On Rayleigh-type surface wave in incompressible nematic elastomers

In this paper, the propagation of a Rayleigh-type wave is explored in a half-space of an incompressible nematic elastomer with a uniform director aligned orthogonal to the surface. The nematic elastomer is idealized so as to fit within the framework of linear viscoelasticity theory. The governing equations of nematic elastomers are subjected to the Tiersten-type impedance boundary conditions. An explicit secular equation of the Rayleigh wave is obtained which depends upon the non-dimensional anisotropy parameter, impedance parameters, frequency, rubber relaxation time, director rotation times, and the dynamic soft elasticity of nematic elastomers. The numerical computations of the Rayleigh wave speed are restricted for the case of ideal nematic rubbers. The Rayleigh wave speed is illustrated graphically to observe the effects of non-dimensional anisotropy parameter, frequency, impedance parameters, rubber relaxation time, and director rotation times.