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.

A review of theories for the modeling and analysis of functionally graded plates and shells

“…Chakraverty and Pradhan [24] improved their previous work [23] by accounting for the effect of thermal environments. Ruan and Wang [25] investigate the vibration and stability of moving FG skew plates using the CPT and DQM.…”

Analytical Investigation of Sound Radiation from Functionally Graded Thin Plates Based on Elemental Radiator Approach and Physical Neutral Surface

“…where c and m denote ceramic and metal, respectively, rho denotes density, and E denotes the FGM plate's Young's modulus of elasticity. Because the plate is thin, the variation in Poisson's ratio (v) along the thickness direction is considered negligible [50][51][52][53]. Material properties of different P-FGM plates can be deduced from [28,[54][55][56].…”

New Shape Function for the Bending Analysis of Functionally Graded Plate

“…The effect of a gradient distribution of materials in thin square and rectangular FGM plates was studied in terms of different cases of dynamic load. The papers [18,19] analyze free vibrations of the FGM plates using CPT for different boundary conditions in the area of geometric linearity. Von Karman’s type of nonlinearity has been used in the papers [20,21].…”