The Piezoelectric Beam Models Based on both Displacement and Stress Fields
Date Issued
2004
Date
2004
Author(s)
Tseng, Kuo-Kang
DOI
zh-TW
Abstract
A piezoelectric beam is often used as a sensor or actuator. Because the output signals and input efforts are always passing through the surface of the beam, it would be grateful if the surface behavior of the beam can be predicted rapidly and precisely. However, the analyses of piezoelectric beams nowadays are always based on the assumed displacement fields. Such models cannot satisfy the traction-prescribed boundary conditions on beam surface. As a consequence, the behavior of the surface cannot be predicted precisely. In this thesis, piezoelectric beam models based on Hellinger-Reissner principle are derived. Since it requires no variational constraint, beam models satisfy both the traction-prescribed and displacement-prescribed boundary conditions become possible. Therefore, good tools to predict piezoelectric behavior precisely and rapidly can be obtained.
The Hellinger-Reissner principle for piezoelectric materials is created in this thesis. Displacement, electric potential, stress, and electric displacement field are independent variables that are expanded by double power series in the depth and width directions. And the three-dimensional equations are further simplified into one-dimensional piezoelectric beam model. Under brief setting, the easy-using coupled sets of differential equations are obtained. The model has been verified with the FEM package “ANSYS”, all fields are predicted properly, and displacement and electric potential are especially precise. Therefore, this developed piezoelectric beam model can indeed predict the piezoelectric behavior fast and precisely.
Subjects
變分法
壓電
樑
piezoelectric
beam
variation
Type
thesis
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