Free vibrations analaysis of functionally graded composite rectangular na-noplate based on nonlocal exponential shear deformation theory in thermal environment

In the present study the free vibration analysis of functionally graded composite rectangular nanoplates in thermal environment 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. Nonlocal elasticity theory is employed to investigate effect of small scale on natural frequency of the functionally graded rectangular nanoplate. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The govering equations are derived by implementing Hamilton’s principle. To show the accuracy of the formulations, present result’s in specific cases are compared with available results in literature and good agreement are seen. Finally, the effect of various parameters such as nonlocal parameter, power law indexes, width to length ratio, the thickness to length ratio, and temperature fields on the natural frequencies of rectangular FG nanoplates are presented and discussed in detail.