A generalized hypergeometric function method for axisymmetric vibration analysis of a piezoelectric actuator

Axisymmetrical piezoelectric vibration is a classical problem. Generally, the Lommel function method is used to solve this problem, so, the conventional electro-mechanical solutions take the form of infinite series, which converge relatively slowly and are a bit unsuitable for engineering application. For the first time, the present work constructs the exact solutions to axisymmetric electro-mechanical fields of transversely isotropic piezoceramics in terms of generalized hypergeometric functions instead, which can help to avoid the calculation of infinite series to a large extent. Though the mathematical essence of the present solutions is the same as that of the infinite series solutions, the present expression form and numerical computation are more straightforward and thus more suitable for engineering applications. As an example, the current solutions are used to analyze the axisymmetric vibration of a radially polarized cylindrical piezoelectric actuator installed on a metal shaft. Numerical results of the electrical and mechanical resonant fundamental frequencies are verified in the special case of a single hollow piezoelectric cylinder. In addition, the effects of interfacial imperfection and the portion of piezoelectric layer are also discussed.