The Effect of Radiation on the Vibrations of a Circular Diaphragm

Circular plate with a fluid on one side: The free and forced vibration problems of a clamped plate in an infinite baffle are solved exactly in terms of a set of self- and mutual radiation impedances Zmn(ω), associated with the normal modes of a plate vibrating in a vacuum. Computations of these impedances have been made for the lowest four modes over a sufficient range in frequency to solve the forced vibration problems that occur in practice as well as the free vibration problem of these modes. The magnitude of the influence of the fluid on the plate is shown to depend only on the frequency of vibration and the non-dimensional parameter β = ρ0R/2ρh, where R is the radius of the plate, 2h the thickness, and ρ0/ρ the relative density of fluid to plate. The shift in resonant frequency, and the change in shape of the lowest four modes due to the reaction of the fluid on the plate are computed as a function of β. These changes are found to be important in the range 1 < β < 8. They are negligible for β < 1, the case of radiation into air.