Single-phase medium nonlinear metasurface schottky wave dispersion relation calculation method and system

Abstract

This invention relates to the field of physical acoustics, and in particular to a method and system for calculating the dispersion relation of Schulte waves on a single-phase medium nonlinear metasurface. The method includes the following steps: obtaining expressions for the displacement and stress components of the single-phase medium under the action of a Schulte wave; obtaining expressions for the fluid displacement component and the fluid normal stress, as well as expressions for the relative motion of the resonator; based on all expressions, applying stress and displacement continuity boundary conditions at the interface between the single-phase medium and the fluid layer to obtain the characteristic equation of the dispersion characteristics of the coupled system, solving it, and finally obtaining the dispersion curve of the coupled system. This invention improves the computational efficiency and prediction accuracy of wave propagation at the interface of a single-phase medium nonlinear metasurface by providing an explicit dispersion relation for Schulte waves on a single-phase medium nonlinear metasurface, which is beneficial for reducing the computational cost and design cycle of acoustic metasurface design, vibration suppression, and waveguide control.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of physical acoustics, in particular to a single-phase medium nonlinear super-surface Scholte wave dispersion relation calculation method and system. BACKGROUND

[0002] Scholte-Stoneley waves are a general term for a type of elastic guided wave existing at the interface of two closely contacting media. Among them, the one propagating at the fluid-solid interface (such as the seabed) is called Scholte wave, which is a special case of Stoneley wave in the fluid-solid case. This type of wave propagates along the interface, and the energy is concentrated near the interface, and its amplitude decays exponentially in the direction perpendicular to the interface.

[0003] In acoustic detection, underwater sensing and seismic engineering applications, accurate control and prediction of the propagation behavior of interface waves are the key to improving equipment performance and structural safety. However, the description of the coupling mechanism of Scholte wave and surface resonant array in the prior art is still not perfect, especially in the single-phase elastic medium-fluid interface system involved in actual engineering, there is generally a lack of efficient and reliable coupled dynamic model. This leads to a serious dependence on empirical trial and error or large-scale numerical simulation in the design of acoustic super-surface, vibration suppression and waveguide regulation, resulting in high computational cost, long design cycle and difficulty in ensuring accuracy. Therefore, it is necessary to explore a method for efficiently and accurately calculating the dispersion relation of nonlinear super-surface Scholte wave on single-phase medium. SUMMARY

[0004] In view of the defects in the prior art, the present application provides a single-phase medium nonlinear super-surface Scholte wave dispersion relation calculation method and system.

[0005] In order to achieve the above-mentioned purpose, in a first aspect, the present application provides a single-phase medium nonlinear super-surface Scholte wave dispersion relation calculation method, which comprises the following steps: obtaining the expressions of displacement components and stress components of single-phase medium under the action of Scholte wave based on linear elastic dynamics theory and Helmholtz vector decomposition theorem; obtaining the expressions of fluid displacement components and fluid normal stress based on the basic control equations of fluid dynamics, and obtaining the expression of relative motion of discrete mass nonlinear spring resonator based on Newton's second law; based on all the expressions, stress and displacement continuity boundary conditions are applied at the interface between single-phase medium and fluid layer, and then the characteristic equation of the dispersion characteristics of the coupled system is obtained; the wave number and frequency in the characteristic equation are solved by using a numerical method, and finally the dispersion curve of the coupled system is obtained. By providing the explicit dispersion relation of single-phase medium nonlinear super-surface Scholte wave, the calculation efficiency and prediction accuracy of the propagation of nonlinear super-surface interface waves on single-phase medium are improved, which is beneficial to reduce the computational cost and design cycle of acoustic super-surface design, vibration suppression and waveguide regulation.

