Dynamic Characteristics of a Two-stage Quasi-zero-stiffness Vibration Isolation System with Electromagnetic Shunt Damping

doi:10.3901/JME.2024.05.157

Abstract

Abstract: Two-stage quasi-zero-stiffness vibration isolator (TQZS VI) can effectively suppress low-frequency vibrations and quickly attenuate high-frequency vibrations. An electromagnetic shunt damping (ESD) has also been proven to be a feasible way to harvest energy from vibrating structures. By integrating the TQZS VI and the ESD, a novel TQZS VI that realizes dual functions of vibration control and energy harvesting is proposed. Both layers of quasi-zero-stiffness are achieved by a vertical spring connected in parallel with two symmetrical transverse springs, and electromagnetic shunt damping as a viscous dissipative element between the upper and lower layers is provided by an ESD connected to an external resonant resistance-capacitance-inductance (RCI) series circuit. First, the mechanical and mathematical models of the two-stage quasi-zero-stiffness vibration isolator with electromagnetic shunt damping (ESD-TQZS VI) are established. Then, the amplitude-frequency response equation of the ESD-TQZS VI is solved using the harmonic balance method (HBM) and the arc length continuation method. Moreover, the force transmissibility and output power of the ESD-TQZS VI are defined, and the effects of system parameters on vibration isolation and energy harvesting are analyzed. It is found that a sizeable damping ratio is beneficial for attenuating resonance peaks while having a negligible effect on energy harvesting. Significant shunt resistance is not conducive to attenuating resonant peaks and can narrow the isolation frequency band of the system. Finally, the bifurcation and attractor coexistence characteristics of the ESD-TQZS VI system after parameter optimization are revealed. The results indicate that the ESD-TQZS VI can considerably attenuate resonance peaks of low-frequency vibration and achieve vibration energy harvesting at the same time.

Key words: quasi-zero-stiffness, two-stage vibration isolation, low-frequency vibration, energy harvesting, electromagnetic shunt damping

CLC Number:

TH113

MA Zhaozhao, ZHOU Ruiping, YANG Qingchao, LEE Heow Pueh, CHAI Kai. Dynamic Characteristics of a Two-stage Quasi-zero-stiffness Vibration Isolation System with Electromagnetic Shunt Damping[J]. Journal of Mechanical Engineering, 2024, 60(5): 157-168.

