Study on Propagation Characteristics of Guided Waves in Plate Structure via Semianalytical Wavelet Finite Element Method

Abstract

The propagation characteristics of guided wave in waveguide structure plays an indispensable role in guided wave inspection. However, the analytical matrix method fails to solve the problems of wave propagation in waveguides with complex cross-section. The finite element method (FEM) has high computational cost for guided wave propagation problems. To overcome those shortcomings, a novel semi-analytical wavelet finite element (SAWFE) method is presented in this paper to study the guided wave propagation characteristics of plate structures. With the advantage of multi-scale and multi-resolution, the B-spline wavelet on the interval (BSWI) scale functions are adopted to construct one-dimensional BSWI elements and form the shape function. The element displacement field represented by the coefficients of wavelet expansions is transformed from wavelet space to physical space through the corresponding transformation matrix. Then, the constructed one-dimensional BSWI elements are employed to discretize the cross-section of waveguide structure, meanwhile, the wave displacement field in the wave propagation direction is described in an analytical way as a harmonic exponential function. The propagation characteristics of guided wave in aluminum plate and composite laminate are studied by using the proposed method, and the results show that the SAWFE method has high accuracy and efficiency in calculating dispersion curves and analyzing wave structure. The simulation analysis and experimental validation results further verify the effectiveness of the proposed method.