[0006] Optionally, the expression of displacement component and stress component of single-phase medium under the action of Scholte wave is obtained based on the theory of linear elasticity dynamics and Helmholtz vector decomposition theorem, and comprises the following steps:

[0007] According to the theory of linear elasticity dynamics, a motion control equation in single-phase medium is established under the condition of no body force;

[0008] The displacement field is decomposed into a combination of scalar potential and vector potential using Helmholtz decomposition theorem to obtain a basic expression of displacement component;

[0009] According to the basic expression of displacement component and the motion control equation, a wave equation for decoupling P wave and S wave is obtained;

[0010] When a harmonic wave propagates along the interface, according to the wave equation and the basic expression, the expression of displacement component and stress component of single-phase medium under the action of Scholte wave is obtained.

[0011] Optionally, the expression of displacement component is:

[0012]

[0013] wherein, is the displacement component in the X-axis direction, x and z are spatial coordinates, i is an imaginary unit, k is a wave number, A and B are amplitude values, and are reference symbols, , , is the velocity of P wave in single-phase medium, is the velocity of S wave in single-phase medium, is an angular frequency, and t is time, is the displacement component in the Z-axis direction.

[0014] Optionally, the expression of stress component is:

[0015]

[0016] wherein, is a normal stress component, is the displacement component in the X-axis direction, x and z are spatial coordinates, i is an imaginary unit, k is a wave number, A and B are amplitude values, and are reference symbols, is an angular frequency, and t is time, is the displacement component in the Z-axis direction, and are Lame constants, is a tangential stress component.

[0017] Optionally, the expression of the fluid displacement component and the fluid normal stress is obtained according to the basic governing equation of fluid dynamics, and the expression of the relative motion of the discrete mass nonlinear spring resonator is obtained based on Newton's second law, including the following steps:

[0018] For the incompressible acoustic fluid, the scalar potential function is introduced to describe the fluid motion according to the basic governing equation of fluid dynamics, and then the expression of the fluid displacement component and the fluid normal stress is obtained;

[0019] Based on Newton's second law, the expression of the relative motion of the discrete mass nonlinear spring resonator is obtained by considering the nonlinear stiffness of the spring.

[0020] Optionally, the expression of the relative motion of the discrete mass nonlinear spring resonator is obtained based on Newton's second law by considering the nonlinear stiffness of the spring, including the following steps:

[0021] For the discrete mass nonlinear spring resonator arranged at the interface between the single-phase medium and the fluid layer, the dynamic balance equation of the resonator is established according to Newton's second law by considering the nonlinear stiffness of the spring;

[0022] The nonlinear term in the dynamic balance equation is processed by using the first harmonic balance method, and the expression of the relative motion of the discrete mass nonlinear spring resonator is obtained.

[0023] Optionally, the expression of the relative motion of the discrete mass nonlinear spring resonator is:

[0024]

[0025] wherein, is the mass of the discrete mass nonlinear spring resonator, is a symbol, is the amplitude of the excitation source, is the angular frequency, Y is the harmonic amplitude, i is the imaginary unit, and k is the wave number, is the natural frequency of the discrete mass nonlinear spring resonator, is the nonlinear coefficient, A and B are amplitudes, is a symbol.

[0026] Optionally, when the fluid layer has a finite thickness, the characteristic equation is:

[0027]

[0028] wherein, are symbols, , , , , is a reference symbol, is an excitation source amplitude, is a fluid layer thickness, is a unit area of the discrete mass nonlinear spring resonator, and is a reference symbol, is a parameter related to wave number and fluid pressure wave speed, is an angular frequency, is a fluid pressure wave speed, is a mass of the discrete mass nonlinear spring resonator, A and B are amplitudes, is a fluid density, k is a wave number, is a Lame constant, i is an imaginary unit, and is an amplitude, Y is a harmonic amplitude.

[0029] Optionally, when the fluid layer is a semi-infinite space, the characteristic equation is:

[0030]

[0031] wherein, are reference symbols, , , , , is a reference symbol, is an excitation source amplitude, is a unit area of the discrete mass nonlinear spring resonator, and is a reference symbol, is a parameter related to wave number and fluid pressure wave speed, is an angular frequency, is a fluid pressure wave speed, is a mass of the discrete mass nonlinear spring resonator, A and B are amplitudes, is a fluid density, k is a wave number in the X-axis direction, is a Lame constant, i is an imaginary unit, is an amplitude, Y is a harmonic amplitude.

