Wavelet based 2-D spectral finite element formulation for wave propagation analysis in isotropic plates

Abstract

In this paper, a 2-D Wavelet based Spectral Finite Element (WSFE) is developed and is used to study wave propagation in an isotropic plate. Here, first, wavelet approximation is done in both temporal and one spatial (lateral) dimension to reduce the governing partial differential wave equations to a set of Ordinary Differential Equations (ODEs). Daubechies compactly supported orthogonal scaling functions are used as basis which allows finite domain analysis and easy imposition of initial/boundary conditions. However, the assignment of initial and boundary conditions in time and space respectively, are done following two different methods. Next, the reduced ODEs are solved exactly to derive the shape functions which are used to form the elemental dynamic stiffness matrix. Similar to the conventional Fast Fourier Transform (FFT) based Spectral Finite Element (FSFE) method which has problems in handling finite boundaries, the present method also reduces the computational cost substantially compared to conventional Finite Element (FE) method. The proposed method can also be used directly for both time and frequency domain analysis like FSFE. However, importantly, the use of localized basis functions in 2-D WSFE method circumvents several serious limitations of the corresponding 2-D FSFE technique. The formulated 2-D WSFE is used to study axial and transverse wave propagations in isotropic plates of different configurations. The simulated responses are also validated with 2-D FE results.