《Analytical modelling and free vibration analysis of piezoelectric bimorphs》.pdf

938 Zhou et al. / J Zhejiang Univ SCI 2005 6A(9):938-944 Journal of Zhejiang University SCIENCE ISSN 1009-3095 /jzus E-mail: jzus@ Analytical modelling and free vibration analysis of * piezoelectric bimorphs ZHOU Yan-guo (周燕国)†, CHEN Yun-min (陈云敏)†‡, DING Hao-jiang (丁皓江) (Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China) †E-mail: qzking@; cym@ Received Mar. 1, 2005; revision accepted Apr. 20, 2005 Abstract: An efficient and accurate analytical model for piezoelectric bimorph based on the improved first-order shear defor- mation theory (FSDT) is developed in this work. The model combines the equivalent single-layer approach for mechanical dis- placements and a layerwise-type modelling of the electric potential. Particular attention is devoted to the boundary conditions on the outside faces and to the interface continuity conditions of the bimorphs for the electromechanical variables. Shear correction factor (k) is introduced to modify both the shear stress and the electric displacement of each layer. And the detailed mathematical derivations are presented. Free vibration problem of simply supported piezoelectric bimorphs with series or parallel arrangement is investigated for the closed circuit condition, and the results for different length-to-thickness ratios are compared with those ob- tained from the exact 2D solution. Excellent agreements between the present model prediction with k=8/9 and the exact solutions are observed for the resonant frequencies. Key words: Piezoelectric bimorph, Analytical model, Free vibration, Shear correcti