[0032] In a second aspect, the present application provides a single-phase medium nonlinear metasurface Scholte wave dispersion relation calculation system, which comprises a data acquisition device, a data output device, a processor and a storage, the storage comprising a computer readable storage medium, the computer readable storage medium storing a computer program, the computer program comprising program instructions, the program instructions enabling the processor to implement the single-phase medium nonlinear metasurface Scholte wave dispersion relation calculation method provided by the present application when executed by the processor.

[0033] The present application has at least the following beneficial effects:

[0034] 1. The present application establishes an explicit dispersion relation model of the single-phase medium nonlinear metasurface Scholte wave, and realizes closed analytical characterization of the dispersion characteristics of the system.

[0035] 2. The dispersion relation model constructed can accurately reveal the hybridization mechanism of the fundamental mode near the collective resonance frequency and the physical phenomenon of surface wave leakage to the fluid domain, and improves the prediction efficiency and accuracy of the dynamic behavior of the coupled system, providing a reliable theoretical basis and design tool for the design of high-performance acoustic metasurfaces, vibration reduction devices and wave control equipment.

[0036] 3. The present application provides a system adapted to the method, thereby improving the practicability of the present application and facilitating the popularization of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor.

[0038] Figure 1 The flowchart of the single-phase medium nonlinear metasurface Scholte wave dispersion relation calculation method of the present application;

[0039] Figure 2 The dispersion curves of the hardening and softening nonlinear metasurfaces corresponding to the fluid layer with a finite thickness;

[0040] Figure 3 The dispersion curves of the hardening and softening nonlinear metasurfaces corresponding to the fluid layer with a semi-infinite space;

[0041] Figure 4 The flowchart of the single-phase medium nonlinear metasurface Scholte wave dispersion relation calculation method of the present application. DETAILED DESCRIPTION

[0042] Specific embodiments of the present application will now be described in detail with reference to the drawings, like numbers refer to like elements throughout. Specific details are given in the following description to provide a thorough understanding of the application. However, well-known principles, software or methodologies do not have to be enumerated here in detail in order to fully understand the present application. In other instances, well-known circuits, software or methodologies have not been shown in order to avoid obscuring the present application.

[0043] Reference throughout this specification to "one embodiment", "an embodiment", "one example" or "an example" means that a particular feature, structure, or characteristic described in connection with the embodiment or example is included in at least one embodiment of the application. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" or "one example" or "an example" in various places throughout this specification are not necessarily referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics can be combined in any suitable

[0044] It is noted that, in an alternative embodiment, the same symbols or letters appearing in all formulas have the same meaning and values, except where otherwise noted.

[0045] In an alternative embodiment, see Figure 1 The present application provides a method for calculating the dispersion relation of single-phase medium nonlinear metasurface Scholte wave, which comprises the following steps:

[0046] S1, based on the linear elasticity dynamics theory and Helmholtz vector decomposition theorem, the expression of displacement component and stress component of single-phase medium under the action of Scholte wave is obtained.

[0047] Specifically, step S1 comprises the following steps:

[0048] S11, according to the linear elasticity dynamics theory, the motion control equation in single-phase medium under the condition of no body force is established.

[0049] Specifically, in this embodiment, the control motion equation in single-phase medium under the condition of no body force can be written as:

[0050]

[0051] wherein, and is the Lame constant, is the gradient operator, , is the displacement field, and are the displacement components in the X-axis and Z-axis directions respectively, t is time, is the density of the single-phase medium. In the embodiment, the density of the single-phase medium is the density of soil particles.

[0052] S12, the displacement field is decomposed into a combination of scalar potential and vector potential using Helmholtz decomposition theorem to obtain a basic expression of the displacement components.

