A nonlinear rigid-flexible piezoelectric beam model for large in-plane motions

This research focuses on studying the rigid-flexible dynamic response of piezoelectric beams undergoing large-scale in-plane motion. Utilizing a three-dimensional (3D) framework of the piezoelectric effect, coupled with Euler-Bernoulli beam theory and the principles of rigid-flexible coupling dynamics, a nonlinear one-dimensional (1D) model, which considers the rigid displacement, rotation angle, axial deformation, deflection, and electric potential of the piezoelectric beam, is established. Through meticulous analysis based on the developed model, the paper examines the behavior of several key physical quantities, such as the instantaneous axial deformation, tip deflection, maximum first-order electrical potential, torque, and thrust. These quantities are studied under two typical scenarios—translation and rotation of the component model with the rigid hub. Numerical results show that there is a significant coupling effect between the axial deformation of the piezoelectric beam and its internal first-order potential when there is a large-scale planar motion in the piezoelectric beam. These numerical results indicate that there is a consistent change trend between the instantaneous external force, instantaneous acceleration, axial deformation, deflection and electric potential. These phenomena indicate that the motion state and deformation of the component model can be detected through the electric potential distribution generated in the beam by the piezoelectric effect. This study will provide an important theoretical basis for understanding the electromechanical coupling characteristics of piezoelectric structures in dynamic environments and developing robotic structures accordingly.