Modelling of Evanescent and Propagating Modes in Homogenized Phononic Structures in Frequency and Time Domains

Abstract

Abstract. In the paper we deal with analytical and numerical methods for modelling phononic elastic structures subject to harmonic loading. The band gap prediction is based on the analysis of eigenvalues of the effective mass coefficients for a given frequency. Using a spectral decomposition method, the propagating and the evanescent modes can be distinguished in the frequency domain. We also developed a numerical scheme to simulate the wave response of the phononic 3D structures and plates, or beams in the time domain. Using the backward Laplace transformation, we obtain a model involving the intertia effects in terms of time convolutions, where the homogenized mass tensor serves as the convolution kernel. The aim of the reported modelling is to understand behaviour of the phononic structures subject to incident waves of frequencies falling in the partial (so-called weak) band gap intervals in which waves of certain polarizations cannot propagate. We discuss the issues related to the time-space discretization. Numerical examples of how homogenized phononic structures respond to a harmonic loading are presented.