Acoustic scattering by a finite nonlinear elastic plate - II. Coupled primary and secondary resonances

Abstract

A finite thin elastic plate is set in an infinite rigid baffle and the whole is immersed in a compressible inviscid fluid. Plane sound waves are incident on the elastic plate, and the fluid is assumed light compared with the plate density. Nonlinear terms in the plate equation have previously been found to markedly alter the scattered sound field near resonance; and it is shown in this paper that in-plane tension may result in simultaneous primary and secondary resonances. This coincidence of resonances gives rise to two scattered fields, one oscillating at the acoustic forcing frequency and the other at three times or one third of this frequency. Both terms have amplitudes which are of the same order as this incident wave and so under certain circumstances much of the incident energy is found to be scattered back off the plate at the secondary frequency.