Applied Mathematics and Mechanics (English Edition) ›› 2026, Vol. 47 ›› Issue (10): 2209-2232.doi: https://doi.org/10.1007/s10483-026-3438-8

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Nonlinear theoretical analysis and experimental validation of configurations implementing vibration absorbing andenergy harvesting

Mengjie SHANG1, Weiyang QIN1(), Mingming SHI1, Jianan PAN2, Qi LIU3, Kuan LU1   

  1. 1.Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, China
    2.College of Mechanical Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
    3.School of Civil Engineering and Architecture, Nanyang Normal University, Nanyang 473061, Henan Province, China
  • Received:2026-05-07 Revised:2026-07-13 Online:2026-10-12 Published:2026-10-12
  • Contact: Weiyang QIN, E-mail: qinweiyang@nwpu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (No. 52405130) and the Natural Science Basic Research Program of Shaanxi Province of China (No. 2024JC-YBQN-0041)

Abstract:

To isolate vibration and harness vibration energy simultaneously, this study proposes a novel piezoelectric-electromagnetic hybrid vibration energy harvester (HVEH). In the structural design, this harvester introduces a quasi-zero-stiffness (QZS) mechanism and lever amplification to increase the displacements. In the transforming mechanism, it combines the electromagnetic and piezoelectric mechanisms to improve the energy harvesting efficiency. First, an electromechanical dynamic model of the system is established. A time-frequency domain transformation strategy is introduced to evaluate the nonlinear electrical outputs of the electromagnetic harvester (EMH) under alternating magnetic fields. The harmonic balance method (HBM) with slowly varying coefficients, combined with the arc-length method, is utilized to determine the analytical amplitude-frequency responses. The results are verified with the numerical simulation. Next, the analytical model is used to explicitly reveal the effects of the key system parameters on the performance. Finally, a harvester prototype is fabricated, and the corresponding experiments are performed. The experimental results demonstrate that the system achieves high harvesting efficiency; under a stochastic excitation with a power spectral density (PSD) of 0.07 g2/Hz, the root mean square (RMS) output powers of the EMH and piezoelectric harvester (PEH) reach 1.788 mW and 223 μW, respectively. This study provides an efficient, self-powered solution for structural health monitoring and vibration mitigation in critical engineering infrastructure.

Key words: vibration energy harvesting, vibration isolation, nonlinear system, quasi-zero-stiffness (QZS), harmonic balance method (HBM)

2010 MSC Number: 

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