Calculation method for motion response of air back flat plate structure under action of fluid shock waves

Abstract

The invention belongs to a theoretical calculation method for structural dynamic response under the action of shock waves, particularly relates to a calculation method for motion response of an air back flat plate structure under the action of fluid shock waves, and belongs to the technical field of structural impact dynamic response test and evaluation. Comprising the following steps: S1, calculating a post-wave state of an incident shock wave in a fluid medium; s2, calculating the post-wave state of the reflected shock wave in the fluid medium; s3, calculating the sparse wave pressure p3 in the fluid medium caused by the movement of the flat plate structure; s4, calculating the motion response of the flat plate structure; according to the method, the basic principle of fluid dynamics is combined, the acoustic linear hypothesis that fluid cannot be compressed in the Taylor plate theory is replaced with a compressible state equation of substances, the compressibility of the fluid and the plate structure is considered, and meanwhile the influence of sparse wave propagation in a flow field on movement of the plate structure is also considered; according to the method, a quantitative result can be calculated more efficiently and more accurately, and the method is used for guiding underwater explosion test and damage evaluation.

Description

Technical Field

[0001] The present invention relates to a theoretical calculation method for the dynamic response of a structure under the action of a shock wave, and specifically to a calculation method for the motion response of an air-backed flat plate structure under the action of a fluid shock wave, wherein the motion response includes a motion displacement response, a motion velocity response, a motion acceleration response, etc., and belongs to the technical field of structural impact dynamic response testing and evaluation. Background Art

[0002] Air-backed flat plate structures will move under the action of fluid shock waves, where air-backed flat plate structures refer to flat plates with air on the back. Air-backed structures are very common in engineering practice. For example, the outer wall panels in structures such as aircraft tanks filled with fuel and ship tanks filled with ballast water that are in contact with fluids are all air-backed flat plate structures. Because the acoustic impedance of the flat plate structure and the fluid is significantly different, the shock wave will reflect, transmit and radiate at the interface between the flat plate structure and the fluid, resulting in coupled motion between the flat plate structure and the fluid. On the one hand, the acoustic impedance of the flat plate structure is often much greater than the acoustic impedance of the fluid, so the amplitude intensity of the reflected shock wave will be greater than the amplitude intensity of the incident shock wave, resulting in an enhancement of the actual load; on the other hand, the flat plate structure will move under the action of the load. Due to the continuity of the motion of the flat plate structure and the fluid interface, the moving flat plate structure will cause sparse waves to radiate at the interface to propagate toward the fluid, resulting in a weakening of the actual load. The core of calculating the motion of the flat plate structure is to solve the actual load. The increase and decrease of the load caused by the above-mentioned physical phenomena brings great difficulties to the calculation and solution.

[0003] Taylor plate theory is a pioneering theoretical method for calculating the motion response of air-backed plate structures under fluid shock waves. Since the theory assumes that the plate is a rigid wall and the rarefaction wave propagates at the initial sound speed of the fluid, the theory is only applicable to the calculation of the motion response of the plate structure when the shock wave peak is small. In actual military application scenarios such as underwater explosion testing and ship damage assessment, the plate structure is often subjected to large-amplitude fluid shock wave loads. If the Taylor plate theory is still used to calculate the motion response of the plate structure at this time, it will cause large errors and fail to meet the accuracy requirements of related practical applications. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a calculation method for the motion response of an air-backed flat plate structure under the action of a fluid shock wave, which can play a good prediction or calibration effect for experiments and simulations, and is of great significance for damage assessment, wherein the fluid usually refers to water, fuel, etc. In the present invention, the fluid medium is a liquid, and the solid medium is a flat plate structure.

[0005] The technical solution adopted by the present invention is: a method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave, the method comprising the following steps:

[0006] S1. Calculate the post-wave state of the incident shock wave in the fluid medium;

[0007] This step is used to calculate the post-wave medium particle velocity u1 and the post-wave fluid medium density ρ1 of the incident shock wave in the fluid medium when the incident shock wave pressure p1 of the fluid is known.

[0008] For the fluid medium that is only subjected to the incident shock wave loading, the conservation relation before and after the shock wave front is:

[0009] ρ1(D1-u1)=ρ0(D1-u0) (1)

[0010] p1-p0=ρ0(D1-u0) 2 -ρ1(D1-u1) 2 (2)

[0011]

[0012] Among them, the initial state is marked as "0", and the state after the incident shock wave in the fluid medium is marked as "1". p is the pressure, u is the medium particle velocity, c is the medium wave velocity, ρ is the medium density, e is the internal energy, D is the shock wave velocity, and v is the specific volume of the medium, that is, the inverse of the medium density.

