Free vibration analysis using dynamic stiffness method and first-order shear deformation theory for a functionally graded material plate

Abstract

In the current simulation work, free vibration analysis of the levy-type plates made of functionally graded material (FGM) has been carried out using first-order shear deformation theory (FSDT) and dynamic stiffness method (DSM). It is assumed that for functionally graded (FG) plates, density and elastic modulus continuously vary along the transverse direction of the plates following power law distribution. The governing differential equation for the free vibration of a rectangular FG plate and its associated natural boundary conditions are formulated using Hamilton's principle under the assumption of displacement fields following FSDT. Eigen-values for different vibration modes are obtained by implementing the Wittrick-William algorithm on the DSM of the FG plate. Results using the current method have been validated from previously published literature to check their accuracy level. The validation analysis shows the current results are in good agreement with the published literature, which gives us enough confidence to carry out further investigation. The effects of different plate parameters on the frequency such as material gradient index, aspect ratio, and boundary conditions are investigated and discussed in detail.