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Micromachines
Volume 16
Issue 12
10.3390/mi16121307
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Active–Passive Vibration Control of Cantilever Beam Based on Magnetic Spring with Negative Stiffness and Piezoelectric Actuator

by
Min Wang
1,2,3,*,
Zhiwei Jiang
1,2,
Wei Jiang
4,
Xianghui Feng
4,
Jiheng Ding
1,
Yi Sun
1,
Huayan Pu
1,5 and
Songquan Liao
1,*
1
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
2
Shanghai Collaborative Innovation Center of Intelligent Sensing Chip Technology, Shanghai University, Shanghai 200444, China
3
Shangda General Intelligent Robotics Research Institute, Baoshan District, Shanghai 200444, China
4
Beijing Xiaomi Mobile Software Co., Ltd., Beijing 100085, China
5
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China
*
Authors to whom correspondence should be addressed.
Micromachines 2025, 16(12), 1307; https://doi.org/10.3390/mi16121307
Submission received: 14 October 2025 / Revised: 19 November 2025 / Accepted: 19 November 2025 / Published: 21 November 2025
(This article belongs to the Special Issue Exploration and Application of Piezoelectric Smart Structures)
Versions Notes

Abstract

To enhance the low-frequency vibration suppression capability of cantilever beams, a magnetically tunable piezoelectric cantilever beam structure (MTPCBS) is proposed in this paper. A magnetic spring with negative stiffness (NSMS) is fixed at the free end of a cantilever beam, forming a quasi-zero-stiffness structure. Meanwhile, a macro-fiber composite (MFC) patch is bonded near the root of the beam to implement active skyhook damping control for active vibration control. A theoretical model of the cantilever beam, NSMS, and MFC is established, and the displacement transmissibility of the MTPCBS is derived. The influences of the magnet distance of the NSMS and the control gain of the controller are investigated via simulation. Experimental results indicate that compared to the single beam, the effective vibration isolation frequency of the proposed MTPCBS shifts from 15.3 Hz to 4.6 Hz. When subjected to random vibration excitation ranging from 1 to 80 Hz, the root mean square (RMS) value of vibration decreases from 0.03 g to 1.77 × 10−3 g, with the vibration attenuation rate improving from −50% to 91%. The proposed MTPCBS and active–passive vibration control method for cantilever beams significantly enhances low-frequency vibration suppression capabilities, providing a feasible strategy for achieving broadband vibration suppression.
Keywords: vibration suppression of cantilever beam; magnetic spring with negative stiffness; parallel of positive and negative stiffness; macro-fiber composite; skyhook damping control law vibration suppression of cantilever beam; magnetic spring with negative stiffness; parallel of positive and negative stiffness; macro-fiber composite; skyhook damping control law

Share and Cite

MDPI and ACS Style

Wang, M.; Jiang, Z.; Jiang, W.; Feng, X.; Ding, J.; Sun, Y.; Pu, H.; Liao, S. Active–Passive Vibration Control of Cantilever Beam Based on Magnetic Spring with Negative Stiffness and Piezoelectric Actuator. Micromachines 2025, 16, 1307. https://doi.org/10.3390/mi16121307

AMA Style

Wang M, Jiang Z, Jiang W, Feng X, Ding J, Sun Y, Pu H, Liao S. Active–Passive Vibration Control of Cantilever Beam Based on Magnetic Spring with Negative Stiffness and Piezoelectric Actuator. Micromachines. 2025; 16(12):1307. https://doi.org/10.3390/mi16121307

Chicago/Turabian Style

Wang, Min, Zhiwei Jiang, Wei Jiang, Xianghui Feng, Jiheng Ding, Yi Sun, Huayan Pu, and Songquan Liao. 2025. "Active–Passive Vibration Control of Cantilever Beam Based on Magnetic Spring with Negative Stiffness and Piezoelectric Actuator" Micromachines 16, no. 12: 1307. https://doi.org/10.3390/mi16121307

APA Style

Wang, M., Jiang, Z., Jiang, W., Feng, X., Ding, J., Sun, Y., Pu, H., & Liao, S. (2025). Active–Passive Vibration Control of Cantilever Beam Based on Magnetic Spring with Negative Stiffness and Piezoelectric Actuator. Micromachines, 16(12), 1307. https://doi.org/10.3390/mi16121307

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