Applied Mathematics and Mechanics (English Edition) ›› 2026, Vol. 47 ›› Issue (9): 2043-2062.doi: https://doi.org/10.1007/s10483-026-3429-7

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Active quasi-zero stiffness vibration isolator for time-varying load conditions

Tianci JIANG1, Guangdong SUI1, Wentao WU1, Xiaobiao SHAN1(), M. ELSAMANTY2,3   

  1. 1.State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China
    2.Mechanical Department, Faculty of Engineering at Shoubra, Benha University, Cairo 11672, Egypt
    3.Mechatronics and Robotics Department, School of Innovative Design Engineering, Egypt-Japan University of Science and Technology, Alexandria 21934, Egypt
  • Received:2026-03-27 Revised:2026-06-22 Published:2026-09-18
  • Contact: Xiaobiao SHAN, E-mail: shanxiaobiao@hit.edu.cn
  • About author:First author contact:These authors contributed equally
  • Supported by:
    Project supported by the National Natural Science Foundation of China (No. 52375088), the Postdoctoral Fellowship Program and China Postdoctoral Science Foundation (Nos. BX20250470 and 2025M784351), and the Heilongjiang Graduate Excellence Funding Program (No. LJYXLZR2025-027)

Abstract:

To resolve the deteriorated vibration isolation performance of existing passive quasi-zero stiffness (QZS) vibration isolators caused by time-varying loads and stiffness mismatch, this paper proposes a novel load-adaptive QZS vibration isolator (LAQVI) based on radial basis function (RBF) neural network adaptive sliding mode control (SMC). The isolator adopts a composite structure coupling linear springs and electromagnetic units, which delivers adjustable QZS characteristics based on a nonlinear stiffness compensation mechanism. This paper analyzes the influence of various key parameters on the QZS characteristics. Dynamic equation analysis clarifies the relationship between load mismatch and displacement transmissibility, and theoretical studies confirm that excitation current control effectively enhances isolation performance. In addition, a sliding mode controller based on RBF neural network adaptation is designed, leveraging the RBF neural network’s learning and adaptive capabilities for rapid load variation estimation. Simulation results show that the adaptive control of excitation current can effectively compensate for the deviation of the isolation platform and enhance vibration isolation performance. Finally, static experiments verify the QZS characteristics of the isolator, and dynamic load experiments demonstrate the controller’s adaptive adjustment ability for load changes. Vibration test results show that the LAQVI exhibits reliable load adaptability and effective low-frequency vibration isolation performance under time-varying load conditions. The proposed LAQVI provides a theoretical basis for the application of QZS vibration isolators in fields such as intelligent equipment.

Key words: vibration isolation, quasi-zero stiffness (QZS), active vibration control, nonlinear stiffness compensation, sliding mode control (SMC), radial basis function (RBF) neural network

2010 MSC Number: 

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