Abstract: 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.

Key words: coupled flexible structure; absolute nodal coordinate formulation (ANCF); deformation compatibility condition; piezoelectric actuator; soft robots