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Structural Engineering and Mechanics Volume 75, Number 6, September25 2020 , pages 747-769 DOI: https://doi.org/10.12989/sem.2020.75.6.747 |
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Bending and free vibration analysis of laminated piezoelectric composite plates |
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Pengchong Zhang, Chengzhi Qi, Hongyuan Fang and Xu Sun
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| Abstract | ||
| This paper provides a semi-analytical approach to investigate the variations of 3D displacement components, electric potential, stresses, electric displacements and transverse vibration frequencies in laminated piezoelectric composite plates based on the scaled boundary finite element method (SBFEM) and the precise integration algorithm (PIA). The proposed approach can analyze the static and dynamic responses of multilayered piezoelectric plates with any number of laminae, various geometrical shapes, boundary conditions, thickness-to-length ratios and stacking sequences. Only a longitudinal surface of the plate is discretized into 2D elements, which helps to improve the computational efficiency. Comparing with plate theories and other numerical methods, only three displacement components and the electric potential are set as the basic unknown variables and can be represented analytically through the transverse direction. The whole derivation is built upon the three dimensional key equations of elasticity for the piezoelectric materials and no assumptions on the plate kinematics have been taken. By virtue of the equilibrium equations, the constitutive relations and the introduced set of scaled boundary coordinates, three-dimensional governing partial differential equations are converted into the second order ordinary differential matrix equation. Furthermore, aided by the introduced internal nodal force, a first order ordinary differential equation is obtained with its general solution in the form of a matrix exponent. To further improve the accuracy of the matrix exponent in the SBFEM, the PIA is employed to make sure any desired accuracy of the mechanical and electric variables. By virtue of the kinetic energy technique, the global mass matrix of the composite plates constituted by piezoelectric laminae is constructed for the first time based on the SBFEM. Finally, comparisons with the exact solutions and available results are made to confirm the accuracy and effectiveness of the developed methodology. What\'s more, the effect of boundary conditions, thickness-to-length ratios and stacking sequences of laminae on the distributions of natural frequencies, mechanical and electric fields in laminated piezoelectric composite plates is evaluated. | ||
| Key Words | ||
| laminated piezoelectric composite plates; static bending responses; free vibration; the scaled boundary finite element method; the precise integration algorithm | ||
| Address | ||
| Pengchong Zhang, Chengzhi Qi: 1School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 102616, China 2Beijing Advanced Innovation Center for Future Urban Design, Beijing University of Civil Engineering and Architecture, Beijing 100044, China Xu Sun: School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 102616, China Hongyuan Fang: College of Water Conservancy & Environmental Engineering, Zhengzhou University. Zhengzhou 450001, China | ||