Analytic free vibration solutions of rectangular thin plates point-supported at a corner

In a recently published study, we reported the benchmark bending solutions of rectangular thin plates point-supported at a corner by an up-to-date symplectic superposition method. In this paper, for the first time, we extend the approach to the free vibration problems of the same plates and obtain the analytic solutions which cannot be obtained by the conventional symplectic approach. More than three hundred frequencies and the representative mode shapes are presented as the benchmarks for verification of various new approaches developed in future.