Finite Amplitude Sound Beams Resulting from Nonlinear Vibration of a Circular Membrane Undergoing Axisymmetric Resonant Excitation

Summary

This paper analyses the interaction between a vibrating circular membrane contained in an infinite baffle and the resulting sound field radiated into a fluid medium contained in the half-space above the membrane. The case of resonant excitation of the membrane leads to nonlinear coupling between transverse and in-plane displacement. Nonlinearity within the fluid medium is described by a recent general treatment of finite amplitude sound beams resulting from boundary motion. The vibratory response of the membrane is evaluated in a perturbation technique based on the modes of free vibration. The results give amplitude-frequency relations for the plate that account for the inertial and damping impedances of the fluid, as well as expressions that may be solved for the pressure signal in the fluid.