Finite element-based analysis of shunted piezoelectric structures for vibration damping

Piezoelectric patches shunted with passive electrical networks can be attached to a host structure for reduction of structural vibrations. This approach is frequently called “shunted piezo damping” and has the advantage of guaranteed stability and low complexity in implementation. For numerical treatment of such structures, a finite element modelling methodology is presented that incorporates both the piezoelectric coupling effects of the patches and the electrical dynamics of the connected passive electrical circuits. It allows direct computation of the achieved modal damping ratios as a major design criterion of interest. The damping ratios are determined from the eigenvalue problem corresponding to the coupled model containing piezoelectric structure and passive electrical circuit. The model includes local stiffening and mass effects as a result of the attached patches and, therefore, enables accurate prediction of the natural frequencies and corresponding modal damping ratios. This becomes crucial for choosing the patch thickness to achieve optimal modal damping for a given host structure. Additionally, structures with complex geometry or spatially varying material properties can easily be handled. Furthermore, the use of a finite element formulation for the coupled model of piezoelectric patches and a host structure facilitates design modifications and systematic investigations of parameter dependencies. In this paper, the impact of parameters of the passive electrical network on modal damping ratios as well as the variation of the patch thickness are studied. An application of this modelling method is realized by commercial software packages by importing fully coupled ANSYS© – models in MATLAB©. Afterwards, modal truncation is applied, the dynamic equations of the passive electrical network are integrated into the piezoelectric model and eigenvalue problems are solved to extract the increase in modal damping ratios. The numerical results are verified by experiments.