Abstract
An efficient spectral element (SE) with electric potential degrees of freedom (DOF) is proposed to investigate the static electromechanical responses of a piezoelectric bimorph for its actuator and sensor functions. A sublayer model based on the piecewise linear approximation for the electric potential is used to describe the nonlinear distribution of electric potential through the thickness of the piezoelectric layers. An equivalent single layer (ESL) model based on first-order shear deformation theory (FSDT) is used to describe the displacement field. The Legendre orthogonal polynomials of order 5 are used in the element interpolation functions. The validity and the capability of the present SE model for investigation of global and local responses of the piezoelectric bimorph are confirmed by comparing the present solutions with those obtained from coupled 3-D finite element (FE) analysis. It is shown that, without introducing any higher-order electric potential assumptions, the current method can accurately describe the distribution of the electric potential across the thickness even for a rather thick bimorph. It is revealed that the effect of electric potential is significant when the bimorph is used as sensor while the effect is insignificant when the bimorph is used as actuator, and therefore, the present study may provide a better understanding of the nonlinear induced electric potential for bimorph sensor and actuator.
Highlights
Piezoelectric materials generate electric potentials in response to mechanical stresses, and produce mechanical movements in response to electric potentials
To validate the effectiveness and the capability of the present model, numerical simulations for a supported piezoelectric bimorph with two different load cases, i.e., a uniform pressure load applied to the top surface and a uniform potential applied to the top and bottom surfaces, are carried out
A supported rectangular piezoelectric bimorph shown in Figure 1, which has been investigated by Fernandes [1], is considered here
Summary
Piezoelectric materials generate electric potentials in response to mechanical stresses, and produce mechanical movements in response to electric potentials. By carrying out exact 3-D analytical solutions for the supported piezoelectric plate [8,9], it is shown that the distribution of the electric potential across the thickness is nearly quadratic. The ESL model is simple and capable of predicting the global responses of the bimorph, but it does not account for the nonlinear distribution of the electric potential across the thickness. To overcome this shortcoming, the FE model using the layer-wise theory [21,22,23,24] or the sublayer theory [2,25,26,27,28] has been recommended. It is further expected that the quadratic distribution of the electric potential across the plate thickness can be accurately approached with more sublayers adopted
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