sheet dynamic performance degradation test system under basic excitation in a thermal vibration environment;

[0165] The protective coating-composite sheet dynamic performance degradation test system under base excitation in thermal vibration environment is composed of the following equipment: Lianneng JZK-100 exciter and YE5878 power amplifier, Polytec PDV-100 laser vibrometer, LabView-based two-dimensional laser scanning device, high-temperature acceleration sensor CA-YD-136T, heating device and LMS 16-channel data acquisition instrument.

[0166] In the experiment, the plate was clamped with a fixture and M8 bolts to simulate the cantilever boundary conditions, and the vibration energy of the electromagnetic exciter was transferred to the composite sheet through the fixture in the form of basic excitation. The high-temperature accelerometer was installed on the excitation platform for feedback control of the excitation amplitude, and the laser vibration point was used to measure the velocity response of the structure. The heating box provided the required temperature, and the high-temperature glass on the top allowed the laser Doppler vibrometer to penetrate and measure the response signal. The two-dimensional laser scanning device controlled by LabView drove the movement of the laser point. Two types of thermocouples were used in the experiment: one to measure the temperature and the other as a temperature control feedback signal. The vibration and temperature signals were recorded and stored by the LMS SCADA 16-channel data acquisition instrument and a laptop computer.

[0167] Step 3.2: Establish a test system for the dynamic performance degradation of protective coating-composite thin plates under impact excitation in a thermal vibration environment;

[0168] Based on the protective coating-composite thin plate dynamic performance degradation test system under basic excitation in thermal vibration environment, a gas excitation sensor is used to excite the sample, a laser Doppler vibrometer is used to obtain the velocity signal, and the excitation and response signals are collected in real time through the LMS data acquisition instrument to test the time domain signal of the composite thin plate under pulse excitation.

[0169] Step 4: Combining the theoretical model with the structural dynamic response parameters obtained from the experiment, the geometric and material parameters of the specimen are corrected using a multi-level method;

[0170] Step 4.1: Correct the dimensional parameters of the protective coating-composite sheet based on the first level;

[0171] The measured protective coating-composite sheet size parameters (composite sheet length a, width b, thickness h) f And the thickness of protective coating h c ) as a benchmark, considering the error range of 5%-10%, select the appropriate iteration step and construct the size parameter iteration vector. Subsequently, the size parameters are iteratively calculated, with the natural frequency and modal vibration shape of the structure as the correction target. When the theoretically calculated modal vibration shape is consistent with the test result, and the natural frequency error is within the allowable range (such as 10%-15%), the first level of correction can be completed.

[0172] Step 4.2: Correct the elastic modulus and Poisson's ratio of the protective coating-composite sheet based on the second level;

[0173] The average parameters of composite materials and protective coating materials provided by manufacturers (E 1 、E 2 , G 12 , ν 12 、E c , ν c) as the center, considering the 10%-20% error, selecting the appropriate iteration step to construct the material parameter vector, and iterative calculation through permutations and combinations. The natural frequency and modal vibration shape of the structure are used as the correction target. When the modal vibration shape calculated theoretically is consistent with the test result, and the natural frequency error is within a smaller range (such as 5%-10%), the second-level correction is considered successful. At this time, the corresponding material parameters are the actual material parameters of the composite material and protective coating.

[0174] Step 4.3: Correct the loss factor of the protective coating-composite sheet based on the third level;

[0175] Select an appropriate iteration step size to construct the loss factor iteration vector ( , , , ), by iteratively calculating the loss factors of composite materials and protective coatings, the frequency domain resonance response near a certain order of natural frequency obtained by the test is used as the correction target. When the error between the calculated frequency domain response curve and the test curve is within the allowable range (such as 10%), the third level correction can be completed.

[0176] Step 5: Based on the test data under multiple temperature conditions, the dynamic elastic modulus of the composite and coating materials is determined by combining the theoretical model with the particle swarm optimization algorithm;

[0177] Step 5.1: Obtain multiple sets of test data of protective coating-composite sheet at different temperatures and degradation times;

[0178] Based on the thermal vibration dynamic performance degradation test platform built in step 3, the dynamic performance of the protective coating-composite sheet samples is tested at multiple temperatures and degradation times, and the natural frequency and vibration response test data considering the influence of degradation time at different temperatures are obtained.

