Forced vibration analysis of functionally graded anisotropic nanoplates resting on Winkler/Pasternak-foundation

Abstract

This study investigates the forced vibration of functionally graded hexagonal nano-size plates for the first time. A quasi-three-dimensional (3D) plate theory including stretching effect is used to model the anisotropic plate as a continuum one where small-scale effects are considered based on nonlocal strain gradient theory. Also, the plate is assumed on a Pasternak foundation in which normal and transverse shear loads are taken into account. The governing equations of motion are obtained via the Hamiltonian principles which are solved using analytical based methods by means of Navier’s approximation. The influences of the exponential factor, nonlocal parameter, strain gradient parameter, Pasternak foundation coefficients, length-to-thickness, and length-to-width ratios on the dynamic response of the nanoplates are examined. In addition, the accuracy of an isotropic approximate instead of the anisotropic model is studied. The dynamic behavior of the system shows that mechanical mathematics-based models may get better results considering the anisotropic model because the dynamic response can cause prominent differences (up to 17%) between isotropic approximation and anisotropic model.