Rayleigh wave propagation in nematic elastomers

Abstract

In this paper, Rayleigh wave propagation in nematic elastomers (NEs) is investigated. Characteristic equations for Rayleigh waves in the NEs are derived based on the viscoelastic theory of nematic elastomers in the low-frequency (hydrodynamic) limit. The dispersion and attenuation properties of the Rayleigh waves in the NEs are analyzed numerically. By considering the effects of the director, the rubber relaxation time and the dynamic soft elasticity of the NEs on the propagation characteristics of the Rayleigh waves are investigated. Results show that unlike Rayleigh waves in pure viscous materials, the Rayleigh wave displays obvious frequency dependence due to the dynamic soft elasticity of the NEs. There exists a critical transition frequency above which the Rayleigh wave velocity is gradually increased to a stable value, and at this frequency the Rayleigh wave velocity is temperature independent. The transition critical frequency where liquid behavior changes to rubber performance is director rotation time dependent, whilst the rubber relaxation time has less of an effect on its value. Although the particle trace is still elliptically polarized, the direction of the major axis is frequency and depth dependent. Clarification of these particular properties of Rayleigh waves is helpful for the further acoustic application of Rayleigh waves in NEs.