[0179] Step 5.2: Determine the thermal dynamic elastic modulus of the composite material and protective coating material;

[0180] Based on the dynamic performance degradation test data of the protective coating-composite sheet under multiple temperature conditions and degradation time obtained in step 5.1, the elastic modulus of the composite material and protective coating under different temperature conditions and degradation time is determined by combining the theoretical model with the particle swarm optimization algorithm (PSO).

[0181] In PSO, a D-dimensional target search space is first selected, and a dynamic elastic modulus vector is formed by randomly assigning I particles to the positions. i It is expressed as a D-dimensional vector, whose elements are the dynamic elastic modulus of the composite sheet and the protective coating, X i It can be expressed as:

[0182] (39)

[0183] In each iteration, the i-th particle X i The velocity V is a D-dimensional vector, which determines its flight direction and speed. The particle updates itself by tracking two extreme values: one is the optimal solution found by the particle itself, called the individual extreme point (the position is recorded as P i ); the second is the optimal solution currently found by the population, called the global extreme point (the position is recorded as P g ). Particle X i Update the velocity and position according to the following rules:

[0184] (40)

[0185] In the formula, Indicates the inertia weight of the particle's previous velocity and current velocity; c 1 and c 2 is a positive constant that controls the maximum step length; r 1 and r 2 is a uniformly distributed random variable in the interval (0, 1); k represents the number of iterations.

[0186] In each iteration, particle X i Each element of takes a random value within its range, takes the material parameters at room temperature as the center, considers the change of the elastic modulus of the composite material and the protective coating at high temperature with time, and sets R v =50%, determine particle X i The value range of each element in a column at a specific temperature and time:

[0187] (41)

[0188] The final particle X i The position (value of each element) is taken as the optimal value of the dynamic elastic modulus, particle X i The performance of the error objective function is defined by the fitness value e f Decide:

[0189] (42)

[0190] In the formula, represents the order of the mode, and They represent the theoretical calculation value and experimental test value of the i-th order natural frequency respectively.

[0191] The iteration termination condition is that the optimal position searched by the particle swarm satisfies the preset minimum error e f (Usually f ≤5%), and output the optimal solution. According to the above steps, the dynamic elastic modulus of the composite material and protective coating at different temperatures and degradation times can be obtained.

[0192] Step 6: Establish the quantitative relationship between the dynamic elastic modulus of composite and coating materials and temperature and degradation time;

[0193] Based on the dynamic elastic modulus parameters of the composite and coating materials subjected to thermal degradation determined in step 5 and combined with the assumptions of formulas (1) and (2), the material parameter expressions of the protective coating-composite sheet degradation model were fitted using CFtool in Matlab to obtain the fitting coefficients related to the degradation time and temperature.

[0194] The specific process is as follows: input different temperatures, degradation time points and corresponding dynamic elastic modulus values; in CFtool, set 'XData', 'YData' and 'ZData' to temperature, degradation time point and dynamic elastic modulus respectively. Use the custom equation fitting tool provided by CFtool to input the material parameter function to obtain the fitting coefficient. To determine the optimal fitting coefficient, it is necessary to repeatedly adjust the fitting parameters in CFtool, and finally use the 'R-square' value (range [0,1]) as the evaluation basis. The closer the value is to 1, the higher the fitting accuracy.

[0195] Step 7: Propose a dynamic stiffness index for quantitative evaluation of thermal vibration degradation resistance;

[0196] Based on the time domain expression of the known pulse vibration response, the exciting force and vibration response of the protective coating-composite sheet are fast Fourier transformed. Assuming F(ω) and X(ω) are the Fourier transforms of F(t) and X(t), respectively, according to the definition of frequency response function, the frequency response function H(ω) of the protective coating-composite sheet structure system can be expressed as:

[0197] (43)

[0198] According to the relationship between dynamic stiffness and frequency response function, the protective coating-composite sheet response point P b Relative to the excitation point P a The dynamic stiffness can be expressed as:

[0199] (44)

[0200] Based on the obtained dynamic stiffness, this index is used to evaluate the system's anti-thermal vibration degradation performance.