[0053] Specifically, in the embodiment, the displacement field is decomposed using Helmholtz decomposition theorem , and the basic expression of the displacement components is:

[0054]

[0055] wherein, and are the scalar potential and the vector potential respectively, x and z are the horizontal and vertical coordinates respectively, is the Y-axis component of the vector potential.

[0056] S13, a wave equation decoupling P wave and S wave is obtained according to the basic expression of the displacement components and the motion control equation.

[0057] Specifically, in the embodiment, the formula in step S12 is brought into the motion control equation in step S11 to obtain a wave equation decoupling P wave and S wave, that is:

[0058]

[0059]

[0060] wherein, and are the velocities of P wave and S wave in the single-phase medium respectively, , .

[0061] S14, when the harmonic wave propagates along the interface, expressions of the displacement components and the stress components of the single-phase medium under the action of Scholte wave are obtained according to the wave equation and the basic expression.

[0062] Specifically, in the embodiment, when the harmonic wave propagates along the interface, that is, propagates along the X-axis direction, the potential function can be selected as:

[0063]

[0064]

[0065] wherein, A and B are amplitude values, is the angular frequency, k is the wave number, A and B represent the amplitude, i is the imaginary unit, and is a reference symbol set for the convenience of writing, , .

[0066] The displacement component of the single-phase medium under the action of the Scholte wave can be obtained by combining the relationship given in step S12 as follows:

[0067]

[0068] The stress component in the single-phase medium is obtained according to the linear elasticity, isotropy and constitutive law, and is specifically as follows:

[0069]

[0070] wherein, is the normal stress component, is the tangential stress component.

[0071] S2, obtaining expressions of fluid displacement component and fluid normal stress based on basic control equations of fluid dynamics, and obtaining expressions of relative motion of discrete mass nonlinear spring resonator based on Newton's second law.

[0072] Specifically, step S2 includes the following steps.

[0073] S21, for a non-viscous acoustic fluid, introducing a scalar potential function to describe fluid motion according to basic control equations of fluid dynamics, and then obtaining expressions of fluid displacement component and fluid normal stress.

[0074] Specifically, in the embodiment, for a non-viscous acoustic fluid, its control equation satisfies:

[0075]

[0076] wherein, is the bulk modulus of the non-viscous fluid, , is the fluid density, is the fluid pressure wave velocity, is the fluid displacement vector, , is the fluid displacement component in the X-axis direction, is the fluid displacement component in the Z-axis direction.

[0077] By introducing a scalar potential , , the control equation of the non-viscous acoustic fluid can be written as:

[0078]

[0079] Under the harmonic propagation, the scalar potential in the fluid layer is assumed as:

[0080]

[0081] where, and are amplitudes, is a parameter related to the wave number and the fluid pressure wave velocity, . Substituting this into , the expression of the fluid displacement component is:

[0082]

[0083] Given the fluid-single phase medium coupling, the expression of the fluid normal stress is derived as follows:

[0084]

[0085] where, is the fluid normal stress.

[0086] S22, based on Newton's second law, considering the nonlinear stiffness of the spring, obtaining the expression about the relative motion of the discrete mass nonlinear spring resonator.

[0087] Wherein, step S22 specifically includes the following steps:

[0088] S221, for the discrete mass nonlinear spring resonator arranged at the interface between the single phase medium and the fluid layer, considering the nonlinear stiffness of the spring, establishing its dynamic balance equation according to Newton's second law.

[0089] Specifically, in this embodiment, considering the dynamic balance equation of the discrete mass nonlinear spring resonator coupled to the interface between the single phase medium and the fluid layer is:

[0090]

[0091] Wherein, is the mass of the discrete mass nonlinear spring resonator, is the linear stiffness of the spring, is the nonlinear stiffness of the spring, represents the second derivative of y, y represents the mass displacement of the discrete mass nonlinear spring resonator and the relative motion between the vertical displacement of the single phase medium free surface . .

[0092] The vertical displacement of the single phase medium free surface satisfies the following relationship:

[0093]

[0094] wherein, is the excitation source amplitude, .

