Dynamic characteristics of a cyclic-periodic structure with a piezoelectric network

This paper deals with a cyclic-periodic structure with a piezoelectric network. In such a system, there is not only mechanical connection but also electrical connection between adjacent periodic sectors. The objective is to learn whether the presence of a piezoelectric network would change the dynamic characteristics of the system. The background of the research is about vibration reduction of a bladed disk in an aero-engine, and the system is simulated by a lumped parameter model. The dynamic equations of the system are derived, and then the analytical solution corresponding to the eigenvalue problem is given. The vibration responses to single traveling wave excitations (EO excitations) and multiple traveling wave excitations (NEO excitations) are studied. The results show that the presence of a piezoelectric network would change the natural frequencies of the system compared with those of the system with the piezoelectric shunt circuit. The forced response is sensitive to the connection type and the elements of the network. An energy analysis of the electro-mechanical coupling system has been performed to understand its dynamic behavior, and the following conclusion is obtained: a vibration reduction to excitations whose primary harmonic component is not zero can be achieved by a parallel piezoelectric network, while a reduction to other excitations should be based on a series piezoelectric network.