Modelling moving one-dimensional waveguides using waves and finite element analysis

One approach to the numerical analysis of complex waveguides is the Wave Finite Element (WFE) method. In this method conventional Finite Elements (FEs) are used to discretise a small segment of a waveguide. The FE model of just this small part of the structure is post-processed using periodicity conditions, and an eigenproblem is then solved to predict dispersion characteristics and wavemodes. Once the wave characteristics are predicted, free vibration and response of the structure as a whole can be modelled in terms of these waves. This paper presents an extension of the method to moving one-dimensional waveguides. In particular an axially moving beam is considered. The FE formulation of a moving beam element is developed and the WFE method is applied to find the wave properties of such a beam. Natural frequencies are obtained using the Phase Closure Principle and the Dynamic Stiffness Matrix, both formulated in terms of wavemodes and dispersion relation obtained from the WFE eigenproblem. The analytical equation of transverse motion of the travelling beam is also solved in terms of propagating and decaying waves, and the frequency equation is obtained using the phase closure principle. Numerical results are shown.