The manta ray, exemplifying an agile swimming mode identified as the median and paired fin (MPF) mode, inspired the development of underwater robots. Robotic manta typically comprises a central rigid body and flexible pectoral fins. Flexible fins provide excellent maneuverability. However, due to the complexity of material mechanics and hydrodynamics, its dynamics are rarely studied, which is crucial for the advanced control of robotic manta (such as trajectory tracking, obstacle avoidance, etc.). In this paper, we develop a multibody dynamic model for our novel manta robot by introducing a pseudo-rigid body (PRB) model to consider passive deformation in the spanwise direction of the pectoral fins while avoiding intricate modeling. In addressing the rigid-flexible coupling dynamics between flexible fins and the actuation mechanism, we employ a sequential coupling technique commonly used in fluid-structure interaction (FSI) problems. Numerical examples are provided to validate the MPF mode and demonstrate the effectiveness of the dynamic model. We show that our model performs well in the rigid-flexible coupling analysis of the manta robot. In addition to the straight-swimming scenario, we elucidate the viability of tailoring turning gaits through systematic variations in input parameters. Moreover, compared with finite element and CFD methods, the PRB method has high computational efficiency in rigid-flexible coupling problems. Its potential for real-time computation opens up possibilities for future model-based control.

In this paper, a new Stroh formalism for gradient electro-mechanics is derived for the first time, which is both mathematically concise and numerically powerful, applicable to generally coupled anisotropic material systems. Based on this new formalism, the complicated Lamb wave in flexoelectric and piezoelectric plates is investigated. The dispersion equation is obtained by solving the eigenvalue problem along with the unconditionally stable dual-variable and position method. From the obtained dispersion equation, the dispersion curves and mode shapes of the Lamb wave are calculated by the 1D form of the multidimensional moduli ratio convergence method. Two important and interesting features are observed from our analysis: One is the difference in the mode shape symmetry between the piezoelectric and flexoelectric cases, and the other is the size-dependent property of the flexoelectric effect as observed by nondimensionalization. These features are further illustrated by comparing the dispersion curves and wave-mode shapes among the three different material models (purely piezoelectric, purely flexoelectric, and flexoelectric and piezoelectric coupled). The newly derived Stroh formalism offers a robust, concise, and unified approach for dealing with strain gradient electro-mechanic materials with crystal systems of general anisotropy. The present work also explains the physical mechanism of symmetry breaking observed, as induced by flexoelectric coupling in piezoelectric materials.

This paper presents the principle of virtual work (PVW) for piezoelectric semiconductors (PSs), which extends the piezoelectric dielectrics to involve the semiconducting effect. As an application of the PVW, a one-dimensional (1D) approximation theory for the extension and bending of PS nanowires is established by directly applying the PVW and Bernoulli–Euler beam theory with the aid of the second-order approximation of electrostatic potential. To illustrate the new model, the mechanical displacement, electrostatic potential, and concentration of electrons for extension and bending deformation of n-type ZnO nanowires are analytically determined. Additionally, numerical results show that, for n-type Zinc Oxide nanowires, the distribution of electrostatic potential is anti-symmetric along the thickness direction for extension deformation. In contrast, the bending deformation causes a symmetric distribution of electrostatic potential characterized by the zeroth-order and the second-order electrostatic potential. Furthermore, these two different deformations result in the redistribution of electrons. The electrostatic potential can be tuned by adjusting the amplitude of the applied mechanical load. Moreover, we find that the increase in doping level will reduce the magnitude of electrostatic potential due to the screening effect. The presented PVW provides a general approach to establishing structural theories and an effective way of implementing numerical methods.