Analytical and numerical approaches to piezoelectric bimorph |
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| Institution: | 1. Laboratoire de Modélisation en Mécanique (UMR 7607), Université Pierre et Marie Curie, Case 162, 4 Place Jussieu, 75252 Paris Cedex 05, France;2. Laboratoire d’Etudes Mécaniques des Assemblages (FRE 2481), Université de Versailles/Saint-Quentin-en-Yvelines, Bâtiment Descartes, 45 Ave des Etats-Unis, 78035 Versailles Cedex, France;1. School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, Gansu, PR China;2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi''an Jiaotong University, Xi''an, 710049, Shaanxi, PR China;3. School of Science, Lanzhou University of Technology, Lanzhou, 730050, Gansu, PR China;1. Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt;1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, PR China;2. Institute of Mechanical and Transportation Engineering, Guangxi University of Science and Technology, Liuzhou 545006, PR China;1. Key Lab of Structures Dynamic Behaviour and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China;2. Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China |
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| Abstract: | We propose an efficient and accurate approach to piezoelectric bimorph based on a refined expansion of the elastic displacement and electric potential. The field approximation of the through-the-thickness variation accounts for a shear correction and a layerwise modelling for the electric potential. A particular attention is devoted to the boundary conditions on the bottom and top faces of the plate as well as to the interface continuity conditions for the electromechanical variables. The continuity condition on the electric potential imposes some restrictions on the approximation of the electric potential. Moreover, the continuity condition on the normal component of the electric induction at the bimorph interface is ensured by a Lagrange multiplier. The equations of the piezoelectric bimorph are obtained by using variational formulation involving the appropriate boundary and continuity conditions.A selection of numerical illustrations is presented for the series and parallel piezoelectric bimorphs simply supported under cylindrical bending conditions. Two types of electromechanical load are considered (i) a surface density of force applied on the top face and (ii) an electric potential applied on the bottom and top faces of the bimorph. The results thus obtained are compared to those provided by finite element computations performed for the full 3D model and by a simplified model without shear effect. At last, the problem of piezoelectric bimorph vibration is also examined for both closed and open circuit conditions. Excellent predictions with low error estimates of the local (profile) and global responses as well as resonant frequencies are observed. The comparisons assess of the effectiveness of the present approach to piezoelectric bimorph. |
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