Evanescent waves in FGM spherical curved plates: an analytical treatment

A deep understanding of both guided propagating and evanescent waves is very essential for non-destructive evaluation. Guided propagating waves have received considerable attention, but the research on guided evanescent waves is quite limited, especially for functionally graded structures. This paper presents an analytical approach, based on the orthogonal function technique, to solve the evanescent waves in a spherical curved plate with functionally graded material in the radial direction. The proposed approach can obtain all the real, imaginary and complex solutions but without iterative process. The validity of the proposed approach is illustrated by comparison with available results. The convergence of the approach is also discussed through a numerical example. Dispersion characteristics of the guided waves in various graded spherical curved plates are studied and three dimensional dispersion curves are plotted in frequency-complex wavenumber space. The effects of different radius-thickness ratios and graded fields on the dispersion curves of the guided evanescent waves are illustrated. The displacement distributions are also discussed to analyze the characteristics of the guided evanescent waves.