[0013] For condensed media, the state equation can be adopted in the following form:

[0014]

[0015] Among them, c 01 is the initial medium sound velocity, is the Hügoniot data of the fluid medium, which can be obtained by referring to the Introduction to Physical Equation Theory and Computation (2nd Edition) by Tang Wenhui et al. p2 is the pressure of the reflected shock wave, γ1 is the state equation parameter of the fluid medium, and γ2 is the state equation parameter of the solid medium, which can be expressed in the form of Hügoniot data as parameters:

[0016]

[0017] Among them, s1 is the Hügoniot data of fluid medium, and s2 is the Hügoniot data of solid medium, which can be obtained by referring to the book "Introduction to Physical Equation Theory and Computation (2nd Edition)" written by Tang Wenhui et al. p is the initial solid density, ρ p1 is the solid density after the incident shock wave.

[0018] Substituting equation (4) into equation (3), we can obtain the impact adiabatic line of the fluid medium in the form of p-ρ:

[0019]

[0020] Substituting equation (1) into equation (2) and eliminating ρ0 or ρ1, we can obtain:

[0021]

[0022] Substitute equation (1) into equation (2) and eliminate (D1-u0) 2 or (D1-u1) 2 We can get:

[0023]

[0024] Multiplying equation (8) and equation (9) yields:

[0025]

[0026] After multiplying the two equations in equation (7), substitute equation (10) to obtain:

[0027] (u1-u0) 2 =(p1-p0)(v0-v1) (11)

[0028] The density of the fluid medium behind the incident shock wave can be deduced from formula (6):

[0029]

[0030] From formula (12), we can deduce:

[0031]

[0032] Substituting equation (13) and equation (6) into equation (11), we can obtain the impact adiabatic line in the form of fluid medium pu:

[0033]

[0034] According to equation (14) and equation (6), after inputting the known incident shock wave pressure p1 in the fluid medium, the post-wave medium particle velocity u1 and the post-wave fluid medium density ρ1 of the incident shock wave in the fluid medium can be obtained. S2, calculate the post-wave state of the reflected shock wave in the fluid medium;

[0035] This step is used to calculate the reflected shock wave pressure p2 in the fluid medium, the velocity u2 of the medium particles after the wave, the density ρ2 of the fluid medium after the wave, the incident shock wave pressure p1 of the flat plate structure, and the velocity u1 of the medium particles after the wave and the density ρ1 of the fluid medium after the wave, given the incident shock wave pressure p1 in the fluid medium and the velocity u2 of the medium particles after the wave and the density ρ2 of the fluid medium after the wave, given the velocity u1 of the medium particles after the wave and the density ρ1 of the fluid medium after the wave, given ...1p1 and the velocity of the particles in the medium after the wave p1 .

[0036] After the incident shock wave in the fluid medium is reflected at the fluid-plate structure interface, a reflected shock wave is formed in the fluid medium. This reflected shock wave is loaded on the post-wave state of the incident shock wave, so it can be regarded as a secondary shock wave. For the reflected shock wave, its wavefront pressure and internal energy cannot be ignored. The reflected shock wave satisfies the following relationship:

[0037] ρ2(D2-u2)=ρ1(D2-u1) (15)

[0038] p2-p1=ρ1(D2-u1)(u2-u1) (16)

[0039] e2+p2v2+(D2-u2) 2 / 2=e1+p1v1+(D2-u1) 2 / 2 (17)

[0040] Wherein, the subscript “2” represents the post-wave state of the reflected shock wave in the fluid medium.

[0041] By rearranging equations (15) to (17), we can obtain the Hügoniot relation of the reflected shock wave:

[0042]

[0043] For condensed media, when the state equation is used as in equation (4), e2 and e1 are expressed using equation (4), and the state solution of the reflected shock wave p-ρ in the fluid medium is obtained by substituting it into equation (18):

[0044]

[0045] Where p* = ρ0c 01 2 is the characteristic pressure, and equation (19) can be used to derive the density ρ2 of the fluid medium behind the reflected shock wave.

