Electromechanical modelling and vibration control analysis of cyclic symmetric structures with a piezoelectric vibration absorber

Abstract

This study explored the application of piezoelectric vibration absorbers (PVAs) equipped with synthetic circuits for the vibration control of cyclic symmetric structures. A cyclic symmetric electromechanical model (CSEM) integrated with PVAs was introduced to facilitate the design and optimization of the PVAs. This model was formulated analytically based on the circulant matrix theory, and the dynamic response was computed using the complex mode superposition method with explicit consideration of the intrinsic resistance within the PVA. A case study involving a simplified blisk model and an experimental test rig was conducted to validate the proposed CSEM. The validity of the model was confirmed through a comparative analysis of both the natural and dynamic characteristics obtained using the finite element model and experimental results. Furthermore, the impact of synthetic circuit parameters (inductance and negative capacitance values) and the placement of piezoelectric patches on the vibration control performance of PVA were investigated. The results suggested that the optimal inductance coincide with the analytical value, whereas the optimal negative capacitance of the series was slightly greater than the intrinsic capacitance of the patch. Additionally, mounting the piezoelectric patch on the blade root improved the vibration control.