Modelling and comparison of cantilever beams withan active-passive hybrid piezoelectric network
LI Mingming1,HUANG Chunrong2,FANG Bo3,DUAN Lei1
1. Beijing Mechanical Equipment Institute, Beijing 100854, China；
2.Military Representative Office at No. 206 Institute of the Aerospace Second Academy, Beijing 100854, China；
3.School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
Taking an Euler-Bernoulli cantilever beam as the study object, active-passive hybrid piezoelectric network (APPN) was analyzed and optimized. Hamilton’s principle and Rayleigh-Ritz method were used to build the dynamic models of the cantilever beam with integrated and separated APPNs, respectively. Parametric optimization was performed for resistance and inductance in the APPN. Furthermore, the velocity feedback control was employed to design the active controller and the open-loop and closed-loop characteristics of the cantilever beams with integrated and separated APPNs, respectively were simulated andn analyzed. The numerical results showed that both integrated and separated APPNs can suppress the structures’ vibrations effectively; compared with the pure active control, the integrated APPN has a better vibration control performance in narrow frequency bands, while the separated APPN has a better vibration control performance in broader frequency bands than both the integrated APPN and the pure active control do.
[1] Li F M, Lyu X X. Active vibration control of lattice sandwich beams using the piezoelectric actuator/sensor pairs[J]. Com- posites: Part B, 2014, 67: 571-578.
[2] Gao L, Lu Q Q, Fei F, et al. Active vibration control based on piezoelectric smart composite[J]. Smart Materials and Struc- tures, 2013, 22(12): 125032.
[3] Zhang S Q, Schmidt R, Qin X S. Active vibration control of piezoelectric bonded smart structures using PID algorithm[J]. Chinese Journal of Aeronautics, 2015, 28(1): 305-313.
[4] Casadei F, Beck B S, Cunefare K A, et al. Vibration control of plates through hybrid configurations of periodic piezoelectric shunts[J]. Journal of Intelligent Material Systems and Struc- tures, 2012, 23(10): 1169-1177.
[5] Jeon J Y. Passive vibration damping enhancement of piezo- electric shunt damping system using optimization approach[J]. Journal of Mechanical Science and Technology, 2009, 23(5): 1435-1445.
[6] Agnes G S. Development of a modal model for simultaneous active and passive piezoelectric vibration suppression[J]. Jour- nal of Intelligent Material Systems and Structures, 1995, 6(4): 482-487.
[7] Li M M, Fang B, Cao D Q, et al. Modeling and analysis of cantilever beam with active-passive hybrid piezoelectric net- work[J]. Science China: Technological Sciences, 2013, 56(9): 2326-2335.
[8] Tsai M S, Wang K W. Control of a ring structure with multiple active-passive hybrid piezoelectrical networks[J]. Smart Mate- rials and Structures, 1996, 5(5): 695-703.
[9] Zhao Y H. Vibration suppression of a quadrilateral plate using hybrid piezoelectric circuits[J]. Journal of Vibration and Con- trol, 2010, 16(5): 701-720.
[10] Godoy T C, Trindade M A. Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks[J]. Journal of Sound and Vibration, 2011, 330(2): 194-216.
[11] Tang J, Wang K W, Philen M. Sliding mode control of struc- ture vibrations via active-passive hybrid piezoelectric network [C]// Wereley N W. Proceedings of SPIE, Newport Beach, CA: SPIE, 1999, 3668: 543-554.
[12] Tsai M S, Wang K W. On the structural damping characteris- tics of active piezoelectric actuators with passive shunt[J]. Journal of Sound and Vibration, 1999, 221(1): 1-22.
[13] Moon S H, Kim S J. Suppression of nonlinear composite panel flutter with active/passive hybrid piezoelectric networks using finit element method[J]. Composite Structures, 2003, 59(4): 525-533.
[14] Hagood N W, Chung W H, Flotow A V. Modelling of piezoele- ctric actuator dynamics for active structural control[J]. Journal of Intelligent Material Systems and Structures, 1990, 1(3): 327-354.
[15] duToit N E, Wardle B L, Kim S G. Design considerations for MEMS-scale piezoelectric mechanical vibration energy harve- sters[J]. Integrated Ferroelectrics, 2005, 71(1): 121-160.
[16] Dietl J M, Garcia E. Beam shape optimization for power har- vesting[J]. Journal of Intelligent Material Systems and Struc- tures, 2010, 21(6): 633-646.
[17] Tang J, Wang K W. Active-passive hybrid piezoelectric net- works for vibration control: comparisons and improvement[J]. Smart Materials and Structures, 2001, 10(4): 794-806.