[0201] Step 8: Study the degradation mechanism of the dynamic performance of protective coating-composite thin plate under thermal vibration environment;

[0202] Based on the theoretical model and dynamic stiffness index, the dynamic characteristics of the protective coating-composite thin plate at different temperatures and degradation times are calculated, and the influence mechanism of degradation time, the presence or absence of protective coating and coating parameters on the degradation of the system dynamic performance under thermal vibration environment is systematically studied.

[0203] Specific Examples

[0204] like Figure 2 As shown, the protective coating-composite sheet structure includes a carbon fiber / resin composite sheet and a protective coating. Among them, six identical TC500 carbon fiber / epoxy resin-based composite sheet specimens were manufactured by Jiangxi Jiujiang Diwei Composite Materials Co., Ltd. and were symmetrically orthogonally laid. 5 / 0 / (90 / 0) 5 ], a total of 21 layers, each layer has the same thickness and fiber volume fraction; the coating uses 380 series ceramic coatings produced by Jiangsu Junyuan New Materials Co., Ltd., which are applied on specimens IV, V, and VI to form a protective coating with a thickness of 0.6 mm. The coating adhesive is a nano-inorganic sol, which is organically modified and added with inorganic high-temperature resistant fillers. It can form a film at room temperature or high temperature and has strong high-temperature resistance. The specimen is clamped on one side by a fixture with a clamping length of 30 mm. The size after clamping is 230 mm×130 mm×2.36 mm. The parameters of the composite material and protective coating are provided by the manufacturer, see Table 1.

[0205] Table 1 Specimen material parameters

[0206]

[0207] Based on the analysis process of step 2, the dynamic response characteristics of the protective coating-composite sheet considering the influence of temperature and degradation time are solved. Figure 7 and 8 The theoretical and experimental comparison results of the first four natural frequencies and the first two resonant displacement responses of the protective coating-composite thin plate structure at different temperatures and degradation times are shown respectively. The maximum errors are 8.2% and 11.9%, respectively. The solution results are in good agreement with the experimental results, verifying the effectiveness of the theoretical model.

[0208] Figure 9-11 The influence mechanism of the existence effect of protective coating (comparison of coating and non-coating) on ​​the dynamic response characteristics of the structure (including natural frequency and resonance response) under temperature conditions of 100°C and 200°C was systematically analyzed, and the influence of the protective coating thickness ratio parameter on the first three-order resonance response of the structure was revealed. Fig.12 An innovative quantitative evaluation method based on dynamic stiffness index was proposed to achieve accurate characterization of the structure's anti-thermal vibration degradation performance.

Claims

1. The dynamic performance degradation analysis method of protective coating-composite thin plate under thermal vibration environment is characterized by The following steps are involved: Step 1: Select fiber-reinforced composite sheet specimens, prepare protective coating and coating-composite sheet specimens, and determine the geometry and material parameters of the sheet and coating; Step 2: Establish a theoretical dynamic model of protective coating-composite sheet considering the effects of temperature and degradation time; Step 3: Build a thermal vibration degradation test system to measure the dynamic response characteristics of the sample at room temperature and different degradation times under multi-temperature conditions; Step 4: Combining the theoretical model with the structural dynamic response parameters obtained from the experiment, the geometric and material parameters of the specimen are corrected using a multi-level method; Step 5: Based on the test data under multiple temperature conditions, the dynamic elastic modulus of the composite and coating materials is determined by combining the theoretical model with the particle swarm optimization algorithm; Step 6: Establish the quantitative relationship between the dynamic elastic modulus of composite and coating materials and temperature and degradation time; Step 7: Propose a dynamic stiffness index for quantitative evaluation of thermal vibration degradation resistance; Step 8: Study the degradation mechanism of dynamic performance of protective coating-composite thin plate under thermal vibration environment.

