Modeling and analysis of in-plane and out-of-plane elastic wave propagation in a phononic-crystal circular beam

Abstract

An efficient formulation of a circular Timoshenko beam is developed for static, vibration, and wave propagation problems. The B-spline wavelet on the interval (BSWI) interpolation functions are used to construct wavelet-based elements, which have analytical expressions at all levels and sufficient continuity. This paper derives static equilibrium, vibration, and wave propagation wavelet-based finite element models of in-plane and out-of-plane motions of circular beams according to the Hamilton's principle. Wave propagation characteristics of in-plane and out-of-plane waves in a phononic-crystal (PC) circular beam are analyzed using the wavelet-based finite element method (WFEM) based on the Bloch's theorem. Effects of geometric and material parameters on in-plane and out-of-plane wave propagation characteristics of the PC circular beam are discussed. Numerical simulations show that the WFEM is more effective for static, vibration, and wave propagation problems than the traditional finite element method (TFEM). The WFEM can achieve the same accuracy as the TFEM with much fewer elements and degrees of freedom. It is shown that both in-plane and out-of-plane elastic wave band gaps exist in the PC circular beam, which exhibits some interesting phenomena due to coupling effects. This study can provide good support for wave filtering and vibration control of PC circular beam structures.