Static electromechanical response of piezoelectric tubes as sensors and actuators

This article deals with the fully coupled electromechanical response of an infinitely long piezoelectric tube as a sensor or an actuator. By adopting the variational approach for generalized loading conditions and utilizing Hamilton's principle, we derive the governing differential equations of an infinitely long piezoelectric tube subjected to natural boundary conditions. For studying the direct and converse effects of the piezoelectric tube, the governing equations obtained are solved to give the exact solutions corresponding to different boundary conditions prescribed for the tube functioning as a sensor or an actuator. For numerical illustrations of our analysis, an application is investigated where optical fibers are coated with polyvinylidene difluoride or lead zirconate titanate. The same problems are also solved by ANSYS for numerical comparisons. With a discrepancy of 3-5% at most, good agreements between both results are observed.