The dynamic stability of functionally graded material (FGM) skew thin plate subjected to uniformly distributed tangential follower force is investigated. The material properties are assumed to vary continuously through their thickness according to a power-law distribution of the volume fractions of the plate constituents based on the Voigt model. In skew coordinate system, the differential equations of motion of the FGM skew plate subjected to uniformly distributed tangential follower force are derived by the Kirchhoff thin plate theory, and the different boundary conditions are obtained of the plate for arbitrary curve edges. By eliminating the in-plane displacement components on the neutral plane, the differential equations of motion can be expressed in terms of deflection only. Then the equations are discretized by the differential quadrature method, and the curves of real parts and imaginary parts of the first second-order dimensionless complex frequencies vs. uniformly distributed tangential follower force are obtained. The effects of the gradient index, skew angle and aspect ratio on the instability type and the corresponding critical load of the non-conservation FGM skew plate are analyzed.
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.
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