Wave Propagation In Axisymmetric Structures From Finite Element Analysis

This paper describes a wave and finite element (WFE) method for the numerical prediction of wave propagation in axisymmetric structures. A small segment of the structure is modelled using conventional finite element methods, commonly using a commercial package, and the mass and stiffness matrices found. This typically involves a single shell element or, especially for laminate structures, a stack of solid elements meshed through the thickness. Internal fluid can be included straightforwardly. Periodicity conditions are then applied. An eigenvalue problem results, the solutions of which yield the dispersion relations and the wave modes. The circumferential order of the wave can be specified in order to define the phase change a wave experiences as it propagates across the element in the circumferential direction. The resulting eigenproblem then relates the wavenumber and frequency. The WFE method is described and illustrated by application to cylinders in vacuo and filled with fluid and curved panels. These include various isotropic and laminated constructions. Complex dispersion curves and wave modes are presented and discussed. The method is seen to be simple in application and provides accurate results with very little computational cost.