[0046] Shock adiabatic line of pu form of reflected shock wave in fluid medium:

[0047]

[0048] According to the force balance and motion balance conditions at the fluid-plate structure interface, the state after the reflected shock wave in the fluid medium is equal to the state after the incident shock wave of the plate structure. In order to calculate the pu-type shock adiabatic line of the incident shock wave of the plate structure, it is necessary to replace the Hügoniot data c of the fluid in equation (14) with 01 and s1 is replaced by the solid Hügoniot data c02 and s2, that is:

[0049]

[0050] When solving the post-wave state of the reflected shock wave, the essence is to use the graphical method to solve the intersection of the fluid medium reflected shock wave curve expressed by equation (20) and the flat plate structure incident shock wave curve expressed by equation (21); the details are as follows:

[0051] First, according to formula (20), the pu curve of the reflected shock wave of the fluid medium with p2 and u2 as the wavefront state is obtained; then, according to formula (21), the pu curve of the incident shock wave of the flat plate structure with p1 and u1 as the wavefront state is obtained; finally, the intersection of the pu curve of the reflected shock wave with the wavefront state and the pu curve of the incident shock wave of the flat plate structure with p1 and u1 as the wavefront state is calculated, which is the pressure p2 of the reflected shock wave in the fluid medium and the pressure p of the incident shock wave of the flat plate structure. p1 And the velocity of the medium particle after the wave u2 and the velocity of the medium particle after the wave of the flat plate structure u p1 .

[0052] According to the force balance and motion balance conditions at the fluid-plate structure interface, the pressure p2 of the reflected shock wave in the fluid medium is equal to the incident shock wave pressure p of the plate structure. p1 , the velocity of the medium particle after the wave u2 is equal to the velocity of the medium particle after the wave of the flat plate structure u p1 According to formula (19), the density ρ2 of the fluid medium behind the reflected shock wave can be derived.

[0053] S3, calculate the rarefaction wave pressure p3 in the fluid medium caused by the motion of the flat plate structure;

[0054] This step is used to calculate the rarefaction wave pressure p3 in the fluid medium when S2 calculates the reflected shock wave pressure p2 in the fluid medium and its post-wave states ρ2 and u2.

[0055] The problem of the motion of a flat plate structure in a condensed medium can be simplified to the following one-dimensional problem: suppose there is a flat plate structure at position x = 0 in the pipe, the right side of the flat plate structure is air, and the semi-infinite pipe on the left is filled with high-pressure condensed medium, and its initial state is the post-wave state of the reflected shock wave, that is: p2, ρ2, c2, u2. Driven by the high-pressure condensed medium, the flat plate structure begins to move to the right at t = 0. Since the density of the flat plate structure is much greater than the air on the right, its right side can be assumed to be a vacuum state, and the flat plate structure is assumed to be a rigid body. Obviously, while moving to the right, the flat plate structure will propagate a sparse wave moving to the left into the condensed medium, which is called a backward sparse wave. The pressure of the backward sparse wave is p3, and its post-wave state is c3, u3, ρ3, e3. The subscript "3" represents the post-wave state of the sparse wave in the fluid medium. The post-wave particle velocity u3 of the sparse wave is equal to the motion velocity u of the flat plate. p .

[0056] Assume that the motion trajectory of the plate structure is:

[0057] x=x(t) (22)

[0058] Where x represents the displacement of the plate, and x(t) represents the function of displacement changing with time;

[0059] The Riemann invariant on the backward rarefaction wave is a constant value:

[0060]

[0061] When the condensed medium adopts the state equation as shown in equation (4), its isentropic state equation is:

[0062]

[0063] Among them, g(ρ,S) is the isentropic state equation, A(S) is a function of S, S is entropy, γ is a function related to the medium density ρ, when the subscript is 1, it means fluid medium, and when the subscript is 2, it means solid medium. The speed of sound c in the medium can be expressed as:

[0064]

[0065] Substituting equation (24) into (25), we can obtain the expressions of the medium sound velocity c2 after the reflected wave and the medium sound velocity c3 after the rarefaction wave:

[0066]

[0067] Combining equation (26) and equation (24), we can get:

[0068]

[0069] Substituting equation (27) into equation (23), we can solve the Riemann invariant expression of the backward rarefaction wave:

[0070]

[0071] Substituting equation (26) into equation (28), we obtain the backward sparse wave solution with p2,u2 as the wavefront state:

[0072]

[0073] Since rarefaction waves are simple waves, on the same isentropic line, we have:

[0074] A(S3)=A(S2) (31)

[0075] Among them, S2 is the entropy of the reflected shock wave, and S3 is the entropy of the rarefaction wave.

[0076] Substituting the isentropic state equation of the condensed medium (24) into (31), we obtain the pressure solution of the backward rarefaction wave:

[0077]

[0078] Substituting equation (33) into equation (30), we obtain the pu-form sparse wavefront state solution with p2,u2 as the wavefront state:

[0079]

[0080] Where p* = ρ0c 01 2 is the characteristic pressure. According to formula (34), after inputting the reflected shock wave pressure p2 and its post-wave state ρ2,u2 in the fluid medium calculated by S2, the post-wave state pressure p3 of the rarefaction wave in the fluid medium is obtained.