[0095] Assuming the relative motion of the resonator The harmonic solution expression form of the resonator is:

[0096]

[0097] wherein, Y is the harmonic amplitude.

[0098] The dynamic balance equation can be written in the following form:

[0099]

[0100] S222, the nonlinear term in the dynamic balance equation is processed by using the first harmonic balance method, to obtain an expression about the relative motion of the discrete mass nonlinear spring resonator.

[0101] Specifically, in the embodiment, the Euler formula and the first harmonic balance method are used to approximately ignore the low-frequency harmonics generated by nonlinearity, and the dynamic balance equation can be converted into the following expression about the relative motion of the discrete mass nonlinear spring resonator:

[0102]

[0103] wherein, is a reference symbol, is the natural frequency of the discrete mass nonlinear spring resonator, , is a nonlinear coefficient, It can be found that when , the discrete mass nonlinear spring resonator degenerates into a linear one.

[0104] S3, based on all the expressions, stress and displacement continuity boundary conditions are applied at the interface between the single-phase medium and the fluid layer, and then a characteristic equation of the dispersion characteristics of the coupled system is obtained.

[0105] Specifically, in the embodiment, based on the analysis of steps S1 and S2, when the fluid layer has a finite thickness, the Scholte wave dispersion relationship of the nonlinear super surface on the single-phase medium can be obtained by performing a first group of boundary conditions, and the first group of boundary conditions is:

[0106]

[0107] wherein, for the fluid layer thickness, for the resonator stress.

[0108] Since the fluid does not support shear stress, at its free surface only the first boundary condition in the first set of boundary conditions is satisfied, i.e. At the single-phase medium-fluid interface z = 0, the continuity of the normal stress and the vertical displacement is imposed. The first set of boundary conditions neglects any direct kinematic coupling between the resonator and the fluid. This simplification is justified when the size of the discrete mass nonlinear spring resonator is significantly smaller than the Scholte wave wavelength.

[0109] Substituting the expressions for the single-phase medium displacement component, the single-phase medium stress component, the fluid displacement component, the fluid normal stress, and the discrete mass nonlinear spring resonator relative motion into the first set of boundary conditions, the characteristic equation for the dispersion properties of the coupled system composed of the single-phase medium, the fluid, and the discrete mass nonlinear spring resonator for a finite thickness of the fluid layer can be obtained, which is in the matrix form:

[0110]

[0111] where, are all place holders, , , , , is the unit area of the discrete mass nonlinear spring resonator.

[0112] When the fluid layer is a semi-infinite space, i.e. in this case the body can be modeled as a half-space, and the scalar potential in the fluid layer can be rewritten by assuming to avoid the unbounded solution of

[0113]

[0114] Therefore, the relevant dispersion relation can be obtained by simplifying the first set of boundary conditions, which are as follows:

[0115]

[0116] Substituting the expressions for the single-phase medium displacement component, the single-phase medium stress component, the fluid displacement component, the fluid normal stress, and the discrete mass nonlinear spring resonator relative motion into the simplified boundary conditions, the characteristic equation for the dispersion properties of the coupled system composed of the single-phase medium, the fluid, and the discrete mass nonlinear spring resonator for a semi-infinite space of the fluid layer can be obtained, which is in the matrix form: ​

[0117]

[0118] S4, solving the wave number and frequency in the characteristic equation by using numerical method, and finally obtaining the dispersion curve of the coupling system.

[0119] Specifically, in the present embodiment, for the characteristic equation when the fluid layer is of finite thickness, a non-zero solution is found by imposing that the determinant of a 6x6 matrix is equal to zero , and the dispersion curve of the Scholte wave interacting with the metasurface located at the interface between the fluid layer and the single-phase medium half-space, i.e., the relationship curve of k and , is derived. Since the analytical solution of the system is not easy to obtain, Newton iteration method is used to calculate the root. Similarly, for the characteristic equation when the fluid layer is of semi-infinite space, a non-zero solution is found by imposing that the determinant of a 5x5 matrix is equal to zero , and the corresponding dispersion curve is obtained.

