EXACT SOLUTION FOR FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED MICROPLATES BASED ON THE STRAIN GRADIENT THEORY

This paper deals with free vibration analysis of thin functionally graded rectangular microplates. Along with classical plate theory, strain gradient theory is implemented to capture microstructure effects. Using the variational approach and the principle of minimum total potential energy, the governing equations for rectangular microplates are developed. In accordance with the functionally graded distribution of material properties through the thickness, higherorder governing equations are coupled in terms of displacement fields. Applying a new and novel methodology, these equations are decoupled, with the special benefit of being solved analytically. Using the variational approach all simply supported, clamped and free boundary conditions are determined. Consequently, on the basis of the Navier solution, free vibrational analysis of simply supported rectangular microplates is carried out. Finally the effects of material properties, microstructure parameters and dimensions on the nondimensional natural frequencies of microplates are explored. Also, it is shown that length scale parameters affect both governing equations and boundary conditions.