Optimization of the Location of Piezoelectric Patches Bonded on a Rotor Shaft Surface Using an Iterative Optimization Framework

This paper presents an optimization-based framework for active vibration control of rotor bearing systems using external surface-bonded piezoelectric patches. The rotor bearing system is modelled using the Finite Element Method (FEM), enabling the coupling between the shaft and the flexible piezoelectric actuators. A Linear Quadratic Regulator (LQR) is adopted to achieve optimal feedback control considering the balance between vibration reduction and control effort. The central contribution of this work is a comprehensive actuator placement optimization of the axial and angular position of the piezoelectric patches along the shaft. Firstly, axial positions are selected by maximizing a multimodal weighted Modal Strain Energy (MSE) criterion over a selected number of bending modes. In the second stage, which constitutes the main novelty of this work, the angular position of each pair of bonded piezoelectric patches is optimized. Each piezoelectric pair generates control moments at each extremity of the patch. The influence of the angular separation between independent piezoelectric pairs bonded at different axial locations is investigated through an iterative optimization framework. The optimized actuator placements are subsequently employed within an LQR-based active vibration control framework. The parameters of the controller are selected using a Genetic Algorithm (GA). Numerical simulations are performed on a bi-disk flexible rotor bearing system. The results of the numerical simulations demonstrate that the combined axial-circumferential optimization significantly enhances the controllability of the rotor system and improves the multimodal vibration suppression capability, achieving an improvement of approximately 93%. The proposed methodology offers a physically meaningful and computationally efficient framework, guaranteeing symmetric and effective vibration control.