Three-Dimensional Elasticity Solution for Free Vibrations of Exponentially Graded Plates

A three-dimensional exact free vibration solution for plates made of functionally graded materials is provided in the current study. An analytical solution in the form of a power series and numerical results for plates having material with an exponential distribution of properties across the thickness are established. Exact solutions for linearly elastic, simply supported, and rectangular plates based on three-dimensional elasticity theory are derived. A power series method is used to find the natural frequencies. An assumed displacement field identically satisfies all the boundary conditions. Numerical results for frequencies are provided for exponentially graded thick and thin plates. The presented results should serve as benchmark frequencies for exponentially graded plates. (C) 2014 American Society of Civil Engineers.