Flexural vibration of rectangular plates subjected to sinusoidally distributed compressive loading on two opposite sides

Natural frequencies and mode shapes of rectangular plates subjected to sinusoidally distributed in-plane compressive loading on two opposite edges were considered in this work. Although vibration analysis of rectangular plates was investigated by numerous authors, flexural vibration of plates with nonlinearly distributed in-plane loading received much less attention. However, certain problems involving thermal stresses may have such nonlinear loading conditions in the plane of the plate. The analysis procedure for the title problem involves first finding a plane elasticity solution for the in-plane problem satisfying all boundary conditions. Then using this in- plane solution, flexural vibration analysis has to be carried out. In a related work investigated recently by the present authors, an in-plane elasticity solution was developed and was compared with existing analytical solutions in the literature and with the finite element method. One aspect of this study was the stress diffusion (i.e., reduction of stress) phenomenon along the length of the plate as well as the presence of all three in-plane stress components. Using this in-plane solution, vibration analysis of rectangular plates was carried out for various plate aspect ratios and the results were compared with corresponding values from finite element analysis.