Coupled flexible structures are widely applied on soft robots as actuators, which are combined with hard electric actuating material and flexible medium. The accurate description for the rigid-flexible coupling and large deformation is of great importance for the structure design and accurate control of the actuators and soft robots. In this paper, a flexible beam-plate coupled structure is established based on the deformation compatibility condition, the deformation of the structure is described with absolute nodal coordinate formulation, and the dynamic equations are developed based on Hamilton’s principle. To investigate the influence of actuation, piezoelectric material constitutive equations are imposed to the beam element as a piezoelectric actuator of the structure. The results indicate that the deformations of the coupled flexible structure under piezoelectric actuation increase linearly with the increase of input voltage. The structure conducts periodical vibrations under actuation, the amplitude and the period of the vibration increase nonlinearly with the decrease of Young’s modulus.
YI Canming，YU Haidong，WANG Hao
. Dynamic Behavior of Coupled Flexible Plate Structure with
Piezoelectric Actuator via Absolute Nodal Coordinate Formulation[J]. Journal of Shanghai Jiaotong University, 2019
, 53(6)
: 665
-672
.
DOI: 10.16183/j.cnki.jsjtu.2019.06.005
［1］SHABANA A A. Dynamics of multibody systems［M］. Cambridge: Cambridge University Press, 2013.
［2］潘科琪. 曲梁和板壳结构多体系统刚-柔耦合动力学研究［D］. 上海: 上海交通大学, 2012.
PAN Keqi. Investigation on rigid-flexible coupling dynamics for curved beam and plate-shell structure multibody system［D］. Shanghai: Shanghai Jiao Tong University, 2012.
［3］CARRERA E. Historical review of zig-zag theories for multilayered plates and shells［J］. Applied Mechanics Reviews, 2003, 56(3): 287-308.
［4］ZHAO C, YU H, ZHENG B, et al. New stiffened plate elements based on the absolute nodal coordinate formulation［J］. Proceedings of the Institution of Mechanical Engineers. Part K: Journal of Multi-body Dynamics, 2016, 231(1): 213-229.
［5］SHABANA A A, YAKOUB R Y. Three dimensional absolute nodal coordinate formulation for beam elements: Theory［J］. Journal of Mechanical Design, 2001, 123(4): 606-613.
［6］SHABANA A A. Computational continuum mechanics［M］. Cambridge: Cambridge University Press, 2011.
［7］MIKKOLA A M, SHABANA A A. A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications［J］. Multibody System Dynamics, 2003, 9(3): 283-309.
［8］赵春璋, 余海东, 王皓, 等. 基于绝对节点坐标法的变截面梁动力学建模与运动变形分析［J］. 机械工程学报, 2014, 50(17): 38-45.
ZHAO Chunzhang, YU Haidong, WANG Hao, et al. Dynamic modeling and kinematic behavior of variable cross-section beam based on the absolute nodal coordinate formulation［J］. Journal of Mechanical Engineering, 2014, 50(17): 38-45.
［9］李彬, 刘锦阳. 大变形柔性梁系统的绝对坐标方法［J］. 上海交通大学学报, 2005, 39(5): 827-831.
LI Bin, LIU Jinyang. Application of absolute nodal coordination formulation in flexible beams with large deformation［J］. Journal of Shanghai Jiao Tong University, 2005, 39(5): 827-831.
［10］GILARDI G, BUCKHAM B J, PARK E J. Finite element modeling of a highly flexible rotating beam for active vibration suppression with piezoelectric actuators［C］//ASME 2007 International Mechanical Engineering Congress and Exposition. Seattle, Washington: American Society of Mechanical Engineers, 2007: 2041-2050.
［11］NADA A A, EL-ASSAL A M. Absolute nodal coordinate formulation of large-deformation piezoelectric laminated plates［J］. Nonlinear Dynamics, 2012, 67(4): 2441-2454.
