Abstract
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.
Similar content being viewed by others
References
Rao, S.S. and Sunar, M., Piezoelectricity and its use in disturbance sensing and control of flexible structures: asurvey. ASME Applied Mechanics Reviews, 1994, 47: 113–123.
Adelman, N.T., Stavsky, Y. and Segal, E., Axisymmetric vibration of radially polarized piezoelectric ceramic cylinders. Journal of Sound and Vibration, 1975, 38: 245–254.
Ding, H.J., Guo, Y.M., Yang, Q.D. and Chen, W.Q., Free vibration of piezoelectric cylindrical shells. Acta Mechanica Solida Sinica, 1997, 10(1): 48–55.
Sarma, K.V., Torsional wave motion of a finite inhomogeneous piezoelectric cylindrical shell. International Journal of Engineering Science, 1980, 18: 449–454.
Shul’ga, N.A., Grigorenko, A.Y. and Loza, I.A., Axisymmetric electroelastic waves in a hollow piezoelectric ceramic cylinder. Prikladnaya Mekhanika, 1984, 20: 23–28.
Paul, H.S. and Venkatesan, M., Vibration of a hollow circular cylinder of piezoelectric ceramics. Journal of the Acoustical Society of America, 1987, 82: 952–956.
Du, J.K., Shen, Y.P. and Tian, W.P., Anti-plane shear waves scattering from a partially debonded magneto-electro-elastic circular cylindrical inhomogeneity. Acta Mechanica Solida Sinica, 2004, 17(1): 4–14.
Feng, W.J., Wang, L.Q., Jiang, Z.Q. and Zhao, Y.M., Shear wave scattering from a partially debonded piezoelectric cylindrical inclusion. Acta Mechanica Solida Sinica, 2004, 17(3): 71–82.
Li, F.M., Wang, Y.S. and Chen, A.L., Wave localization in randomly disordered periodic piezoelectric rods. Acta Mechanica Solida Sinica, 2006, 19(1): 53–60.
Zhu, J.Q., Shen, Y.P. and Chen, C.Q., Analysis of the dynamic stability of electrical graded piezoelectric cylindrical shells. Acta Mechanica Solida Sinica, 2004, 17(2): 21–28.
Ding, H.J., Wang, H.M. and Hou, P.F., The transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems. International Journal of Solids and Structures, 2003, 40: 105–123.
Loza, I.A. and Shul’ga, N.A., Forced axisymmetric vibrations of a hollow piezoelectric sphere with an electrical method of excitation. Soviet Applied Mechanics, 1990, 26: 818–822.
Li, H.Y., Liu, Z.X. and Lin, Q.R., Spherical-symmetric steady-state response of piezoelectric spherical shell under external excitation. Applied Mathematics and Mechanics, 2000, 21: 947–956.
Chen, W.Q., Ding, H.J. and Xu, R.Q., Three dimensional free vibration analysis of a fluid-filled piezoelectric hollow sphere. Computers and Structures, 2001, 79: 653–663.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y607087).
Rights and permissions
About this article
Cite this article
Ying, Z., Zhu, X. Response analysis of piezoelectric shells in plane strain under random excitations. Acta Mech. Solida Sin. 22, 152–160 (2009). https://doi.org/10.1016/S0894-9166(09)60100-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S0894-9166(09)60100-2