Wavelet spectral element for wave propagation studies in pressure loaded axisymmetric cylinders

Abstract

We study transient wave propagation in a pressure loaded isotropic cylinder under axisymmetric conditions. A 2-D wavelet based spectral finite element (WSFE) is developed to model the cylinder with radial and axial displacements. The method involves a Daubechies compactly supported scaling function approximation in the temporal dimension and one spatial (axial direction) dimension. This reduces the governing partial differential wave equation into a set of variable coefficient ODEs, which are then solved using Bessel's function approximation. This spectral method captures the exact inertial distribution and thus results in large computational savings compared to the conventional finite element (FE) formulation. In addition, the use of localized basis functions in the present formulation circumvents several serious limitations of the previous FFT based techniques. Here, the proposed method is used to study radial and axial wave propagation in cylinders with different configurations. The analysis is performed in both time and frequency domains. The time domain responses are validated with 2-D FE results.