Layerwise Laminate Analysis of Functionally Graded Piezoelectric Bimorph Beams

Abstract

A layerwise finite element formulation developed for piezoelectric materials is used to investigate the displacement and stress response of a functionally graded piezoelectric bimorph actuator. The formulation is based on the principles of linear thermopiezoelectricity and accounts for the coupled mechanical, electrical, and thermal responses of piezoelectric materials. The layerwise laminate theory is implemented into a linear beam element in order to provide a more accurate representation of the transverse and shear effects that are induced by the increased inhomogeneities introduced through-the-thickness by the functionally graded materials. The accuracy of the formulation is verified with previously published experimental results for a piezoelectric bimorph actuator. Additional studies are conducted to analyze the impact of electric and thermal loads on the deflections and stresses in a bimorph actuator. Results of the study help to demonstrate the capability of the layerwise theory to provide a more complete representation of the through-the-thickness effects that are no longer negligible even in thin piezoelectric beams. In addition, the effects of varying piezoelectric properties through-the-thickness of the beam are shown to provide additional benefits in minimizing the induced deformations and stresses.

Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere

“…Ma et al [11] investigated the electroelastic behavior of a Griffith crack in a functionally graded piezoelectric strip. A layerwise finite element formulation developed by Lee [12] for piezoelectric materials was used to investigated the displacement and stress response of a functionally graded piezoelectric bimorph actuator. Ootao and Tanigawa [13] studied the transient piezothermoelastic problem of a thick functionally graded thermopiezoelectric strip due to nonuniform heat supply.…”

A numerical efficiency study on the active vibration control for a FGPM beam

“…These FGPM are generally made of a mixture of two piezoelectric materials. Several authors studied FGPM beams or plates under thermo-electro-mechanical loads: static analysis have been performed in [4][5][6][7] and modal analysis in [8][9][10][11][12]. The geometrically non linear transient thermo-elastic response of FGM beam integrated with a pair of FGPM sensors has been investigated in [13].…”

A three-dimensional Peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending

“…Lee [22] used a layerwise nite element formulation to investigate the displacement and stress response of an FGP bimorph actuator. By using the re ned 2D models, Brischetto and Carrera [23] studied the static response of a single layered FGP plate. In this work, Carrera's uni ed formulation has been extended to FGP plates in the framework of the principle of virtual displacements.…”