Calculation of frequency dispersion curves of submerged elastic cylindrical shells based on spectral method

Abstract

Study on the frequency dispersion curve of elastic cylindrical shells is the foundation of nondestructive testing and target recognition. The traditional calculation method for frequency dispersion curves is based on thin shell theory and ‘Regge track’, which is beset by low computational efficiency. The spectral method is regarded as a novel approach of solving ordinary or partial differential equations after the Finite Difference Method (FDM) and Finite Element Method (FEM). The solution of the differential equation is expressed as a sum of certain orthogonal functions and differential operators are replaced by differentiation matrices. Then a series of linear equations takes the place of ordinary or partial differential equations. In this paper, a calculation method on the frequency dispersion curves of elastic cylindrical shells based on spectral method is presented. Chebyshev polynomials are adopted to calculate the differentiation matrices. According to the continuity of displacement and stress on the boundary, the eigenvalue problem involving differential equations is translated into a matrix eigenvalue problem. Unlike previous studies, we calculate frequency dispersion curves of submerged elastic cylindrical shells in which external fluid and perfect matching layer(PML) are considered. Numerical simulations show that the frequency dispersion curves obtained by the spectral method are in good agreement with those of the traditional method. However, the former has a greater advantage in computation speed relative to the latter.