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A new method based on Legendre orthogonal polynomials method (LOPM) is proposed to calculate the acoustic reflection and transmission coefficients at liquid/solid interfaces. The displacement solutions of each layer in a multilayer plate are fitted approximately by multiple groups of Legendre orthogonal polynomials. The stress components and the governing wave equations in the plate are derived. Reassembling the boundary conditions of liquid/solid interfaces, solid/solid interfaces and governing wave equations, the linear independent equations are established to calculate the reflection and transmission coefficients and the expansion coefficients of Legendre polynomials in displacement solutions. The transfer matrix method (TMM) is used to verify the accuracy of this proposed method. The relationship between reflection and transmission coefficients with oblique incident angles and frequencies is discussed. The influence of the polynomial cut-off order on the calculation results is analyzed, and the displacement and stress profiles in multilayer plate are reconstructed. The research extends the applicable range of LOPM, moreover, lays the foundation of non-destructive testing and inversion of mechanical properties and bonding quality of the multilayer structures by acoustic waves.

In this research, a numerical approach for analyzing the analytical solution of guided wave propagation characteristics in multilayer two-phased porous media is presented. Combing the global matrix method and Biot theory, and introducing the modulus-porosity-poisson’s ratio relation, the global dispersion equations of multi-layered porous materials are established. Also, the complex boundary conditions in multi-layered two-phase porous media are considered simultaneously. In order to confirm the feasibility and accuracy of the proposed method, the dispersion curves of the guided waves propagation in a single-layer porous graphite layer and a triple-layer graphite/copper/graphite model (porosity close to 0) were numerically calculated. The results were compared with the propagation characteristics of the guided waves in the corresponding stacked sequential laminates without porosity, which is done by the state-vector formalism and the Legendre polynomials method based on our previous work. Then, this approach is further applied to lithium ion battery. The change of porosity in graphite is used to simulate the state of charge of lithium-ion battery. The influence of porosity change on mode coupling effect of guided waves is analyzed, and the mapping relationship between porosity and corresponding dispersion curves is explored. Meanwhile, the research shows that, with the decrease of porosity (which means the state of charge increases), the phase velocity of the fundamental modes gradually increases, making the corresponding time of flight decrease gradually. Moreover, the theoretical model captures a meaningful relationship between state of charge and acoustic behavior. It gives theoretical support for nondestructive evaluation and quantitative estimation of the state characteristics of lithium-ion batteries.