Dynamic stability of functionally graded materials skew plates subjected to uniformly distributed tangential follower forces

Abstract

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.