Dispersion Properties of Micropolar Plates Through the Partial Wave Technique

Abstract

The focus of this study is on the dynamic problem of free guided propagation of harmonic elastic waves in homogeneous plates modeled as a linear micropolar continuum, in the absence of dissipation. The plate is modeled as an infinite layer with finite thickness, bounded by two parallel traction-free planes. The analysis is carried out using the analytical partial wave technique, which returns the dispersion relation in terms of wavenumber as a function of frequency, as well as the wavemode shapes. The dispersion relation for the micropolar continuum differs markedly from that of a Cauchy continuum, above all for the presence of microrotation modes – unique to the Cosserat continuum. Morphological modification of the standing wavemodes, as well as the occurrence of internal resonance conditions and inter-wave transfer of mechanical energy, are observed among microrotation waveforms and other waveforms.