On the local/nonlocal piezoelectric nanobeams: Vibration, buckling, and energy harvesting

Abstract

Based on a paradox-free nonlocal theory—two-phase local/nonlocal elasticity—vibration, buckling, and energy harvesting of piezoelectric nanobeams are investigated for the first time. By the means of the differential form of two-phase elasticity and Hamilton's principle, governing equations and boundary conditions are obtained. The exact solution as well as a numerical solution, Generalized Differential Quadrature Method (GDQM), are presented to extract results. Also, for the sake of obtaining equations for the forced vibration and energy harvesting analysis, the Galerkin method is utilized to discretize the governing equation. Given the fact that the differential nonlocal elasticity is not able to apply the size dependency on uniform loads, for the first time, the size-dependent piezoelectric load is taken into account through the two-phase elasticity. Also, vibration and energy harvesting of a clamped free nanobeam – which is a really good case for harvesting energy and cannot be accurately studied by differential nonlocal – are investigated employing the two-phase elasticity. To validate the present formulation and solution procedures, several comparison studies are conducted. Comparison between the common differential nonlocal elasticity and two-phase theory reveals that differential nonlocal elasticity is incompetent to yield reliable results for studying the vibration and energy harvesting of piezoelectric-based materials. Therefore, to study the mechanics of piezoelectric nano structures, other nonlocal theories such as two-phase local/nonlocal elasticity should be used. This paper can be a useful basis to investigate the vibration, buckling, and energy harvesting of nano piezoelectric devices and to improve their design.