Free Vibrations Analysis of Functionally Graded Rectangular Nano-plates based on Nonlocal Exponential Shear Deformation Theory

In the present study the free vibration analysis of the functionally graded rectangular nanoplates is investigated. The nonlocal elasticity theory based on the exponential shear deformation theory has been used to obtain the natural frequencies of the nanoplate. In exponential shear deformation theory an exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. The nonlocal elasticity theory is employed to investigate the effect of the small scale on the natural frequency of the functionally graded rectangular nanoplate. The govering equations and the corresponding boundary conditions are derived by implementing Hamilton’s principle. To show the accuracy of the formulations, the present results in specific cases are compared with available results in the literature and a good agreement is seen. Finally, the effect of the various parameters such as the nonlocal parameter, the power law indexes, the aspect ratio , and the thickness to lenghth ratio on the natural frequencies of the rectangular FG nanoplates is presented and discussed in detail.

Keywords:

vibration , Functionally graded nanoplates , Nonlocal elasticity , Exponential shear deformation theory