[0120] Further, for the hardening and softening nonlinear metasurfaces, the parameter settings when obtaining the dispersion curve are shown in Table 1.

[0121] Table 1 Parameter settings

[0122]

[0123] When the fluid layer is of finite thickness, the dispersion curves of the hardening and softening nonlinear metasurfaces are shown in (a) and (b) of Figure 2 , respectively. It can be found that due to the effect of the nonlinear resonator, two branches are generated and the Scholte wave velocity is less than the shear wave velocity; for the hardening nonlinear metasurface, the upper branch generates three branches, and part of the wave solution is less than the fluid wave velocity, while the lower branch wave solution frequency is expected to exceed the inherent frequency of the resonator; for the softening nonlinear metasurface, the upper branch generates two branches, one of which is lower than the inherent frequency of the resonator, and the lower branch wave solution is always lower than the inherent frequency of the resonator.

[0124] When the fluid layer is of semi-infinite space, the dispersion curves of the hardening and softening nonlinear metasurfaces are shown in (a) and (b) of Figure 3 , respectively. At this time, the nonlinear resonator also causes the dispersion curve to be divided into two branches, and the Scholte wave velocity is less than the fluid pressure wave velocity. For the hardening nonlinear metasurface, the starting frequency of the upper branch is higher than the inherent frequency of the resonator and intersects with the fluid pressure wave velocity; while the wave solution frequency of the lower branch exceeds the inherent frequency of the resonator. In the softening nonlinear metasurface, the starting frequency of the upper branch is almost equal to the inherent frequency of the resonator, and the wave solution frequency of the lower branch is always lower than the inherent frequency.

[0125] It should be noted that in some cases, the actions described in the specification can be performed in different order and still achieve the desired result, in the present embodiment, the order of the steps given is merely to make the embodiment look clearer and more convenient to explain, not to limit it.

[0126] In an alternative embodiment, referring to Figure 4 In order to improve the practicability of the method and facilitate the popularization of the method, the present application further provides a single-phase medium nonlinear super surface Schottky wave dispersion relation calculation system, which comprises a data acquisition device 1, a data output device 2, a processor 3 and a storage 4, the storage 4 comprises a computer readable storage medium, the computer readable storage medium stores a computer program, the computer program comprises program instructions, the program instructions make the processor 3 realize the contents of steps S1 to S4 when the processor 3 executes the program instructions.

[0127] In summary, the present application has at least the following beneficial effects: the present application establishes an explicit dispersion relation model of single-phase medium nonlinear super surface Schottky wave, realizes closed analytical characterization of system dispersion characteristics; the dispersion relation model constructed can accurately reveal the hybridization mechanism of the fundamental mode near the collective resonance frequency and the physical phenomenon of surface wave leakage to the fluid domain, improve the prediction efficiency and accuracy of the coupled system dynamics, and provide a reliable theoretical basis and design tool for the design of high-performance acoustic super surface, vibration reduction device and wave control equipment; a system adapted to the method is provided, thereby improving the practicability of the method and facilitating the popularization of the method.

[0128] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the specification of the present application.

