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Variational Principles for Acoustic Radiation and Diffraction from Underwater Structures

机译：水下结构声辐射和衍射的变分原理

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A variational principle derived from the Kirchhoff-Helmholtz integral theorem applied to various acoustic radiation and diffraction problems. Specific examples include sound radiation from transversely vibrating thin disks and finite cylinders in axisymmetric oscillations. The formulation has the acoustic pressure on the vibrating surface as the unknown variable, with the normal velocity of the surface taken as given. The general implementation of the variational formulation is the Rayleigh-Ritz technique in which the unknown surface pressure is represented by an expansion of preselected basis functions. The unknown coefficients corresponding to the basis functions are determined by a system of simultaneous equations. It is demonstrated that substantially less computational time in many cases can be achieved if one conscientiously uses physical insight and good common sense in selecting the basis functions for the expansion of the unknown surface pressure. Numerical results agree well with the previous ones obtained by using other numerical methods. The uniqueness of the variational formulation is also discussed. It is shown that solutions to variationally formulated acoustic radiation problems are (1) unique for the surface pressure distributions on infinitesimally thin disks and plate-like bodies for which each surface point is oscillating either in phase or 180 degrees out of phase; (2) nonunique for the acoustic pressure on surfaces of bodies with finite volumes; and (3) unique for the total radiated acoustic power.

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