Analysis of Rayleigh-Lamb wave scattering by a crack in an elastic plate

This paper considers the scattering of low-frequency elastic waves by a crack in a plate. A simple formula is derived for the re ̄ection coef®cient which serves as a lower bound to the re ̄ection coef®cient at higher frequencies. Notation a half crack length c speed of S-waves in plate cL speed of longitudinal waves in an in®nite medium cT speed of transverse waves in an in®nite medium d half thickness of plate f real function de®ned in (41) g real function de®ned in (42) r constant de®ned by (27) u; v displacements in x; y directions uN displacement due to normal stress de®ned by (40) uS displacement due to shear stress de®ned by (40) û integrated displacement de®ned by (16) x; y cartesian coordinates A function de®ned by (26) B function de®ned by (26) K dimensionless wave number de®ned by (29) R re ̄ection coef®cient S0 zero-order symmetric Lamb wave Txx stress component Txy stress component X dimensionless coordinate de®ned by (24) a constant de®ned by (4) b constant de®ned by (4) j wave number de®ned by (3) k wavelength k1; l1 Lame constants m Poisson ratio q density of plate /; w potentials de®ned in (17) U function de®ned by (47) x angular frequency X nondimensional frequency de®ned by (6)