Large Bending Deformation of Piezoelectric Nanobeam with Surface Energy Model

In the present paper, we analyze the influence of surface effect on the nonlinear bending behavior of piezoelectric nanobeams by Euler-Bernoulli model and surface energy model. Based on the principle of minimum potential energy and the electromagnetic theory, the nonlinear governing equation as well as the boundary conditions is deducted incorporated surface effects and piezoelectric effects. The effect of surface effect on bending deformation and induced charge of piezoelectric beams under different boundary conditions is discussed under the condition of small deformation and large deformation. The results show that, under the condition of small deformation, the surface effect reduces the bending deformation and the inductive charge, under the condition of large deformation, the surface effect has little effect on the bending deformation of piezoelectric nanobeams. Furthermore, the external constraints and cross-section width b of the piezoelectric nanobeam have significant effect on the bending deformation stiffness. these conclusions have important guiding significance for the design and correction of nanobeams-based nanomechanical systems and piezoelectric nanofunctional devices.

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

The fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the nanobeams include an internal damping feature. To this end, a closed-circuit condition is considered taking converse piezo–flexoelectric behavior. The kinematic displacement of the classical beam using Lagrangian strains, also applying Hamilton’s principle, creates the needed frequency equation. The natural frequencies are measured in nanoscale by the available nonlocal strain gradient elasticity model. The linear Kelvin–Voigt viscoelastic model here defines the inner viscoelastic coupling. An analytical solution technique determines the values of the numerical frequencies. The best findings show that the viscoelastic coupling can directly affect the flexoelectricity property of the material.

A Nonlinear Electro-Mechanical Analysis of Nanobeams Based on the Size-Dependent Piezoelectricity Theory

Nonlinear formulation of isotropic piezoelectric Euler-Bernoulli nano-beam is developed based on consistent size-dependent piezoelectricity theory. By considering geometrically nonlinear and axial displacement of the centroid of beam sections, basic nonlinear equations of piezoelectric nanobeam are derived using Hamilton's principle and variational method. Afterwards, in the special case for the formulation derived, hinged-hinged piezoelectric nanobeam is studied, and static deflection as well as free vibrations of the nanobeam under mechanical loads is determined. In this case, results of the linear formulation of the size-dependent theory are compared to those of the linear and nonlinear classical continuum theory.