The reflection of a symmetric Rayleigh-Lamb wave at the fixed or free edge of a plate

1573-2681

Springer Online Journal Archives 1860-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Physics

Abstract A semi-infinite plate of homogeneous isotropic, linearly elastic material occupies the region x≥0, |y|≤1, -∞〈z〈∞; the faces y=±1 are free of tractions, the end x=0 may be either fixed or traction free, and there are no body forces. A plane strain, time-harmonic, symmetric Rayleigh-Lamb wave propagates in the plate and is normally incident upon the end x=0. The problem of determining the resulting reflected wave field is solved by the “method of projection”, a method developed by the authors for solving corresponding problems in elastostatics. The solutions obtained for the dynamic problem fully satisfy the equations and boundary conditions of the linear theory, and (in the fixed-end case) proper account is taken of the singularities of the stress field at the corners x=0, y=±1. In each case the division of energy between the various reflected modes is found, and the dynamical stress intensity factors at the corners are determined in the fixed-end case. The existence of an “edge-mode” for the free-end case at a single isolated value of the frequency is confirmed, but a careful search revealed no similar phenomenon for the fixed-end case.

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