Plane strain dynamics of elastic solids with intrinsic boundary elasticity, with application to surface wave propagation

摘要: In this paper, in a development of the static theory derived by Steigmann and Ogden (Proc. Roy. Soc. London A 453 (1997) 853), we establish equations motion for non-linearly elastic body plane strain with an surface coating on part or all its boundary. The (linearized) incremental motions superposed finite deformation are then obtained applied to problem (time-harmonic) wave propagation pre-stressed incompressible isotropic half-space thin secular equation (dispersive) speeds is respect general form strain-energy function bulk material energy material. Specialization enables be cast as quartic therefore focus illustrative purposes. An explicit thereby obtained. This involves number parameters, including residual stress moment properties coating. It shown how relates previous work waves overlying layer set classical elasticity and, particular, significant effect omission rotatory inertia term, even at small numbers, emphasized. Corresponding results membrane-type coating, which bending moment, terms absent, also Asymptotic formulas speed large (high frequency) it these influence character throughout range values. bifurcation criterion from setting zero, generalizing 853) situation present Numerical show dependence various parameters described graphically. features differ those arising highlighted.