Determination of the lower natural frequencies of circular plates with mixed boundary conditions

The natural frequencies are obtained for elastic circular plates with mixed boundary conditions. The boundary conditions of the plate were combinations of clamped, simply supported, free, and guided. The natural frequencies are presented as a function of the angle over which the circumference of the plate is treated as one boundary and the remainder as another boundary condition.It was found that the axisymmetric modes exhibit continuous variation of the natural frequency from one pure condition to the other pure boundary condition, while the asymmetric modes show two branches of varying curvature and magnitude fluctuation, depending on the magnitude of the angles of mixed boundaries.