The free vibrations of circular plates having flexible edge supports have been studied by several researchers for the restricted case when the supports are represented by springs having constant stiffness. In the present paper a general method is presented for dealing with supports having translational and rotational flexibilities which vary in an arbitrary manner around the boundary. It is shown that the varying stiffnesses can be represented as accurately as desired by expanding them into trigonometric series in the polar angle. The exact solution in polar coordinates of the differential equation of motion for the plate is then substituted into the elastic boundary conditions. The resulting infinite characteristic determinant is solved by successive truncation. As an example the case of a plate having a simply supported edge (infinite translational stiffness) with rotational stiffness varying according to L0+L1 cos ϑ (L0 and L1 being constants) is considered. Numerical results are obtained by the method described above and also by using the Ritz method with functions which approximate both the differential equation and the boundary conditions.
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