Analytical Solution of Buckling and Vibration of Functionally Graded Nanop late Embedded in Elastic Medium Considering Nonlocal Effects

In this paper buckling and free vibration behavior of functionally graded nanoplate resting on elastic foundation is investigated. Small scale effects are taken into consideration with employing elasticity nonlocal theory. The governing equations of functionally graded nanoplate are derived based on the Hamilton's principle and solved by using Navier method for boundary conditions simply support. Mechanical properties of the functionally graded nanoplate are assumed to vary continuously along its thickness according to a power law function. The elastic foundation is modeled as two parameter Winkler-Pasternak foundation. To show the accuracy of the present analytical solution, present results are verified with the results available in the literature. The effects of nonlocal parameter, power index, thickness, Winkler and shear module parameters on the critical buckling load and natural frequency of nanoplate are investigated. The results is shown that the natural frequency and critical buckling load decreases with increase in the aspect ratio, nonlocal parameter and index power. Also Winkler and Pasternak foundations lead to incre ase structure stiffness.