TRANSVERSE VIBRATION OF THICK RECTANGULAR-PLATES .3. EFFECTS OF MULTIPLE ECCENTRIC INTERNAL RING SUPPORTS

Part III of this series of four papers presents the free vibration analysis of thick rectangular plates with multiple internal ring supports of arbitrary orientation. The aim of this paper is to investigate the effects of different numbers of rings and boundary conditions on the vibratory response of the plates. The first order shear deformation theory proposed by Mindlin is employed in the theoretical formulation. Through the process the resulting energy functional is minimized using the Rayleigh-Ritz method with sets of admissible mathematically complete two-dimensional polynomials in the displacement (transverse deflection) and rotation functions. This leads to a governing eigenvalue equation which can be solved to determine the vibration frequencies. Rectangular plates resting on multiple eccentric ring supports with different combinations of boundary conditions have been solved to demonstrate the effectiveness and accuracy of the method. In this paper, sets of reasonably accurate vibration frequencies are presented for various plate aspect ratios a/b and relative thickness ratios t/b. For some cases where established literature exists, comparisons have been made to verify the present solution process.