Eigenfrequencies and modified eigenmodes of a rectangular plate with free edges

A solution of the problem of the oscillations of a rectangular plate with free edges, which enables exact values of the eigenfrequencies and approximate eigenmodes to be obtained, is given. The use of the results obtained to design plates on an elastic foundation is proposed. The calculation is carried out by the Ritz method in which the eigenmodes of the plate obtained are taken as the coordinate functions, which considerably speeds up the process of obtaining a solution compared with existing approaches.