Vibro-acoustic analysis of a rectangular plate elastically reinforced at arbitrary points

A general solution for the vibrations of a uniform rectangular plate reinforced by finite springs at arbitrary locations is expressed as a linear combination of the flexural modes of the unconstrained plate. Although these modes can no longer decouple the equations so that the expansion coefficients can be independently determined, it is still advantageous to use them as a complete set of basis functions to represent any reasonably well-behaved variable such as the flexural deflection of the plate. The relationship is discussed between the two groups of modes corresponding to the unconstrained (or free) and reinforced cases. The sound radiation from the reinforced plate is determined by using the near-field sound power formulation that requires the calculation of quadruple integrals defined over the plate area. A frequency interpolation scheme is developed to significantly reduce the computational burden of determining the sound radiation. The maximum allowable frequency spacing is specified to insure the accuracy of the solution. Numerical results are presented.