[0081] S4. Calculate the motion response of the plate structure;

[0082] Steps S1-S3 are used to calculate the reflected wave pressure p2, rarefaction wave pressure p3, incident shock wave velocity u1, and reflected shock wave velocity u2 in the fluid medium corresponding to the specific moment p1 when the incident wave pressure p1 at the specific moment is known.

[0083] In practical applications, the incident wave pressure p1 is often a load that is continuously distributed over time, that is, a function of time, called p1(t). Correspondingly, the reflected wave pressure and the rarefaction wave pressure should also be functions of time, p2(t) and p3(t), respectively. Therefore, the particle velocity after the incident shock wave, the particle velocity after the reflected shock wave, the particle velocity after the rarefaction wave, and the response speed of the air-back plate should also be functions of time, u1(t), u2(t), u3(t), u4(t), u5(t), u6(t), u7(t), u8(t), u9(t), u10(t), u11(t), u12(t), u13(t), u14(t), u15(t), u16(t), u17(t), u18(t), u19(t), u20(t), u31(t), u42(t), u53(t), u64(t), u7(t), u8(t), u9(t), u10(t), u11(t), u12(t), u13(t), u14(t), u15(t), u16(t), u17(t), u18(t), u19(t), u20(t), u31(t), u p (t). This step aims to calculate u3(t), u p (t) process and methods.

[0084] According to Newton's second law, the motion control equation of the flat plate structure can be written as:

[0085]

[0086] Where m is the mass per unit area of ​​the flat plate structure, m = hρ p , h is the thickness of the plate, ρ p is the density of the plate.

[0087] The velocity continuity condition at the interface between the fluid and the plate is:

[0088] u3(t)=u p (t) (36)

[0089] Since the incident shock wave pressure p1(t) at each time step is known, the reflected shock wave pressure p2(t) can be obtained from equations (20) and (21) as a function of the incident shock wave pressure p1(t), and the rarefaction wave pressure p3(t) can be obtained from equation (33) as a function of the reflected shock wave pressure p2(t) and the post-wave particle velocity u3(t) of the rarefaction wave, that is, the rarefaction wave pressure p3(t) is a function of the post-wave particle velocity u3(t) of the rarefaction wave and t. And since the plate starts to move at time 0, that is, u3(0) is 0, combining equations (34) and (35) yields:

[0090]

[0091] u′3(t) represents the derivative of u3(t), p3[u3,t] represents the independent variables of function p3 are u3 and t, u3(t) is a function that is continuously distributed over time, and the time t is divided into N equally spaced time intervals with an interval spacing (i.e., discrete time step) of Δt, forming a time series t n ,Right now:

[0092] t n =t n-1 +Δt (38)

[0093] Where n = 1, 2, ..., N. Determine the corresponding function value at each time point of the time series. Use the value of the original continuous function u3(t) at the time point to replace the discrete function The function value at this time point. That is, convert the continuous u3(t) into discrete

[0094] According to the numerical integration method Euler method and formula (36), the nth moment It can be solved by the following formula:

[0095]

[0096] in, is the particle velocity after the rarefaction wave at the nth moment, is the particle velocity after the rarefaction wave at the n-1th moment. From equation (39), we can see that each time we solve All need to be used According to the velocity continuity condition at the interface between the fluid and the plate, we know that u3(t) and u p (t) is equal, thus obtaining the motion speed u of the flat plate structure p (t), which is the motion response of the plate structure.

[0097] The beneficial effects of the present invention are:

[0098] The present invention combines the basic principles of fluid dynamics and replaces the acoustic linear assumption of incompressible fluid in Taylor's plate theory with the compressible state equation of matter. While considering the compressibility of the fluid and the plate structure, it also considers the influence of rarefaction wave propagation in the flow field on the motion of the plate structure. The present invention transforms the problem of solving the motion response of the plate structure into the problem of solving the differential equation. By numerically solving the differential equation, quantitative results can be calculated more efficiently and accurately, which can be used to guide underwater explosion testing and damage assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 Schematic diagram of the interaction process between the fluid shock wave and the flat plate structure: (a) indicates that the incident wave p1 is a right-moving wave; (b) indicates that the incident wave p1 will be reflected after interacting with the flat plate, forming a left-moving reflected wave p2. (c) indicates that the flat plate will move to the right under the action of the shock wave and emit a left-moving rarefaction wave p3;

[0100] Figure 2 Schematic diagram of high-pressure fluid driving the movement of a flat plate structure and generating rarefaction waves;

