RT Journal Article ID 73f048da3d9381fa A1 Farahmand , H. A1 Mohammadi, M. A1 Iranmanesh, A. A1 Naseralavi, S. S. T1 EXACT SOLUTION FOR FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED MICROPLATES BASED ON THE STRAIN GRADIENT THEORY JF International Journal for Multiscale Computational Engineering JO JMC YR 2015 FD 2015-12-20 VO 13 IS 6 SP 463 OP 474 K1 rectangular microplate K1 strain gradient theory K1 functionally graded K1 Kirchhoff plate theory K1 free vibration AB 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. PB Begell House LK https://www.dl.begellhouse.com/journals/61fd1b191cf7e96f,1e3cf40c0f154bbb,73f048da3d9381fa.html