A NEW GENERALIZED TIMOSHENKO MODEL FOR PIEZOELECTRIC CYLINDRICAL RODS BY USING THE VARIATIONAL ASYMPTOTIC METHOD

Based on the Variational Asymptotic Method (VAM), a new generalized Timoshenko model is constructed for piezoelectric rods, of which no electric potential along lateral surfaces is specified. The model is to accurately capture the effects of the dielectric, the polarization of piezoelectric materials as well as the coupled electromechanical nature. The three-dimensional (3D) electromechanical enthalpy is asymptotically approximated by the VAM, using the ratio of the cross-sectional radius to the length of the rod as the small parameter. As a result, an equivalent one-dimensional electromechanical enthalpy is developed. In the meantime, the energy terms, which are asymptotically corrected up to the second order, are kept in the approximated enthalpy expression. For ease of practical application, the approximated enthalpy is then transformed into a generalized Timoshenko model which involves the traditional six mechanical degrees of freedom along with an additional electrical degree of freedom. The cross-sectional polarization example of a cantilever piezoelectric bar shows that results from the proposed model agree well with the ANSYS 3D multiphysical simulation, confirming the reliability of the model as well as its capability in simplifying the analysis with insignificant loss in accuracy.