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 引用本文: 王郡, 朱永宁, 徐鉴. 自主泳动弹性绳的轨迹模拟[J]. 力学学报, 2019, 51(1): 198-208.
Wang Jun, Zhu Yongning, Xu Jian. TRAJECTORY SIMULATION OF SELF-PROPELLED ELASTIC RODS IN FLUID[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 198-208.
 Citation: Wang Jun, Zhu Yongning, Xu Jian. TRAJECTORY SIMULATION OF SELF-PROPELLED ELASTIC RODS IN FLUID[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 198-208.

## TRAJECTORY SIMULATION OF SELF-PROPELLED ELASTIC RODS IN FLUID

• 摘要: 研究柔性结构与流体间耦合作用,可以促进软体机器人的发展.通过速度快、精度高的数值模拟方法模拟水下机器人的实时运动轨迹,可以为真实实验提供测试方向与理论牵引,增大实验成功的可能性.本文研究有自主运动趋势的弹性绳在二维流场中的运动轨迹.首先,对弹性绳离散化建模并同时考虑拉压与扭转弹性力,从能量角度建立动力学方程,此模型可以较为真实地反映弹性绳内力对其运动产生的作用.然后基于半拉格朗日法建立流体求解器. 最后,提出简化的基于动量方程的浸入边界法作为耦合算法,通过直接修正网格速度代替浸入边界力法中力源项的作用.使用这种算法求解耦合作用兼具简便性与快速性.对弹性绳模型、流体模型与简化耦合模型依次解算,模拟了正弦形式波动弹性绳在水中的运动轨迹.结果显示,弹性绳在弹性内力与流固相互作用力共同影响下,该种新的浸入边界法可以实现对水下弹性绳运动轨迹的模拟.数值实验显示弹性绳的自主运动参考模型的初相位改变时,其前进方向会发生改变.该仿真模拟算法与平台可以为细长形软体水生机器人的研发提供参考.

Abstract: The research for flexible structures coupling with fluid simulates and promotes the development of soft robotics. A fast and accurate numerical method is significant for a real-time simulation of robots. This research provides theoretical and critical information for experiments to reduce the possibility of failure, by anticipating the path of the underwater soft robots and the possible requiring parameters for materials. This paper researches for bio-swimming elastic rods coupling with two-dimensional incompressible Newton fluid. First, we discretize elastic rods to extensive springs and rotational springs and stablish the kinetic equations based on energy reflecting the influence of internal force on swimming rods, and solve the governing equation by leap-frog algorithm. Second, semi-Lagrangian method is used to establish a fluid solver. Finally, the simplified coupling algorithm based on immersed-boundary method is raised, calling immersed-boundary method for momentum equations. These equations update the velocity of grid near the coupling interface directly to replace the function source force play in immersed-boundary method. Combining the fluid solver, rods solver and the coupling algorithm, a integral program solving the problem of the dynamics for immersed rods numerically. Simulating the rods swimming with a referenced pose of sine curvature. Comparing the simulating result to existed experiments of filament swimming and to the swimming trajectory of soft-body fish, we find the numerical result conform to experiment result, leading to the conclusion that this algorithm and dynamic model can simulate the trajectory of discrete elastic rods swimming underwater smoothly under the influence of both internal elastic force and coupling soft body-fluid interaction. Using this program, we test several critical parameters relating to swimming performance of rods, including iteration numbers, frequency and initial phases, finding that changing the initial phase of rods will alter onward direction of elastic rods. These results prove the feasibility and possibility of this algorithm and program being used for guiding development of real soft swimmers.

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