Solution modification of a piezoelectric bimorph cantilever under loads

Abstract

Most of the previous investigations on the static performances of piezoelectric bimorph cantilevers are based on the elementary theory of piezo-elasticity. In fact, one fundamental problem has not been solved yet from the view of the theory of piezo-elasticity, that is, a piezoelectric bimorph cantilever covered fully with electrodes on the upper and lower surfaces and subjected to a transversely concentrated load at the free end of the beam. The major obstacle to find the solution is the equipotential conditions on both the upper and lower surfaces of the cantilever. In this article, by establishing suitable boundary conditions and introducing an appropriate Airy stress function, the analytical solutions of a piezoelectric bimorph cantilever under three different loading conditions have been obtained. Numerical analysis is also conducted and the results are consistent with the present theoretical predictions. This investigation amends the corresponding works given by other investigations based on the elementary theory. It is found that the amendments to the end deflections of a PZT-4 piezoelectric bimorph cantilever caused by an end shear force, an end moment, or a voltage difference between the upper and lower surfaces are about 10.46%, 12.78%, and 3.52%, respectively. In addition, it is also found that these amendments depend just on the material parameters, have nothing to do with the geometric parameters of the bimorph cantilever. The Airy stress function proposed in this article can also be used to study other different piezoelectric cantilevers including multilayer piezoelectric cantilevers under corresponding loads.

Stress and active control analysis of functionally graded piezoelectric material cylinder and disk under electro-thermo-mechanical loading

“…In this study, it was assumed that heterogeneous thick-walled cylinders were long and their behavior in the longitudinal direction could be neglected and electro-mechanical behaviors of thick-walled cylinders in the form of the radial and circumferential directions proposed. Shi et al (2015) illustrated the static performance of piezoelectric bimorph cantilever which is covered fully with electrodes on the upper and lower surfaces, under loads based on the theory of piezoelasticity and using the Airy stress function technique. They derived out the analytical solutions which can satisfy all the boundary conditions of the cantilevers.…”

One-Dimensional Theoretical Solution and Two-Dimensional Numerical Simulation for Functionally-Graded Piezoelectric Cantilever Beams with Different Properties in Tension and Compression

“…Under different loading cases and different boundary conditions, Yao and Shi [19] studied the steady-state forced vibration of a FGPM beam. By proposing a solution modification of a piezoelectric bimorph cantilever under loads, Shi et al [20] obtained the analytical solutions of a piezoelectric bimorph cantilever under three different loading conditions. There are many other topics on FGPM beams; due to the length limit of the paper, the review in detail is not presented here.…”

An electroelastic solution for functionally graded piezoelectric material beams with different moduli in tension and compression

“…Yao and Shi (2011) studied the steady-state forced vibration of a FGPM beam under different loading cases and different boundary conditions. Shi et al (2015) proposed a solution modification of a piezoelectric bimorph cantilever under loads and obtained the analytical solutions of a piezoelectric bimorph cantilever under three different loading conditions. There are many other topics on FGPM beams; due to the length limit of this article, they are not reviewed here.…”