Transverse vibrations of moving skew plates made of functionally graded material

Abstract

The present paper investigates the transverse vibrations and stability of a moving skew thin plate made of functionally graded ceramic–metallic material. The material properties are assumed to vary continuously through the thickness according to a power-law distribution of the volume fractions of the constituents. The Voigt's rule is used to estimate the effective material properties from the volume fractions and the properties of the constituent materials. By the coordinate transformation, the differential equations of motion of the moving functionally graded material (FGM) skew plate are obtained in oblique coordinate system. The boundary conditions with simply supported and clamped edges are obtained in oblique coordinate system. The vibration frequencies are obtained from the solution of a generalized eigenvalue problem. The entire computational work is carried out in a normalized square domain obtained through an appropriate domain mapping technique. Results of the reduced problem revealed excellent agreement with other studies. The dimensionless complex frequencies of the moving FGM skew plate are calculated by the differential quadrature method. The effects of gradient index, aspect ratio, and dimensionless moving speed on the transverse vibration and stability of the moving FGM skew plate are analyzed. Results are furnished in dimensionless amplitude–frequency curves for different dimensionless moving speed and representations of some vibration mode shapes are shown.