Claims

1. A method for calculating the Schottky wave dispersion relation of a single-phase medium nonlinear metasurface, characterized in that, The method comprises the following steps: According to the theory of linear elasticity dynamics, the motion control equation in single-phase medium is established under the condition of no body force; The displacement field is decomposed into the combination form of scalar potential and vector potential by using Helmholtz decomposition theorem, and the basic expression of displacement component is obtained; According to the basic expression of displacement component and the motion control equation, the wave equation of P wave and S wave decoupling is obtained; When the harmonic wave propagates along the interface, according to the wave equation and the basic expression, the expressions of displacement component and stress component of single-phase medium under the action of Scholte wave are obtained; For the incompressible acoustic fluid, the scalar potential function is introduced to describe the fluid motion according to the basic control equation of fluid dynamics, and then the expressions of fluid displacement component and fluid normal stress are obtained; For the discrete mass nonlinear spring resonator arranged at the interface between single-phase medium and fluid layer, the nonlinear stiffness of the spring is considered, and the dynamic equilibrium equation of the resonator is established according to Newton's second law; The nonlinear term in the dynamic equilibrium equation is processed by using the first harmonic balance method, and the expression of relative motion of the discrete mass nonlinear spring resonator is obtained; The expression of relative motion of the discrete mass nonlinear spring resonator is: wherein, is the mass of the discrete mass nonlinear spring resonator, is a reference symbol, is the excitation source amplitude, is the angular frequency, Y is the harmonic amplitude, and i is the imaginary unit, is the wave number, is the natural frequency of the discrete mass nonlinear spring resonator, is the nonlinear coefficient, A and B are amplitudes, is a reference symbol; Based on all the expressions, the stress and displacement continuity boundary conditions are applied at the interface between single-phase medium and fluid layer, and then the characteristic equation of the dispersion characteristics of the coupled system is obtained; The wave number and frequency in the characteristic equation are solved by using numerical method, and finally the dispersion curve of the coupled system is obtained.

2. The method of claim 1, wherein the single-phase medium nonlinear metasurface SPOD relation is calculated by, The expression of displacement component is: wherein, is the displacement component in the x-axis direction, x and z are spatial coordinates, and i is an imaginary unit, is the wave number, and A and B are amplitude values, and is a reference symbol, , , is the velocity of a P wave in a single medium, is the velocity of an S wave in a single medium, is an angular frequency, and t is time, is the displacement component in the z-axis direction.

3. The method of claim 1, wherein the single-phase medium nonlinear metasurface SPOD relation is calculated by, The expression of stress component is: wherein, is the normal stress component, is the displacement component in the x-axis direction, x and z are spatial coordinates, i is the imaginary unit, is the wave number, A and B are the amplitude, and is the reference symbol, is the angular frequency, t is time, is the displacement component in the z-axis direction, and is the Lame constant, is the tangential stress component.

4. The method of claim 1, wherein the single-phase medium nonlinear metasurface SPOD relation is calculated by, When the fluid layer is of finite thickness, the characteristic equation is: wherein are reference symbols, , , , , are reference symbols, is the excitation source amplitude, is the fluid layer thickness, is the unit area of the discrete mass nonlinear spring resonator, and are reference symbols, is a parameter related to the wave number and the fluid pressure wave speed, is the angular frequency, is the fluid pressure wave speed, is the mass of the discrete mass nonlinear spring resonator, A and B are the amplitudes, is the fluid density, is the wave number, is the Lame constant, i is the imaginary unit, and is the amplitude, Y is the harmonic amplitude.

5. The method of claim 1, wherein the single-phase medium nonlinear metasurface SPOD relation is calculated by, When the fluid layer is of semi-infinite space, the characteristic equation is: wherein are reference symbols, , , , , are reference symbols, is the excitation source amplitude, is the unit area of the discrete mass nonlinear spring resonator, and are reference symbols, is a parameter related to the wave number and the fluid pressure wave speed, is the angular frequency, is the fluid pressure wave speed, is the mass of the discrete mass nonlinear spring resonator, A and B are the amplitudes, is the fluid density, is the wave number of the wave in the X-axis direction, is the Lame constant, i is the imaginary unit, is the amplitude, Y is the harmonic amplitude.

6. A system for calculating the Schottky wave dispersion relation of a single-phase medium nonlinear metasurface, characterized in that, The single-phase medium nonlinear metasurface Scholte wave dispersion relation calculation system comprises a data acquisition device, a data output device, a processor and a storage, the storage comprises a computer readable storage medium, the computer readable storage medium stores a computer program, the computer program comprises program instructions, and the program instructions enable the processor to realize the single-phase medium nonlinear metasurface Scholte wave dispersion relation calculation method according to any one of claims 1-5 when executed by the processor.

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