Abstract
This paper presents the study on the free flexural vibration of a complete elliptical plate with clamped edge according to the Mindlin's theory including the effect of shear deformation and rotary inertia. The analysis is rigorously made by the use of the Mathieu function and modified Mathieu function which are the solutions of the equation of motion expressed in terms of the elliptical coordinates. The frequency equation is derived by-applying the orthogonality of the Mathieu function. The eigenfrequencies calculated numerically are given in tables and figures for a variety of ratios of the minor axial length to the thickness and of the major axial length to the minor axial one. It can be seen that the calculated results approach to the ones due to the classical theory neglecting the effect of shear deformation and rotary inertia with decreasing thickness.
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