Wave damping and evanescence: how to combine the spatial and temporal visions of the same problem? 1

Abstract

It is proposed to analyze the forced response of periodic structures using a 2D Fourier transform using continuous time and discrete space. The simple example of compression waves is used to show that this response can be used to define poles in the wavenumber domain corresponding to evanescent waves or poles in the frequency domain corresponding to damped periodic modes. Link with classical computational methods based on FEM models of cells was done for both the periodic solution and wave based approach (SAFE, WFE). Two examples are analyzed in more detail: a simple train track model exhibiting a band-gap and the more complex case of a honeycomb panel where cell wall bending occurs within the band of interest.