Propagation of waves in an incompressible rotating transversely isotropic nonlocal elastic solid

Abstract

In this paper, the nonlocal elasticity theory is applied to study the propagation of plane wave and Rayleigh-type surface wave in an incompressible, rotating and transversely isotropic material. The governing equations of motion for an incompressible, rotating, transversely isotropic and nonlocal elastic medium are specialized for a plane. The medium is assumed rotating about an axis perpendicular to the plane. The transverse isotropy axis is taken perpendicular to the surface. The specialized governing equations are first applied to derive a velocity equation for homogeneous plane wave. The specialized governing equations along with traction free boundary conditions are also applied to derive the secular equation governing the wave speed of Rayleigh wave. The speeds of plane wave and Rayleigh wave are computed and illustrated graphically to observe the effects of nonlocality, rotation, anisotropy, frequency and propagation direction. It is noticed from the theory and numerical results that the speeds of both plane wave and Rayleigh wave decrease sharply with an increase in nonlocal parameter or rotation parameter. The speeds of plane wave and Rayleigh wave increase logarithmically with anisotropy material parameter. The feasible ranges of nonlocality, rotation or anisotropy parameters for the existence of plane wave or Rayleigh surface wave are determined for a given wave speed when the values of other parameters are fixed.