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<p>This study presents a multi-channel design and optimization framework for active vibration control of ring shell structures using flexoelectric actuators. The novelty of this work is three-fold: (i) a coupled electromechanical dynamic model that captures both membrane and bending responses of a freely floating ring under localized flexoelectric actuation; (ii) a practical actuation mechanism based on AFM-probe–generated nonuniform electric fields to produce highly localized converse-flexoelectric driving forces; and (iii) a multi-objective Sequential Quadratic Programming (SQP) procedure that simultaneously optimizes actuator positions and drive voltages to minimize a physically motivated roundness function measuring deviation from circularity. Numerical case studies for a ring (radius 0.05&#xa0;m, thickness 0.001&#xa0;m; flexoelectric patch thickness 50&#xa0;μm; AFM tip radius 50&#xa0;nm; actuation voltages up to 10&#xa0;V) demonstrate that the SQP routine robustly identifies actuator configurations that cancel overall vibration across multiple excited modes, yielding near-zero residual deformation where single-channel schemes fail. We further show that the optimal actuator distributions obey cyclotomic-polynomial symmetry and that control benefit saturates as the actuator count increases (computational cost also rises), indicating an effective practical range for actuator number. The approach offers a systematic route for precision deformation control in ring-shaped micro- and nano-devices and informs design choices for multi-actuator flexoelectric systems.</p>

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Optimization of ring shell structures with multiple flexoelectric actuators based on sequential quadratic programming

  • 期刊论文

  • 发表日期：

    2025年12月25日

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  • Yiming Li,
  • Jie Zhang,
  • Mu Fan,
  • Zhongmin Xiao

摘要

This study presents a multi-channel design and optimization framework for active vibration control of ring shell structures using flexoelectric actuators. The novelty of this work is three-fold: (i) a coupled electromechanical dynamic model that captures both membrane and bending responses of a freely floating ring under localized flexoelectric actuation; (ii) a practical actuation mechanism based on AFM-probe–generated nonuniform electric fields to produce highly localized converse-flexoelectric driving forces; and (iii) a multi-objective Sequential Quadratic Programming (SQP) procedure that simultaneously optimizes actuator positions and drive voltages to minimize a physically motivated roundness function measuring deviation from circularity. Numerical case studies for a ring (radius 0.05 m, thickness 0.001 m; flexoelectric patch thickness 50 μm; AFM tip radius 50 nm; actuation voltages up to 10 V) demonstrate that the SQP routine robustly identifies actuator configurations that cancel overall vibration across multiple excited modes, yielding near-zero residual deformation where single-channel schemes fail. We further show that the optimal actuator distributions obey cyclotomic-polynomial symmetry and that control benefit saturates as the actuator count increases (computational cost also rises), indicating an effective practical range for actuator number. The approach offers a systematic route for precision deformation control in ring-shaped micro- and nano-devices and informs design choices for multi-actuator flexoelectric systems.