Three-dimensional analysis of an antiparallel piezoelectric bimorph

Abstract

Summary. Three-dimensional electromechanical responses of a piezoelectric bimorph are studied. The bimorph is antiparallel in the sense that it consists of two identical, plate-like piezoelectric elements with opposite poling directions. Both the top and bottom surfaces of the bimorph are fully covered with negligibly thin conductive electrodes. By introducing a small parameter and using the transfer matrix method it is shown that a three-dimensional solution of the problem can be readily constructed, provided the solution to a set of two-dimensional equations very similar to those in the classic plate theory is obtainable. The three-dimensional solution satisfies all the field equations as well as the boundary conditions on the major surfaces and at the interface between the two piezoelectric plates. In many special cases, the electric edge condition can be fulfilled point by point, and thus the solution is exact in SaintVenant's sense. The formulation and new analytical results for a strip-shaped cantilever bimorph under the action of applied voltage and end moment are presented.

Micro-Sensing Characteristics and Modal Voltages of Linear/Non-Linear Toroidal Shells

“…(Note that since the in-plane electric fields are negligible for most widely used piezoelectric materials, e.g., polyvinylidene fluoride (PVDF), the sensing signals resulting from the in-plane electric fields are not considered here. However, it has been reported that, for some specific piezoelectric structures, the in-plane electric field could be more significant than the through-the-thickness electric field and the throughthickness electric potential is not linear even in the case of a thin-walled structure [15,16]. )…”

Static analysis of 2-2 cement-based piezoelectric composites

“…In the following numerical calculation, polarization direction is the positive z-axis and the piezoelectric coefficient will be defined as e 33 . Otherwise, the polarization direction lies along the negative z-axis and the piezoelectric coefficient will be defined as (−e 33 ) [14]. Other dielectric coefficients and elastic coefficients are assumed to be constant for all the piezoelectric layers.…”

“…From the above equations (8), (9), (13)(14)(15) and (17), the unknown constants A Ck , A Pk , B Ck , B Pk , C 21 , C 2k can be determined as follows:…”

A new two-dimensional model for electro-mechanical response of thick laminated piezoelectric actuator

“…Piezoelectric layers are also frequently used as sensing/actuating elements for control of structures, such as in the postbuckling analysis of thick laminated plates (Shen, 2001) and laminated cylindrical shells (Shen, 2002). Other relevant works include those of Lee and Moon (1989), Wang and Rogers (1991), Koconis et al (1994a,b), Mitchell and Reddy (1995), Reddy and Mitchell (1995), Saravanos and Heyliger (1995), Batra et al (1996a,b), Cheng et al (1999Cheng et al ( , 2000, He et al (2000), , He (2001, 2004), Meguid and Chen (2001), Meguid and Zhao (2002), Cheng and Reddy (2002), He and Lim (2003), Wang and Liew (2003), Liew and Liang (2003), . Recently, Lin et al (2000) derived an analytic solution of a laminated piezoelectric beam based on the two-dimensional constitutive relationships.…”