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.

Analysis of periodic laminated fiber-reinforced composite beams in free vibration

“…The WFE method has been also used to model the free wave propagation in structural networks (Renno and Mace 2014), pipes with helical characteristics (Manconi et al, 2018), double helical waveguides (Renno et al 2020), and helically orthotropic cylindrical shells and lattices (Sorokin et al, 2019). It was also used to model the response of waveguides to time-harmonic point loads (Duhamel et al, 2006; Waki et al, 2009a), time-harmonic distributed loads (Renno and Mace 2010), and base excitations (Renno et al, 2021). Takiuti et al (2019) studied wave transmission in damaged waveguides represented as beams with asymmetrical cross-sectional area.…”