Abstract
An efficient spectral element (SE) model for static and dynamic analysis of a piezoelectric bimorph is proposed. It combines an equivalent single layer (ESL) model for the mechanical displacement field with a sublayer approximation for the electric potential. The 2D Gauss-Lobatto-Legendre (GLL) shape functions are used to discretize the displacements and then the governing equation of motion is derived following the standard SE method procedure. It is shown numerically that the present SE model can well predict both the global and local responses such as mechanical displacements, natural frequencies, and the electric potentials across the bimorph thickness. In the case of bimorph sensor application, it is revealed that the distribution of the induced electric potential across the thickness does not affect the global natural frequencies much. Furthermore, the effects of the order of Legendre polynomial and the mesh size on the convergence rate are investigated. Comparison of the present results for a bimorph sensor with those from 3D finite element (FE) simulations establishes that the present SE model is accurate, robust, and computationally efficient.
Highlights
Piezoelectric materials, especially lead zirconate titanate (PZT), can function either as actuator or as sensor for their inherent coupling electromechanical character
A supported rectangular piezoelectric bimorph shown in Figure 1, which was analyzed by Fernandes and Pouget [1], is considered here
The natural frequencies of the bimorph plate predicted by the present model are shown in Table 2 in comparison to the results provided by the 3D finite element (FE) analysis
Summary
Piezoelectric materials, especially lead zirconate titanate (PZT), can function either as actuator or as sensor for their inherent coupling electromechanical character. The most popular simple PZT sensor or actuator consists usually of a slab of piezoelectric ceramic such that the PZT layer expands or contracts mainly in its length direction. To achieve practically meaningful actuation or sensing capabilities in PZT devices, a piezoelectric bimorph consisting of two PZT layers is commonly used for the reason that it can produce flexural deformation significantly larger than the length or thickness deformation of the individual layers [1,2,3,4,5,6]. The applications of the piezoelectric bimorph require the development of admissible approaches entailing capabilities to predict the global responses of the bimorph structure, such as the deflection and natural frequencies. The approaches should address the local responses, such as the through-the-thickness variation of the electric potentials
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