The Generation of Waves in a Semi-Infinite Plate by a Smooth Oscillating Piston

Abstract

A semi-infinite plate is set into plane strain, time-harmonic vibration by a rigid oscillating piston, which is in smooth contact with the edge of the plate. The exact (linearized) solution to this problem is obtained as a series expansion involving the Rayleigh-Lamb modes of the plate, the coefficients being determined by a biorthogonality relation. We compute the amplitude of the resultant force exerted by the piston, the mean total rate of working of the piston, and the proportion of outgoing energy in each of the available propagating modes; resonances are observed at certain of the cut-off frequencies.