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

Experimental verification of the corrected transfer function of a piezoelectric laminate beam

Piezoelectric materials are finding increasing applications in active vibration control of structures. Modeling of a piezoelectric laminate, often results in an infinite-dimensional or a very high-order model. For control design purposes, such a model is simplified by removing higher frequency modes which lie out of the bandwidth of interest. Truncation can considerably perturb the in-bandwidth zeros of the truncated model. This paper suggests a method of minimizing the effect of the removed higher order modes on the low-frequency dynamics of the truncated model of a piezoelectric laminate beam by adding a zero frequency term to the low-order model of the structure. Simulations and experimental results are presented