Calculating the response of waveguides to base excitation using the wave and finite element method

Abstract

The prediction of the response of waveguides to time-harmonic base excitations has many applications in mechanical, aerospace and civil engineering. The response to base excitations can be obtained analytically for simple waveguides only. For general waveguides, the response to time-harmonic base excitations can be obtained using the finite element method. In this study, we present a wave and finite element approach to calculate the response of waveguides to time-harmonic base excitations. The wave and finite element method is used to model free wave propagation in the waveguide, and these characteristics are then used to find the amplitude of excited waves in the waveguide. Reflection matrices at the boundaries of the waveguide are then used to find the amplitude of the travelling waves in the waveguide and subsequently the response of the waveguide. This includes the displacement and stress frequency response transfer functions. Numerical examples are presented to demonstrate the approach and to discuss the numerical efficiency of the proposed method.