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.
