Propagation of elastic waves in an incompressible nonlocal transversely isotropic diffusive medium

Various engineering equipments and devices use elastic vibrations and acoustic waves extensively for non-destructive testing and technical diagnostics of various materials and products. The propagation characteristics of plane and Rayleigh-type surface waves in an incompressible transversely isotropic diffusive material are investigated in context of nonlocal elasticity theory. The governing equations of motion for the medium are specialized in a plane and solved for time-harmonic solutions. A velocity equation for homogeneous plane wave is obtained which indicates the existence of two plane transverse waves. The two-dimensional equations are also solved for surface wave solutions and a Rayleigh characteristic equation is obtained. A numerical example is taken to illustrate graphically the effects of nonlocality, diffusion and material anisotropy parameters on the speeds of plane and Rayleigh surface waves.