Wave propagation in inhomogeneous layered media: solution of forward and inverse problems

Abstract

Wave propagation in anisotropic inhomogeneous layered media due to high frequency impact loading is studied using a new Spectral Layer Element (SLE). The element can model functionally graded materials (FGM), where the material property variation is assumed to follow an exponential function. The element is exact for a single parameter model which describes both moduli and density variation. This novel element is formulated using the method of partial wave technique (PWT) in conjunction with linear algebraic methodology. The matrix structure of finite element (FE) formulation is retained, which substantially simplifies the modeling of a multi-layered structure. The developed SLE has an exact dynamic stiffness matrix as it uses the exact solution of the governing elastodynamic equation in the frequency domain as its interpolation function. The mass distribution is modeled exactly, and, as a result, the element gives the exact frequency response of each layer. Hence, one element may be as large as one complete layer which results in a system size being very small compared to conventional FE systems. The Fast-Fourier Transform (FFT) and Fourier series are used for the inversion to the time/space domain. The formulated element is further used to study the stress distribution in multi-layered media. As a natural application, Lamb wave propagation in an inhomogeneous plate is studied and the time domain description is obtained. Further, the advantage of the spectral formulation in the solution of inverse problems, namely the force identification and system identification is investigated. Constrained nonlinear optimization technique is used for the material property identification, whereas the transfer function approach is taken for the impact force identification.