Nonlinear stability analysis of rotational dynamics and transversal vibrations of annular circular thin plates functionally graded in radial direction by differential quadrature
In this article, the nonlinear analysis of free vibrations, dynamic stability, and rotational dynamics of rotating annular circular thin plates, made of functionally graded material (FGM) is studied. Based on classical plate theory, von Karman's nonlinear plate theory, and assuming the FGM mechanical properties vary in the radial direction, the governing equations of motion are obtained by direct use of Newton's laws. A 1 D differential quadrature is used to solve the governing equations determining the natural frequencies, corresponding transverse mode shapes, and the critical speeds of rotation. The accuracy and convergence of the method are studied by comparing the results with the similar results whenever available in the literature. The influence of different parameters such as inner to outer radii ratio, thickness to outer radius ratio, graded index, angular velocity of the plate, and different boundary conditions on the natural frequencies of FG rotating plate are demonstrated by numerical examples. It is shown that fabricating a rotating disk with FGM can lead to an increase in its critical speed.