Free Vibration Analysis of Piezoelectric Nanobeam Based on a 2D- Formulation and Non-local Elasticity Theory

The present paper presents an accurate and efficient method for the analysis of free vibration of piezoelectric nanobeam. In this method, Eringen's nonlocal elasticity theory is used to apply the small-scale effects. Despite the shear deformation theories, in the present theory, the displacement and strain fields are considered as a general form, and out-of-plane normal strain is not neglected. The governing equations of piezoelectric nanobeam are derived by employing Hamilton's principle. By solving these equations, natural frequencies related to flexural and thickness modes for the free vibration of nanobeam are obtained. The Convergence of the predicted results is studied, and the effects of various parameters such as nonlocal parameter, length to thickness ratio, and applied external voltage are investigated. To verify the accuracy of the present method, the results predicted by the present theory are compared with those of the theories available in the literature and the finite element method. This study shows that the natural frequencies predicted by the present theory are smaller than those of shear deformation theories. The results of this study show that the natural frequency of the piezoelectric nanobeam increases by increasing the negative applied electric voltage as well as tensile axial load and decreasing the nonlocal parameter. The results show that the natural frequencies related to thickness modes are not negligible and the shear deformation theories, the present theory can predict these frequencies.