On formulas for the Rayleigh wave velocity in pre-stressed compressible solids

In this paper, formulas for the velocity of Rayleigh waves in compressible isotropic solids subject to uniform initial deformations are derived using the theory of cubic equation. They are explicit, have simple algebraic forms, and hold for a general strain energy function. Unlike the previous investigations where the derived formulas for Rayleigh wave velocity are approximate and valid for only small enough values of pre-strains, this paper establishes exact formulas for Rayleigh wave velocity being valid for any range of pre-strains. When the prestresses are absent, the obtained formulas recover the Rayleigh wave velocity formula for compressible elastic solids. Since obtained formulas are explicit, exact and hold for any range of pre-strains, they are good tools for evaluating nondestructively prestresses of structures.

Research highlights
► Exact formulas for the velocity of Rayleigh waves in pre-stressed compressible solids are derived.
► They are valid for any range of pre-strains and hold for a general strain energy function.
► For deriving these formulas the method of cubic equation is employed.
► The obtained formulas are good tools for nondestructively evaluating prestresses of structures.