Free vibration and buckling analysis of thin rectangular plates with classical boundary conditions under unilateral in-plane loads.

Abstract

Interest in the free vibration of thin rectangular plates has emerged due to the rapid growth in computer technology. Delicate electronic components mounted on circuit boards may be placed in environments under dynamic loadings. The designer may need to control the natural frequency or mode shape of a specific board if a known excitation is causing reliability problems in the hardware. Fortunately, constant in-plane loads can be applied to the plate, affecting its stiffness, and hence dynamic characteristics. This method of control is convenient since the circuit board does not need to be redesigned. The method of superposition is used to obtain analytical-type solutions for the free vibration of thin rectangular plates under constant in-plane loads in this thesis. A total of nine plate configurations are examined, each of which possess at least one free edge. Eight building blocks are derived and used to solve the plates under consideration. Each building block solution is of the Levy-type and is analytically exact. Since plate buckling is a limiting case of plate vibration, the solutions obtained can also be used to solve plate buckling problems. Results are calculated for nine plate aspect ratios. Buckling loads, frequencies, and mode shapes are shown. Excellent agreement is found in comparisons with other solution methods.