This paper is dedicated to Prof. Peter Hagedorn, Darmstadt University of Technology, Germany, on the occasion of his 60th birthday.
Usually piezoelectric actuators are nowadays simulated with the help of finite element codes. Analytical models are only used for very simple geometries like beams and plates or in those cases where piezoelectric patches are bonded to a beam or plate. Examples can be found in literature. However, it has to be kept in mind that there are still some problems for which standard finite element codes like ANSYS might get difficulties. One such problem is a piezoelectric transformer with an arbitrary load impedance connected to the electrodes of one of the piezoceramics. Such a system is investigated in this paper. To obtain results which are still valid if the diameter of the rod is not small compared to the wave length, a refined rod theory is used which takes into consideration also the inertia effects due to transverse contraction. To derive the equations of motion and the boundary conditions for such a system Hamilton’s principle for electromechanical systems is used. The equations of motion are solved and compared with experimental results. A comparison with results of a finite element analysis is also given for one special case which could be handled by ANSYS.