Application of Legendre orthogonal polynomial method in calculating reflection and transmission coefficients of multilayer plates

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.