عنوان مقاله [English]
In this paper, using displacement potential functions, the exact solution of a three dimension elasticity problem is presented for free vibration of rectangular isotropic plates. It is assumed that the materials of the plate are
homogeneous, linearly elastic, arbitrary, but with a constant thickness, and all four edges of the plate are on simple supports. The governing equations in terms of displacement potential functions are two differential equations of fourth and second orders. Assuming harmonic motion and using a separation of variables, the solution of the governing differential equations for displacement potential functions results in exponential and trigonometric expressions along the plate thickness and the other two lengths, respectively. The boundary condition are zero vertical displacement and zero bending moments on all four edges, and all components of stresses, including normal and shear stresses on the top and bottom of the plates, are zero. Applying these boundary conditions result in a characteristic equation of the free vibration of the plate, with which solution, the plate frequency vibration can be calculated.In order to verify the solutions, the obtained results are compared with other analytical work that are largely based on first and higher order deformations theories for moderately thick plates. The most important characteristic of the method presented in this paper is that there is no limitation for thickness in determining free vibration frequency and its validation for thin, moderately thick and thick plates. The investigations have been done for a wide range of aspect ratio (length to width) and thickness to length. The obtained results show that increasing plate thickness decreases nondimensional frequency, and that this decrease intensifies at higher modes of vibration. In addition, investigations show that the Poissons ratio has little effect on nondimensional frequency increasing the thickness of the plate. This phenomenon is negligible when the thickness of the plate is decreased.