Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates

In this paper, a modified single variable shear deformation plate theory is developed for free vibration analysis of rectangular functionally graded plates. By using the equilibrium equations of forces, the relationship between bending and shear parts is established, so that the displacement fields and the governing equation of the modified single variable plate theory contain only one unknown variable. As a consequence, the number of unknown variables is reduced, so it is effective for computation of solid mechanics. The advantage of proposed theory is that it consists of only one unknown variable but it is capable for analysis of heterogeneous plate such as functionally graded plates. The numerical results of the free vibration of functionally graded plates are carried out and compared with other published data to ensure the accurateness and effectiveness of this modification. The paper also explores the impact of some parameters on the free vibration of the functionally graded plates. © 2020 Institution of Structural Engineers