Investigation of Imperfection Effects in Dynamic Behavior of FG Strucure

In this study, the effect of material imperfection on the free vibration response of perfect and imperfect FG plate is studied. A new hyperbolic shear deformation function is presented in this paper. The new hyperbolic function is chosen in such a way that the degree of the function is reduced as much as possible, despite the sufficient accuracy, so that the calculation speed is greatly reduced. The properties of the FG plate varied along the thickness according to power law. The material composition in production process cannot be completely in accordance with the expected pattern, which leads to the production of imperfect FG material. The governing differential equations are derived using the Hamilton’s principle. The obtained equations were solved using the Navier method with simple boundary conditions. The effects of important geometric and mechanical parameters of perfect model and two types of imperfect model, including length to thickness ratio, length to width ratio, wave number and power-law exponent on natural frequency response of imperfect FG plate are investigated. To verification, the analytical results obtained in this study are compared with the results presented in the literature, and in this comparison, a good agreement was obtained, which shows the correctness theory, deriving and solving equations.