Optimization of cantilever beams with multiple flexoelectric actuators based on Newton–Raphson iteration

This study delves into the complexity of optimizing multiple actuators on a cantilever beam, focusing on the flexoelectric effect caused by the non-uniform electric field generated by an atomic force microscope (AFM) probe. Multiple actuators control has significant research value in enhancing the flexoelectric effect, greatly alleviating stress concentration and achieving precise vibration control. The current challenge in multiple flexoelectric actuators research is multi-objective optimization, addressed here using the Newton–Raphson iterative method, known for its robustness in the convex function domain, as an optimization framework. By analyzing structural parameters and flexoelectric actuator parameters, significant influencing factors are selected to form the vector space, determining actuator positions and driving voltages. These variables constitute the optimization space and are incorporated into the Newton–Raphson general iterative equation to derive the iteration matrix, which is computed using MATLAB. Case studies confirm that the Newton–Raphson method effectively identifies optimal actuator positions and driving voltages at different modes without external force, significantly improving flexoelectric control efficiency. Additionally, it quickly stabilizes vibrations at different modes under external force. However, the study has limitations, as the Newton–Raphson method cannot effectively solve non-convex function optimization in linear space. This research advances the understanding of multiple actuators optimization control structure dynamics and promotes the development of more effective engineering solutions, particularly in achieving more precise actuation and control in the field of micro- and nano-structure engineering.