Structural Engineering and Mechanics

  • 제75권6호
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  • Pages.747-769
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  • 2020
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Bending and free vibration analysis of laminated piezoelectric composite plates

  • Zhang, Pengchong (School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture) ;
  • Qi, Chengzhi (School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture) ;
  • Fang, Hongyuan (College of Water Conservancy & Environmental Engineering, Zhengzhou University) ;
  • Sun, Xu (School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture)
  • 투고 : 2019.07.02
  • 심사 : 2020.03.19
  • 발행 : 2020.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

This research is supported by Grants 2018M641168 from China Postdoctoral Science Foundation, Grants 51908022, 2015CB57800 and 51774018 from the National Natural Science Foundation of China, Grant IRT_17R06 from program for Changjiang Scholars and Innovative Research Team, Grants 19YJC630148 from the Humanity and Social Science Youth foundation of Ministry of Education of China, for which the authors are gratefully acknowledged.

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