Waves in a Smoothly Jointed Plate and Half-Space

Propagating dilatational and distortional disturbances in a half-space, generate wave motion in a plate that covers the half space. The motion of the plate is described by the Bernoulli-Euler-Kirchhoff theory. The half-space (subgrade) is homogeneous, isotropic and linearly elastic. Plate and subgrade are in smooth contact and thus only normal disturbances are transmitted at the plate subgrade interface. The response of the plate to plane dilatational and distortional waves is examined. Explicit expressions are derived for the plate deflection, the bending moment, and the reflection coefficients. Several special cases such as normal incidence, grazing incidence, and wave incidence—for which the plate effect vanishes—are examined. Diagrams show the deflection and the bending moment as functions of the angle of emergence, the frequency, and the plate-subgrade parameters. The modifications of the equations, if a perfect bond between plate and half-space is assumed, are examined briefly.