A parametric anomaly of the Rayleigh-Lamb spectrum in a thin elastic layer

Abstract

We analyze variation of the Rayleigh-Lamb (RL) vibration spectrum of a free isotropic layer on parameters motivated by a previously unnoticed anomaly of its dependence on constituent materials, when some RL modes would reduce their propagation speed in a medium with higher bulk velocities. We explore the spectrum in more detail by following the arguments of parametric scaling and find the location of its anomalous non-monotonic dependence on bulk velocity at finite wavelengths for the S1 and A2 modes. These modes are well known for the anomaly of their dispersion that has recently attracted much interest related to the phenomenon of negative refraction. We demonstrate that the parametric and dispersion anomalies occupy adjacent areas on the spectral surfaces in the wavenumber-parameter space. We argue that such close connection may be found in other waveguides and can present interest for acoustic technologies as well as for quantum applications of anomalous scattering and transport by RL phonons.