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Smart Structures and Systems
  Volume 1, Number 3, September 2005, pages 309-324

Analytical solutions to piezoelectric bimorphs based on improved FSDT beam model
Yan-guo Zhou, Yun-min Chen and Hao-jiang Ding

    This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.
Key Words
    piezoelectric bimorph; beam model; first-order shear deformation theory; shear correction factor; electric potential; analytical solution.
Department of Civil Engineering, Zhejiang University, Hangzhou 310027, P. R. China

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