Free and forced flexural vibration analysis of cantilever plates with attached point mass

In this paper, the method of superposition or the Gorman method is employed to obtain an analytical solution for free and forced vibrations of cantilever plates carrying point masses. The free lateral vibration analysis is carried out by employing five building blocks—four for the cantilever plate and one for the point mass. Computed eigenvalues show that the proposed scheme is accurate and convergent for free vibration analysis. Once the eigen-analysis is completed, the modal summation method is then used to deal with the base-induced lateral vibration of cantilever plates carrying a point mass. Effects of mass ratios and locations of the point mass on eigenvalues and modal participation factors are investigated for square and rectangular plates.