鳗鲡模式游动的鱼体变形曲率波的传播特性研究

将鳗鲡模式游动的七鳃鳗简化成材料性质均匀的变截面黏 弹性梁,通过数值方法求解鱼体在主动弯矩波(作为激励的驱动波)的驱动下匀速游动时身体变形曲率波的传播特性. 结果表明,当主动弯矩 的驱动频率高于鱼体结构基频时,可以观察到曲率波相对于驱动波存在相位滞后,且越靠近尾部滞后现象越明显,这意味着曲率波的波速 小于驱动波的波速,也间接地验证了前人的实验结果. 通过参数研究发现,鱼体变形曲率波与驱动波的波速比与表征流体黏性作用的雷诺数无关,而与表征驱动波和鱼体材料属性的 无量纲激励频率、激励波长及鱼体黏性系数有关. 对于鳗鲡模式游动的鱼类,曲率波与驱动波的波速比随着无量纲激励频率和波长的增大而降低,随着鱼体黏性系数的增大而增大. 进一步研究发现,通过小扰动分析得到的组合相似性参数$\varPi$可以统一描述波速比与激励参数、材料参数之间的关系. 

PROPAGATION CHARACTERISTICS OF CURVATURE WAVE ALONG THE BODY IN ANGUILLIFORM FISH SWIMMING 1)

In this study, the homogeneous viscoelastic beam with a variable cross-section is used to model the lamprey, an anguilliform (eel-like) swimmer, and to research the propagation characteristics of the curvature wave driven by an active bending moment wave along the fish body. The results show that as long as the excitation frequency is higher than the structure fundamental frequency of the fish body, there will be a phase lag between the two waves, which increases from the head to the tail of the fish body. The increasing phase lag indicates that there exists a speed difference between propagations of the active bending moment and the body curvature, that is, the speed of the later is lower than that of the former. This features are consistent with the experimental results published. The dimensional analysis indicates the ratio of the speed of bending curvature wave to that of the active bending moment wave is associated with the dimensionless excitation frequency, wavelength and damping coefficient, but independent of the swimming Reynolds number. For anguilliform (eel-like) swimmers, the wave speed ratio decreases with increasing frequency or wave length of active bending moment, and it rises if the damping coefficient becomes larger. In addition, we also carried out a small perturbation analysis to linearize the equations, and found an integrated similarity parameter which includes the dimensionless frequency, wave length and damping coefficient. This parameter can uniformly describe the dependence of the speed ratio on the excitation and material parameters.