A FSDT model for vibration analysis of Nano rectangular FG plate based on Modified Couple Stress Theory under moving load

In present paper, vibration of Nano FGM plate based on modified couple stress and First Order Shear Deformation Theories (FSDT) under moving load has been developed. Basic equations and linear strains are introduced by first order shear deformation theory and Mori Tanaka’s model is used for the plate. The module of elasticity and density are assumed to vary only through thickness of plate. Governing Equations are derived according to the modified couple stress theory and Hamilton’s principle. Constitutive equations are also derived based on modified couple stress and finally, analytical solution for simply supported Nano rectangular FG plate is obtained by using of Navier solution. Examples of length scales parameter and power law index are presented to show effect of this parameter on plate behaviors. Results show that plate’s deflection enhances with power law index increasing and by increasing of length scale parameter, deflection decreases, and for frequencies, the deflection with both raising of power law index and length parameter scales, are reduced