The vibration of a thin, simply supported rectangular plate carrying a number of concentrated masses is considered. It is shown that the addition of the masses has the effect of reducing the eigenvalues within certain bounds. Two numerical methods are developed for calculating the eigenfunctions, eigenvalues and frequency response of the mass loaded plate. These are employed in an attempt to drive a gap in the eigenvalues directly below 110 Hz for a particular test case of a plate carrying five concentrated masses. A small gap is achieved, but to produce a larger gap many more masses would be necessary. The frequency response and eigenvalues are relatively easily obtained and compare well with those obtained by using the finite element method
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