Approximate spectral element for wave propagation analysis in inhomogenous layered media

Abstract

An approximate spectral element (SE) is developed to model isotropic inhomogeneous layered media. As opposed to the case of a homogeneous solid, where the mass distribution is modeled exactly, the SE approach to the inhomogeneous material gives an approximate frequency response of the structure. The element is formulated by approximating wave number over the domain. This wave number has a nontrivial imaginary part justifying the notion of an inhomogeneous wave, which is predominant in inhomogeneous materials. Material properties are made to vary linearly within the element, although any other variation can be incorporated under the proposed scheme. Strains due to temperature are also taken into account, which enables the analysis of a layered structure for thermal burst loading. The formulated element is used to analyze the response of inhomogeneous layer structure subjected to high'frequency mechanical and thermal loading. Furthermore, the inherent advantage of the SE in the solution of inverse problems is utilized to reconstruct the force history applied to an inhomogeneous layer from the measured responses. The finite element responses are used as surrogate experimental data. In particular, a layered structure of functionally graded material (FGM) is taken for the case study, where FGM smoothly blends two different material properties one of metal and the other of ceramic. The fast Fourier transform and Fourier series are used for inversion to the time/space domain.