Acta Mechanica Solida Sinica

, Volume 22, Issue 2, pp 152–160 | Cite as

Response analysis of piezoelectric shells in plane strain under random excitations

  • Zuguang Ying
  • Xinqun Zhu


The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation, which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials, which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained, and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.

Key words

piezoelectric shell random vibration boundary excitation random response 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  1. 1.Department of Mechanics, School of Aeronautics and AstronauticsZhejiang UniversityHangzhouChina
  2. 2.School of EngineeringUniversity of Western SydneyPenrith South DCAustralia

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