Faster Calculations of Sound Radiation from Vibrating Cylinders Using Variational Formulations

Prediction of the sound radiation from a vibrating body often requires a computation of the acoustic pressure on the body’s surface, given the normal surface vibration. This paper explores what computational advantages a variational formulation may have over other formulations, such as those which solve the Helmholtz integral equation directly. The variational formulation is developed here for bodies of revolution in axisymmetric vibration and specialized to finite cylinders. The general implementation technique of the variational formulation is the Rayleigh-Ritz method which yields a set of simultaneous linear equations for the unknown coefficients in the expansion of the surface pressure in terms of a finite set of basis functions. A case is made to the effect that computations based on the variational formulation can often yield results of desirable accuracy with substantially less computational time. A prerequisite for such an achievement is that one makes a good selection of the basis functions. Such a selection may be aided by physical insight and common sense.