Piezoelectric networking for mode delocalization and vibration suppression of nearly periodic structures

by 1979- Yu, Hongbiaoyu

iii This thesis investigates the use of piezoelectric circuitry networking technology for mode delocalization and effective vibration suppression in nearly periodic structures. Periodic structures, such as bladed-disks in turbo-machinery, are well known to be susceptible to vibration localization effect which can be caused by the small differences (also referred to as mistuning) in the substructures. As a result of localization, vibration energy is confined to a small number of substructures, and the dynamic behavior of periodic structures can be drastically changed. Consequently, the localization effect could significantly impact the health of such nearly (mistuned) periodic structures. Extensive studies exist concerning mode localization and forced response of nearly periodic structures. Most investigations have focused on exploring the cause of localization, developing methods to quantify the degree of localization, and predicting the maximum forced response. A few studies have explored means to reduce or eliminate localization effect. Recently, Tang and Wang (2003) proposed a new piezoelectric networking concept for mode delocalization of nearly periodic structures and have shown promising results. This thesis aims to further extend the state of the art of delocalization and vibration control of nearly periodic structures via piezoelectric networking technology. First, piezoelectric networking for mode delocalization is further investigated analytically and experimentally. An active coupling enhancement approach via negative capacitance is proposed for improving the effectiveness of the network for mode delocalization. The analysis is conducted using the transfer matrix approach and Lyapunov exponent. A localization index is defined from the correlation between Lyapunov exponents and the localized modes of the electromechanically bi-coupled system, and is used in a comprehensive parameter study. Experiments are carried out to validate the delocalization concept on a bladed disk specimen. The effect of negative capacitance on the network’s performance is also investigated. Both analysis and experiments verify that the mode localization level of mistuned periodic structures can be effectively reduced by the piezoelectric network, and the performance of the network can iv be further improved by the active coupling enhancement approach via negative capacitance. The investigation on the piezoelectric networking is then extended to vibration suppression of the mistuned bladed disk. Due to the localization effect, mistuned bladed disks in turbo-machinery often suffer from large forced response. This study provides a comprehensive analysis on piezoelectric networking for effective multiple harmonic vibration suppression of mistuned bladed disks. The analysis consists of two parts. In the first part, the bladed disk is modeled as a multi-blade periodic system with disk dynamics neglected. A piezoelectric network is designed and optimized analytically after applying the U-transformation technique. The effectiveness of the optimal network for multiple harmonic vibration suppression is demonstrated and compared to the traditional absorber design. Monte Carlo simulation is performed to further examine the effectiveness of the network for mistuned bladed disk systems. Robustness issues associated with key circuitry elements are also investigated. An approach via negative capacitance to improve the system performance and robustness is explored. The analysis shows that the piezoelectric network is quite effective and robust for multiple harmonic vibration suppression of mistuned bladed disks, and the performance and robustness can be further improved by negative capacitance. Based on the analysis in the first part study, we then extend the investigations to a more complex scenario. A bladed disk model with coupled blade-disk dynamics is developed to better describe the actual system and correspondingly, a new multi-circuit piezoelectric network is proposed and optimized analytically for multiple harmonic vibration suppression. The performance and robustness issues of the network are examined numerically via Monte Carlo simulation. Finally, experiments are carried out to demonstrate the multiple harmonic vibration suppression effect of the newly developed piezoelectric network.