[0101] Figure 3 It is a schematic diagram of the PU graphical method for solving the pressure of the reflected wave of the fluid medium and the state after the wave;

[0102] Figure 4 It is a flow chart of a method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave according to the present invention;

[0103] Figure 5 The present invention provides a comparison of the theoretical solution of the flat plate response of a flat plate structure under the action of a fluid shock wave, the experimental test results and the finite element simulation solution with the incident wave pressure and the rarefaction wave pressure, wherein the theoretical solution is calculated by the method proposed by the present invention. DETAILED DESCRIPTION

[0104] The present invention will be further described below in conjunction with the accompanying drawings:

[0105] Figure 1 Schematic diagram of the interaction between the fluid shock wave and the flat plate structure: (a) indicates that the incident wave p1 is a right-moving wave; (b) indicates that the incident wave p1 will be reflected after interacting with the flat plate, forming a left-moving reflected wave p2; (c) indicates that the flat plate will move to the right under the action of the shock wave and emit a left-moving rarefaction wave p3; Explanation of symbols in the figure: p1 is the post-wave pressure of a shock wave, also expressed as p s ; p2 is the post-wave pressure of the secondary shock wave, which is the reflected secondary shock wave pressure p m The total pressure of the shock wave and the pressure p1 after the shock wave is also expressed as p r ; p3 is the total fluid-solid coupling pressure acting on the left side of the plate, which is composed of the reflected secondary shock wave pressure p2 and the rarefaction wave pressure p m The resultant pressure field; p m It is a rarefaction wave generated by the motion of the flat plate structure, and the propagation speed of the disturbance is D3.

[0106] Figure 2 Schematic diagram of high-pressure fluid driving the motion of a flat plate structure and generating a rarefaction wave: High-pressure fluid driving the motion of a flat plate structure will generate a backward rarefaction wave; Explanation of symbols in the figure: c3 is the sound velocity of the medium behind the rarefaction wave, z(t) is the motion trajectory of the flat plate, p3 is the rarefaction wave pressure, u p is the response speed of the air-back plate.

[0107] Figure 3 This is a schematic diagram of the PU graphical method for solving the reflected wave pressure of the fluid medium and the state after the wave: the intersection of the PU curve of the fluid medium and the PU curve of the reflected shock wave of the fluid medium is (u1, p1), and the intersection of the PU curve of the flat plate structure and the PU curve of the reflected shock wave of the fluid medium is (u2, p2); Explanation of symbols in the figure: u0 is the initial velocity of the fluid particle, u1 is the velocity of the medium particle after the incident wave, u2 is the velocity of the medium particle after the reflected wave, p0 is the initial pressure of the fluid medium, p1 is the pressure of the incident shock wave, and p2 is the pressure of the reflected shock wave.

[0108] The present invention is a method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave. The flow chart is as follows: Figure 4 As shown, the method comprises the following steps:

[0109] S1. Calculate the post-wave state of the incident shock wave in the fluid medium.

[0110] S2. Calculate the post-wave state of the reflected shock wave in the fluid medium

[0111] S3, calculate the rarefaction wave pressure p3 in the fluid medium caused by the motion of the flat plate structure;

[0112] S4. Calculate the motion response of the plate structure.

[0113] Example 1

[0114] According to the calculation equations of the motion response of the flat plate structure and the post-rarefaction state of the fluid and the values ​​of the model-related parameters of the present invention, the model theoretical data of four working conditions corresponding to the water hammer experiment of ballistic impact are calculated.

[0115] In this example, the thickness of the aluminum plate is h, which is 2 mm, and the density of the aluminum plate is ρ p 2.77 g·cm -3 , Hügoniot data for aluminum sheets c 02 5286 m·s -1 , the Hügoniot data s2 of the aluminum plate is 1.4, and the density of water ρ is 1 g·cm -3 , Hügoniot data for water c 01 1448 m·s -1 , the Hügoniot data s1 of water is 1.979.

[0116] Substitute various parameters into the calculation equation of the motion response of the flat plate structure and the state after the rarefaction wave of the fluid to obtain the theoretical data of the model. The comparison chart of the theoretical value and experimental value of the flat plate velocity of the flat plate structure under the action of the fluid shock wave and the comparison chart of the simulation value with the incident wave pressure and the rarefaction wave pressure are obtained by drawing with the drawing software origin, as shown in Figure 5 shown.

