In-plane free vibration of FGM rectangular plates with elastically restrained edges by differential quadrature method
PU Yu ，ZHAO Hai-ying ，TENG Zhao-chun
1. College of Civil Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China；
2. Department of Engineering Mechanics, School of Science, Lanzhou University of Technology, Lanzhou 730050, China
The rectangular plate is assumed orthotropic at any point, while material properties change continuously through the width of the rectangular plate and can vary according to power law distributions. Based on the two-dimension theory of linear elasticity, the in-plane free vibration of governing partial differential equations for FGM rectangular plates with elastically restrained edges are derived. The partial differential equations are complicated with variable coefficients. Using differential quadrature method, the dimensionless frequencies of in-plane free vibration of FGM rectangular plates with elastically restrained edges are investigated. All the classical homogeneous boundary for in-plane displacements can be simulated by setting the stiffnesses of the restraining springs to either zero or infinite and material graded index to zero. The application of DQM in this paper have illustrated the analytical method was validated and accurate by comparison of previously reported results with those available in the literature for homogeneous rectangular plates. Finally, The influence of the boundary conditions, geometrical parameter, material graded index and stiffness coefficients on the dimensionless frequencies of the FGM rectangular plates are considered.
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