Band-gap Control And Vibration Suppression Through Piezoelectric Shunting Arrays

Identical piezoelectric patches are periodically bonded to the surface of a controlled structure and each piezoelectric patch is connected to a shunting circuit, forming an array architecture. This array is called piezoelectric shunting array(PSA), while the composite structures which are bonded with PSAs are together named piezoelectric-shunting-array structures(PSAS). Besides the adavantages of the conventional piezoelectric shunt damping technique which is little in adding mass, convenient to mount and easy to use, PSAs also possess phononic band gaps. As such, they are hopeful of achieving the goal of broadband noise and vibration control, and show potential applications in noise and vibration reduction of light-weight and flexible structures. This dissertation is based on the background of noise and vibration control of light-weight and flexible structures, and aiming to suppress the micro-vibration in high-resolution satellites. The major work is centered on one- and two-dimensional PSAs, trying to resolve the relevant theoretical and technical problems. Combing the approaches of theoretical analysis, computational simulation and experimental test, theoretical investigations and explorations of practical application are performed symatically and in depth. The major innovations and contributions of the disseration are as follows:New modeling approaches and calculation methods of PSAS are proposed. The accurate integrating model(AIM) for one-dimensional PSAS is proposed to substitute the conventional long-wavelengh-approximation model(LWM) for the first time. The errors induced by LWM are analysed, too. New calculation methods for band gaps of two-dimensional PSAS are presented, including numerical method and wave field transformation. The numerical method solves the transcendental eigen-problem directly by repeated iteration, while the wave field transformation linearize the eigen-problem. As a result, the propagation constant of two-dimensional PSAS in arbitrary direction can be calculated conveniently. The propsed modeling approaches and calculation methods provide powerful tools for the theoretical analyses and application design of PSAs.The investigation of band-gap properties and physical mechanisms of PSAS are conducted. The properties and formation mechanisms of band gaps are studied symatically and in depth. Different types of shunting circuits, including resistive shunts, resonant shunts and negative capaciatance shunts, are examined, especially the influences of circuit parameters to the propagation constants in band gaps. The resistive shunts cause energy dissipation through damping. Not only the band gaps are affected, but also the the pass bands are attenuated to some degree by damping.In resonant shunts, each inductor forms a resonant element with the inherent capacitance of the connected piezoelectric patch, which induce locally resonant gaps. The introduction of negative capacitance into shunting circuits boosts the electromechanical coupling factor of the piezoelectric shunting system, leading to increases of band-gap widths and attenuation magnitudes. By examing the band-gap properties and mechanisms, the key factors and regularity that affect the band gaps are disclosed. These work offer the theoretical foundation for the design of PSAs.The optimal design of PSAs is achieved. Comprehensively utilizing the foregoing calculation tools and and theoretical achievements, the design of PSAs is optimized by properly selected optimization algorithms. The optimized parameters consist of circuit parameters and geometrical parameters. According to different types of shunting circuit, the circuit parameters include resistance, inductance and negative capacitance. By properly selecting the circuit parameters, the location of band gaps can be tuned conveniently. Furthermore, the optimization of circuit parameters is an effective approach to increasing the band-gap widths and attenuations within the gap. The geometrical parameters contain dimensions of the piezoelectric patch and lattice constant. The size of the piezoelectric patch are critical factors determine the fill fraction and electromechanical coupling efficiency, while the lattice constant is also an important parameter affecting the band-gap properties.The feasibility of applications of PSAs in micro-vibration control of satellites is explored. PSAs absorb both the advantages of convential piezoelectric shunt damping technique and band-gap properties of phononic crystals, and own many distinctive features, such as small adding mass, convenient to mount, easy to use and broadband control, etc. So, PSAs are especially fit for noise and vibration suppression of light-weight and flexible aeronautical structures.Motivated by the persistent demands of noise and vibration control of light-weight and flexible structures, this dissertation dedicates to research on modeling, band gap mechanism, properties and optimization of PSAs. Some preliminary explorations of possible engineering application are performed on micro-vibration suppression of satellites. The achievements of this thesis not only resolve many important theoretical and technical problems in the research of PSAs, but also conduct helpful explorations of their practicl applications in aerospace engineering.