[0117] Figure 5 The two figures on the left show the time history curves of two incident shock waves p1(t), which are known input conditions; the corresponding rarefaction wave p3(t) is also shown. The two figures on the right show the response speed u of the air-back plate under the action of two known incident shock waves p1(t). p (t), the response displacement and response acceleration of the air-back plate can be respectively expressed as u p(t) is obtained by time integration and time differentiation. From the comparison results, comparing the rising stage of the plate velocity and the peak value of the velocity, the theoretical solution calculated by the method proposed in the present invention is very close to the experimental test results and the finite element simulation solution. It should be noted that the calculation method of the present invention is based on one-dimensional theory, so it is impossible to consider the attenuation and decline stage of the plate velocity. However, in engineering practices such as damage assessment, more attention is paid to the peak value of the plate velocity. Therefore, the calculation method of the present invention can meet the actual use requirements of engineering.

Claims

1. A method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave, characterized in that: The method comprises the following steps: S1. Calculate the post-wave state of the incident shock wave in the fluid medium; This step is used to calculate the post-wave medium particle velocity u1 and post-wave fluid medium density ρ1 of the incident shock wave in the fluid medium when the incident shock wave pressure p1 of the fluid is known; For the fluid medium that is only subjected to the incident shock wave loading, the conservation relation before and after the shock wave front is: ρ1(D1-u1)=ρ0(D1-u0) (1) p1-p0=ρ0(D1-u0) 2 -ρ1(D1-u1) 2 (2) Among them, the initial state is marked as "0", and the state after the incident shock wave in the fluid medium is marked as "1"; p is the pressure, u is the medium particle velocity, c is the medium wave velocity, ρ is the medium density, e is the internal energy, D is the shock wave velocity, and v is the specific volume of the medium, that is, the inverse of the medium density; For condensed media, the state equation can be adopted in the following form: Among them, c 01 is the initial medium sound velocity, is the Hügoniot data of the fluid medium; p2 is the pressure of the reflected shock wave, γ1 is the state equation parameter of the fluid medium, and γ2 is the state equation parameter of the solid medium; Substituting equation (4) into equation (3), we can obtain the impact adiabatic line of the fluid medium in the form of p-ρ: Substituting equation (1) into equation (2) and eliminating ρ0 or ρ1, we can obtain: Substitute equation (1) into equation (2) and eliminate (D1-u0) 2 or (D1-u1) 2 We can get: Multiplying equation (8) and equation (9) yields: After multiplying the two equations in equation (7), substitute equation (10) to obtain: (u1-u0) 2 =(p1-p0)(v0-v1) (10) The density of the fluid medium behind the incident shock wave can be deduced from formula (6): From formula (12), we can deduce: Substituting equation (13) and equation (6) into equation (11), we can obtain the impact adiabatic line in the form of fluid medium pu: According to equation (13) and equation (6), after inputting the known incident shock wave pressure p1 in the fluid medium, the post-wave medium particle velocity u1 and the post-wave fluid medium density ρ1 of the incident shock wave in the fluid medium can be obtained; S2, calculating the post-wave state of the reflected shock wave in the fluid medium; This step is used to calculate the reflected shock wave pressure p2 in the fluid medium, the velocity u2 of the medium particles after the wave, the density ρ2 of the fluid medium after the wave, the incident shock wave pressure p1 of the flat plate structure, and the velocity u1 of the medium particles after the wave and the density ρ1 of the fluid medium after the wave, given the incident shock wave pressure p1 in the fluid medium and the velocity u2 of the medium particles after the wave and the density ρ2 of the fluid medium after the wave, given the velocity u1 of the medium particles after the wave and the density ρ1 of the fluid medium after the wave, given ...1 p1 and the velocity of the particles in the medium after the wave p1 ; After the incident shock wave in the fluid medium is reflected at the fluid-plate structure interface, a reflected shock wave will be formed in the fluid medium; this reflected shock wave is loaded on the post-wave state of the incident shock wave, so it can be regarded as a secondary shock wave; for the reflected shock wave, its wavefront pressure and internal energy cannot be ignored; the reflected shock wave satisfies the following relationship: ρ2(D2-u2)=ρ1(D2-u1) (14) p2-p1=ρ1(D2-u1)(u2-u1) (15) <h2 style=";text-align:left;direction:ltr">e2+p2v2+(D2-u2)<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> / 2 = e1 + p1 v1 + (D2 - u1)<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> / 2 (16) In the formula, the subscript "2" represents the post-wave state of the reflected shock wave in the fluid medium; By rearranging equations (14) to (16), we can obtain the Hügoniot relation of the reflected shock wave: For condensed media, when the state equation is used as in equation (4), e2 and e1 are expressed using equation (4), and the state solution of the reflected shock wave p-ρ in the fluid medium is obtained by substituting it into equation (18): Where p* = ρ0c 01 2 is the characteristic pressure, and equation (18) can be used to derive the density of the fluid medium behind the reflected shock wave, ρ2; Shock adiabatic line of pu form of reflected shock wave in fluid medium: According to the force balance and motion balance conditions at the fluid-plate structure interface, the state of the reflected shock wave in the fluid medium is equal to the state of the incident shock wave in the plate structure. In order to calculate the pu-type shock adiabatic line of the incident shock wave of the plate structure, it is necessary to replace the Hügoniot data c of the fluid in equation (13) with 01 and s1 is replaced by the solid Hügoniot data c 02 and s2, that is: When solving the post-wave state of the reflected shock wave, the essence is to use the graphical method to solve the intersection of the fluid medium reflected shock wave curve expressed by equation (19) and the flat plate structure incident shock wave curve expressed by equation (21); According to the force balance and motion balance conditions at the fluid-plate structure interface, the pressure p2 of the reflected shock wave in the fluid medium is equal to the incident shock wave pressure p of the plate structure. p1 , the velocity of the medium particle after the wave u2 is equal to the velocity of the medium particle after the wave of the flat plate structure u p1 ; According to formula (18), the density of the fluid medium behind the reflected shock wave can be deduced as ρ2; S3, calculate the rarefaction wave pressure p3 in the fluid medium caused by the motion of the flat plate structure; This step is used to calculate the rarefaction wave pressure p3 in the fluid medium when S2 calculates the reflected shock wave pressure p2 in the fluid medium and its post-wave states ρ2 and u2; The problem of the motion of a flat plate structure in a condensed medium can be simplified to the following one-dimensional problem: suppose there is a flat plate structure at position x=0 in the pipe, the right side of the flat plate structure is air, and the semi-infinite pipe on the left is filled with high-pressure condensed medium, whose initial state is the post-wave state of the reflected shock wave, namely: p2, ρ2, c2, u2; the flat plate structure starts to move to the right at t=0 under the push of the high-pressure condensed medium; since the density of the flat plate structure is much greater than the air on the right side, its right side can be assumed to be a vacuum state, and the flat plate structure is assumed to be a rigid body; obviously, while moving to the right, the flat plate structure will propagate a rarefaction wave moving to the left into the condensed medium, which is called a backward rarefaction wave, and the pressure of the backward rarefaction wave is p3, and its post-wave state is c3, u3, ρ3, e3, and the subscript "3" represents the post-wave state of the rarefaction wave in the fluid medium; the post-wave particle velocity u3 of the rarefaction wave is equal to the motion velocity u of the flat plate p ; Assume that the motion trajectory of the plate structure is: x=x(t) (21) Where x represents the displacement of the plate, and x(t) represents the function of displacement changing with time; The Riemann invariant on the backward rarefaction wave is a constant value: When the condensed medium adopts the state equation as shown in equation (4), its isentropic state equation is: Among them, g(ρ,S) is the isentropic state equation, A(S) is a function of S, S is entropy, γ is a function related to the medium density ρ, when the subscript is 1, it means fluid medium, when the subscript is 2, it means solid medium; the sound speed c in the medium can be expressed as: Substituting equation (23) into (24), we can obtain the expressions of the medium sound velocity c2 after the reflected wave and the medium sound velocity c3 after the rarefaction wave: Combining equation (25) and equation (24), we can get: Substituting equation (27) into equation (22), we can solve the Riemann invariant expression of the backward rarefaction wave: Substituting equation (25) into equation (28), we obtain the backward sparse wave solution with p2,u2 as the wavefront state: Since rarefaction waves are simple waves, on the same isentropic line, we have: A(S3)=A(S2) (30) Among them, S2 is the entropy of the reflected shock wave, and S3 is the entropy of the rarefaction wave; Substituting the isentropic state equation of the condensed medium (23) into (30), we obtain the pressure solution of the backward rarefaction wave: Substituting equation (32) into equation (29), we can obtain the pu-form sparse wavefront state solution with p2,u2 as the wavefront state: Where p* = ρ0c 01 2 is the characteristic pressure; according to formula (33), after inputting the reflected shock wave pressure p2 and its post-wave state ρ2,u2 in the fluid medium calculated by S2, the post-wave state pressure p3 of the rarefaction wave in the fluid medium is obtained; S4. Calculate the motion response of the plate structure; Steps S1-S3 are used to calculate the reflected wave pressure p2, rarefaction wave pressure p3, incident shock wave velocity u1, and reflected shock wave velocity u2 in the fluid medium corresponding to the specific moment p1 when the incident wave pressure p1 is known; In practical applications, the incident wave pressure p1 is often a load that is continuously distributed over time, that is, a function of time, called p1(t); accordingly, the reflected wave pressure and the rarefaction wave pressure should also be functions of time, namely p2(t) and p3(t), respectively; therefore, the particle velocity after the incident shock wave, the particle velocity after the reflected shock wave, the particle velocity after the rarefaction wave, and the response speed of the air-back plate should also be functions of time, namely u1(t), u2(t), u3(t), u4(t), u5(t), u6(t), u7(t), u8(t), u9(t), u10(t), u11(t), u12(t), u13(t), u14(t), u15(t), u16(t), u17(t), u18(t), u19(t), u20(t), u31(t), u42(t), u53(t), u6(t), u7(t), u8(t), u9(t), u10(t), u11(t), u12(t), u13(t), u14(t), u15(t), u16(t), u17(t), u18(t), u19(t), u20(t), u31(t), u p (t); According to Newton's second law, the motion control equation of the flat plate structure can be written as: Where m is the mass per unit area of ​​the flat plate structure, m = hρ p , h is the thickness of the plate, ρ p is the density of the plate; The velocity continuity condition at the interface between the fluid and the plate is: u3(t)=u p (t) (35) Since the incident shock wave pressure p1(t) at each time step is known, the reflected shock wave pressure p2(t) can be obtained from equations (20) and (21) as a function of the incident shock wave pressure p1(t), and the rarefaction wave pressure p3(t) can be obtained from equation (33) as a function of the reflected shock wave pressure p2(t) and the post-wave particle velocity u3(t) of the rarefaction wave, that is, the rarefaction wave pressure p3(t) is a function of the post-wave particle velocity u3(t) of the rarefaction wave and t; and since the plate starts to move at time 0, that is, u3(0) is 0, combining equations (34) and (35) yields: u′3(t) represents the derivative of u3(t), p3[u3,t] represents the independent variables of function p3 are u3 and t, u3(t) is a function that is continuously distributed over time, and the time t is divided into N equally spaced time intervals with a spacing of Δt, forming a time series t n ,Right now: t n =t n-1 +Δt (37) Where n = 1, 2, ..., N; determine the corresponding function value at each time point of the time series; use the value of the original continuous function u3(t) at the time point to replace the discrete function The function value at this time point, that is, converting the continuous u3(t) into discrete According to Euler numerical integration method and formula (36), at the nth moment It can be solved by the following formula: in, is the particle velocity after the rarefaction wave at the nth moment, is the particle velocity after the rarefaction wave at the n-1th moment; From formula (39), we can see that each time we solve All need to be used According to the velocity continuity condition at the interface between the fluid and the plate, we know that u3(t) and u p (t) is equal, thus obtaining the motion speed u of the flat plate structure p (t), which is the motion response of the plate structure.