References

[1] YAN Bo，YU Ning，WANG Zhihao，et al. Lever-type quasi-zero stiffness vibration isolator with magnetic spring[J]. Journal of Sound and Vibration，2022，527：116865.
[2] WANG Qiang，ZHOU Jiaxi，WANG Kai，et al. Dual-function quasi-zero-stiffness dynamic vibration absorber：Low-frequency vibration mitigation and energy harvesting[J]. Applied Mathematical Modelling，2023，116：636-654.
[3] LU Zeqi，ZHAO Long，DING Hu，et al. A dual-functional metamaterial for integrated vibration isolation and energy harvesting[J]. Journal of Sound and Vibration，2021，509：116251.
[4] SUN Ruqi，ZHOU Shengxi，CHENG Li. Ultra-low frequency vibration energy harvesting：Mechanisms，enhancement techniques，and scaling laws[J]. Energy Conversion and Management，2023，276：116585.
[5] 刘兴天，黄修长，张志谊，等. 激励幅值对准零刚度隔振器特性的影响[J]. 机械工程学报，2013，49(6)：89-94. LIU Xingtian，HUANG Xiuchang，ZHANG Zhiyi，et al. Influence of excitation amplitude and load on the characteristics of a quasi-zero stiffness isolator[J]. Journal of Mechanical Engineering，2013，49(6)：89-94.
[6] WANG Yong，LI Shunming，NEILD S，et al. Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness[J]. Nonlinear Dynamics，2017，(88)：635-654.
[7] ZHOU Jiaxi，WANG Kai，XU Daolin，et al. Vibration isolation in neonatal transport by using a quasi-zero-stiffness isolator[J]. Journal of Vibration and Control，2018，24(15)：3278-3291.
[8] 王晓杰，刘辉，郦文平，等. 准零刚度扭转隔振器振动传递特性研究[J]. 机械工程学报，2018，54(21)：49-56. WANG Xiaojie，LIU Hui，LI Wenping，et al. Vibration transmission characteristics of a quasi-zero-stiffness torsional isolator[J]. Journal of Mechanical Engineering，2018，54(21)：49-56.
[9] 利云云，周徐斌，陈卫东，等. 一类双层高静低动刚度隔振系统动力学特性和应用局限性研究[J]. 振动工程学报，2021，34(2)：364-371. LI Yunyun，ZHOU Xubin，CHEN Weidong，et al. Dynamic characteristics and application restrictions of a two-stage vibration isolation system with high-static-low-dynamic stiffness[J]. Journal of Vibration Engineering，2021，34(2)：364-371.
[10] MOLYNEUX W. Supports for vibration isolation[R]. Great Britain：Aeronautical Research Council，1957.
[11] LIU Xingtian，HUANG Xiuchang，HUA Hongxing. On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector[J]. Journal of Sound and Vibration，2013，332(14)：3359-3376.
[12] SUN Yi，ZHAO Jinglei，WANG Min，et al. High-static-low-dynamic stiffness isolator with tunable electromagnetic mechanism[J]. IEEE/ASME transactions on mechatronics，2019，25(1)：316-326.
[13] YUAN Shujin，SUN Yi，WANG Min，et al. Tunable negative stiffness spring using maxwell normal stress[J]. International Journal of Mechanical Sciences，2021，193：106127.
[14] WANG Qiang，ZHOU Jiaxi，WANG Kai，et al. Design and experimental study of a compact quasi-zero-stiffness isolator using wave springs[J]. Science China Technological Sciences，2021，64(10)：2255-2271.
[15] DENG Tianchang，WEN Guilin，DING Hu，et al. A bio-inspired isolator based on characteristics of quasi-zero stiffness and bird multi-layer neck[J]. Mechanical Systems and Signal Processing，2020，145：106967.
[16] YAN Ge，ZOU Hongxiang，WANG Sen，et al. Bio-inspired vibration isolation：Methodology and design[J]. Applied Mechanics Reviews，2021，73(2)：020801.
[17] YAN Ge，ZOU Hongxiang，WANG Sen，et al. Bio-inspired toe-like structure for low-frequency vibration isolation[J]. Mechanical Systems and Signal Processing，2022，162：108010.
[18] CAI Changqi，ZHOU Jiaxi，WU Linchao，et al. Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps[J]. Composite structures，2020，236：111862.
[19] AHN K. Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat[J]. Journal of Sound and Vibration，2014，333(5)：1245-1268.
[20] CHURCHILLl C，SHAHAN D，SMITH S，et al. Dynamically variable negative stiffness structures[J]. Science advances，2016，2(2)：e1500778.
[21] WANG Kai，ZHOU Jiaxi，OUYANG Huajiang，et al. A semi-active metamaterial beam with electromagnetic quasi-zero-stiffness resonators for ultralow-frequency band gap tuning[J]. International Journal of Mechanical Sciences，2020，176：105548.
[22] PU Huayan，YUAN Shujin，PENG Yan，et al. Multi-layer electromagnetic spring with tunable negative stiffness for semi-active vibration isolation[J]. Mechanical Systems and Signal Processing，2019，121：942-960.
[23] MOHEIMANI S. A survey of recent innovations in vibration damping and control using shunted piezoelectric transducers[J]. IEEE transactions on control systems technology，2003，11(4)：482-494.
[24] YIGIT U，CIGEROGLU E，BUDAK E. Chatter reduction in boring process by using piezoelectric shunt damping with experimental verification[J]. Mechanical Systems and Signal Processing，2017，94：312-321.
[25] MA Hongye，YAN Bo. Nonlinear damping and mass effects of electromagnetic shunt damping for enhanced nonlinear vibration isolation[J]. Mechanical Systems and Signal Processing，2021，146：107010.
[26] SUN Ruqi，WONG Waion，CHENG Li. Optimal design of a tunable electromagnetic shunt damper for dynamic vibration absorber[J]. Mechatronics，2022，83：102763.
[27] FORWARD R. Electronic damping of vibrations in optical structures[J]. Applied Optics，1979，18(5)：690-697.
[28] HAGOOD N，VON FLOTOW A. Damping of structural vibrations with piezoelectric materials and passive electrical networks[J]. Journal of Sound and Vibration，1991，146(2)：243-268.
[29] BEHRENS S，FLEMING A，MOHEIMANI S. Electromagnetic shunt damping[C]//Proceedings 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2003). IEEE，2003，2：1145-1150.
[30] ZUO Lei，CUI Wen. Dual-functional energy-harvesting and vibration control：electromagnetic resonant shunt series tuned mass dampers[J]. Journal of Vibration and Acoustics，2013，135(5)：051018.
[31] SUN Hongxin，LUO Yifan，WANG Xiuyong，et al. Seismic control of a SDOF structure through electromagnetic resonant shunt tuned mass-damper-inerter and the exact H2 optimal solutions[J]. Journal of Vibroengineering，2017，19(3)：2063-2079.
[32] LUO Yifan，SUN Hongxin，WANG Xiuyong，et al. Wind induced vibration control and energy harvesting of electromagnetic resonant shunt tuned mass-damper-inerter for building structures[J]. Shock and Vibration，2017，2017：4180134.
[33] KAKOU P，BARRY O. Simultaneous vibration reduction and energy harvesting of a nonlinear oscillator using a nonlinear electromagnetic vibration absorber-inerter[J]. Mechanical Systems and Signal Processing，2021，156：107607.
[34] JOUBANEH E，BARRY O. On the improvement of vibration mitigation and energy harvesting using electromagnetic vibration absorber-inerter：Exact h2 optimization[J]. Journal of Vibration and Acoustics，2019，141(6)：061007.
[35] WANG Qiang，ZHOU Jiaxi，WANG Kai，et al. A compact quasi-zero-stiffness device for vibration suppression and energy harvesting[J]. International Journal of Mechanical Sciences，2023：108284.
[36] SUN Ruqi，WONG Waion，CHENG Li. Bi-objective optimal design of an electromagnetic shunt damper for energy harvesting and vibration control[J]. Mechanical Systems and Signal Processing，2023，182：109571.
[37] LU Zeqi，BRENNAN M，YANG Tiejun，et al. An investigation of a two-stage nonlinear vibration isolation system[J]. Journal of Sound and Vibration，2013，332(6)：1456-1464.
[38] CHAI Kai，LI Shuang，LOU Jingjun，et al. Line spectra chaotification of the nonlinear vibration isolation system on the flexible foundation based on the open-plus-nonlinear-closed-loop method[J]. Journal of Vibration and Control，2021，27(7-8)：731-742.
[39] HSU C. A theory of cell-to-cell mapping dynamical systems[J]. Journal of Applied Mechanics，1980，47(4)：931-939.
[40] EASON R，DICK A. A parallelized multi-degrees-of- freedom cell mapping method[J]. Nonlinear Dynamics，2014，77：467-479.