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| Free vibration of multi-layered piezoelectric spherical shells with imperfect interfaces |
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Abstract Upon introducing two displacement and stress functions, two independent state equations are established from the three-dimensional piezoelectricity for free vibration of multilayered piezoelectric spherical shells with imperfect interface. The state equations with variable coefficients are then transferred to ordinary differential equations by expanding the state variables into series of spherical harmonic functions and using the approximate laminate model. Also, the behavior of the imperfect interface is described in detail, and the transfer relation of the state vectors at the interface is obtained so that the global transfer relation between state vectors at the outmost and innermost surface of the shell is derived. Two frequency equations corresponding two classes of vibration are then obtained by incorporating the free traction conditions at the surfaces. Numerical examples are performed with indication that the imperfect interface indices for elastic field have significant effects on the natural vibration frequencies of the shell, but the electrically conductivity of the interface has little effect.
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Received: 08 September 2011
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2012, Vol. 33 
