Vibration Analysis of Moderately Thick Rectangular Plates with Internal Line Support Using the Rayleigh-Ritz Approach

Abstract

Abstract. In this study, the free vibration of moderately thick rectangular plates with several internal line supports was analyzed; the plates having twenty one possible boundary conditions (a combination of clamped, simply supported and free classical boundary conditions). The dimensionless equations of the strain (potential) and kinetic energy were derived, based on the Mindlin plate theory, to study the transverse vibration of moderately thick rectangular plates (in terms of the resultant stress, with consideration of transverse shear deformation and rotatory inertia). The Rayleigh-Ritz method, assuming two dimensional polynomial functions as admissible displacement functions, was applied. Numerical results were presented for a wide range of aspect ratios and thickness to length ratios. The in uence of line support location and thickness to length ratio on the frequency parameters was shown graphically.