2. The method for analyzing the degradation of dynamic performance of protective coating-composite sheet in thermal vibration environment according to claim 1 is characterized in that The step 2 comprises the following steps: Step 2.1: Establish the protective coating-composite sheet structure coordinate system; Step 2.2: Define the structure and material related parameters; Step 2.3: Propose the relationship between the dynamic elastic modulus and loss factor of composite materials and coatings considering the influence of temperature and degradation time; Step 2.4: Determine the displacement expression of the protective coating-composite sheet structure; Step 2.5: Determine the constitutive relationship of the protective coating-composite sheet considering the thermal degradation effect; Step 2.6: Determine the resultant internal force and moment of the protective coating-composite sheet; Step 2.7: Determine the natural frequencies and mode shapes of the protective coating-composite sheet; Step 2.8: Determine the frequency vibration response of the protective coating-composite sheet under foundation excitation; Step 2.9: Determine the time domain vibration response of the protective coating-composite sheet under impulse excitation.

3. The method for analyzing the degradation of dynamic properties of protective coating-composite sheet metal under thermal vibration environment according to claim 1 is characterized in that The step 3 comprises the following steps: Step 3.1: Establish a protective coating-composite sheet dynamic performance degradation test system under basic excitation in a thermal vibration environment; Step 3.2: Build a protective coating-composite sheet dynamic performance degradation test system under impact excitation in a thermal vibration environment.

4. The method for analyzing the degradation of dynamic performance of protective coating-composite sheet in thermal vibration environment according to claim 1 is characterized in that The step 4 comprises the following steps: Step 4.1: Correct the dimensional parameters of the protective coating-composite sheet based on the first level; Step 4.2: Correct the elastic modulus and Poisson's ratio of the protective coating-composite sheet based on the second level; Step 4.3: Correct the loss factor of the protective coating-composite sheet based on the third level.

5. The method for analyzing the degradation of dynamic performance of protective coating-composite sheet in thermal vibration environment according to claim 1 is characterized in that The step 5 comprises the following steps: Step 5.1: Obtain multiple sets of test data of protective coating-composite sheet at different temperatures and degradation times; Step 5.2: Determine the thermal dynamic elastic modulus of the composite and protective coating materials.

6. The method for analyzing the degradation of dynamic performance of protective coating-composite sheet in thermal vibration environment according to claim 1, characterized in that: The step 6 considers the influence of temperature and degradation time on the fiber reinforced composite material, and uses the exponential function method to establish the relationship between the dynamic elastic modulus and loss factor of the fiber reinforced composite material in each direction and the temperature and degradation time: the material parameter expression of the protective coating-composite sheet degradation model is fitted using CFtool in Matlab to obtain the fitting coefficient related to the degradation time and temperature.

7. The method for analyzing the degradation of dynamic performance of protective coating-composite sheet in thermal vibration environment according to claim 1, characterized in that: Based on the time domain expression of the known pulse vibration response, the exciting force and vibration response of the protective coating-composite sheet are transformed by fast Fourier transform to obtain the dynamic stiffness of the structure, and this index is used to evaluate the thermal vibration degradation resistance of the system.

8. The method for analyzing the degradation of dynamic properties of protective coating-composite sheet in thermal vibration environment according to claim 1 is characterized in that Step 5.1 combines the theoretical model with the particle swarm optimization algorithm to determine the dynamic elastic modulus of the composite material and protective coating under different temperature conditions and degradation time.

9. The method for analyzing dynamic performance degradation of protective coating-composite sheet in thermal vibration environment according to claim 1, characterized in that: Step 3.1 and step 3.2 obtain the time domain and frequency dynamic response characteristics of the structure.

10. The method for analyzing dynamic performance degradation of protective coating-composite sheet in thermal vibration environment according to claim 1 is characterized in that Step 8 obtains the influence of degradation time, the presence or absence of protective coating and coating parameters on the degradation of dynamic properties of protective coating-composite thin plate under thermal vibration environment.

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