On transmission Zeros of piezoelectric structures

The evaluation of transmission zeros is of great importance for the control engineering applications. The structures equipped with piezoelectric patches are complex to model and usually require finite element approaches supplemented by model reduction. This study rigorously investigates the influence of mesh size, model reduction, boundary conditions (free and clamped), and sensor/actuator configuration (collocated and non-collocated) on the evaluation of transmission zeros of the piezoelectric structures. The numerical illustrations are presented for a thin rectangular plate equipped with a single pair of piezoelectric voltage sensor/ voltage actuator. Through the examples considered in this study, a link is presented between the static response (or static deflected shape) and the transmission zeros of the piezoelectric structures. This interesting observation forms the basis of: (i) a local mesh refinement strategy for computationally efficient estimation of the transmission zeros and (ii) a physical interpretation of the pole-zero pattern in the case of piezoelectric structures. The physical interpretation developed in this study helps in qualitatively explaining the pole-zero patterns observed for different configurations. It is also shown that this understanding of the relation between the static deformed shape and the transmission zeros can be used by the practitioners to modify the pole-zero pattern through a careful selection of the orientation and the size of the piezoelectric patches.