2. The method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave according to claim 1, characterized in that: Initial medium sound velocity c 01 It can be obtained by referring to "Introduction to Theory and Computation of Physical Equations (2nd Edition)" by Tang Wenhui et al.

3. The method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave according to claim 1, characterized in that: The state equation parameter γ1 of the fluid medium and the state equation parameter γ2 of the solid medium are expressed in the form of Hügoniot data as parameters: Where s1 is the Hügoniot data of the fluid medium, s2 is the Hügoniot data of the solid medium, and ρ p is the initial solid density, ρ p1 is the solid density after the incident shock wave.

4. The method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave according to claim 3, characterized in that: The Hügoniot data s1 of the fluid medium and the Hügoniot data s2 of the solid medium can be obtained by referring to the book "Introduction to the Theory and Computation of Physical Equations (2nd Edition)" written by Tang Wenhui et al.

5. The method for calculating the motion response of an air-backed flat plate structure under the action of a fluid shock wave according to any one of claims 1 to 4, characterized in that: When solving the post-wave state of the reflected shock wave, the process of using the graphical method to solve the intersection of the fluid medium reflected shock wave curve expressed by equation (19) and the flat plate structure incident shock wave curve expressed by equation (21) is as follows: First, according to formula (19), the pu curve of the reflected shock wave of the fluid medium with p2 and u2 as the wavefront state is obtained; then, according to formula (21), the pu curve of the incident shock wave of the flat plate structure with p1 and u1 as the wavefront state is obtained; finally, the intersection of the pu curve of the reflected shock wave with the wavefront state and the pu curve of the incident shock wave of the flat plate structure with p1 and u1 as the wavefront state is calculated, which is the pressure p2 of the reflected shock wave in the fluid medium and the pressure p of the incident shock wave of the flat plate structure. p1 And the velocity of the medium particle after the wave u2 and the velocity of the medium particle after the wave of the flat plate structure u p1 .

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