Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

In this research, free vibration of rectangular functionally graded (FG) plates with in-plane exponentially non-homogeneous material is investigated. Young’s modulus and mass density are assumed to vary between a metal-rich and a ceramic-rich zone along one in-plane direction of the plate. The governing differential equation is derived for the case, and a truncated Taylor series expansion technique is utilized to calculate natural frequencies. A Levy-type solution is obtained for plates having two simply supported edges parallel with the material gradient direction. Results for normalized natural frequency are compared with the 4th order Runge-Kutta method, and when possible with exact solution, showing an accurate agreement. Furthermore, a comprehensive parametric study is carried out to determine the effects of different boundary conditions, aspect ratios, and material variations on the free vibration of FGM plates.