Complex Modal Decomposition and Characteristics Analysis of the Midline Motions of Swimming Fish Propelled by Undulating Body and Caudal Fin
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摘要: 在自然界中, 大多数鱼类通过身体和尾鳍的复合波动形成独特的鱼体波曲线, 以获得其快速高效的游动性能。文中以鱼体波为研究对象, 采用复模态正交分解(COD)方法来研究鱼体的复合波动模式。从振动模态的角度看, 鱼类的游动是粘弹性鱼体在流体中的强迫振动, 鱼体波对应的是复模态振型。根据COD方法, 将鱼体波分解为纯行波和纯驻波两部分, 并利用复模态振型实部和虚部的相关系数来定义鱼体波的行波系数。通过分析鳗鲡科乐锦鳚鱼和亚鲹科虹鳟鱼的鱼体波数据, 得到对应鱼体波的行波系数分别为0.793和0.604。结果表明, 乐锦鳚鱼的鱼体波中含有较大的行波成分, 而虹鳟鱼鱼体波则含有较多的驻波成分。该结论从生物学上验证了鱼体波的复模态特性, 该特性与鱼体动力学特性以及游动模式有着密切关系。Abstract: In nature, the majority of fishes obtain their extraordinary swimming abilities of fast speed and high efficiency by propagating their midline motions backward. In this paper, the midline motions and their complex modal characteristics are analyzed by the method of complex orthogonal decomposition(COD). From the perspective of modal analysis, the movement of a swimming fish is in essence the forced vibration of viscoelastic body in fluid environment, and the motions are of complex modal shapes. According to the COD method, the midline motions are decomposed into the travelling and standing components. The correlation coefficient of the real and imaginary parts of complex modal shape is used to define the travelling index. Based on the analysis of the motions of two kinds of anguilliform fish(Pholis Laeta) and subcarangiform fish(Rainbow Trout), the travelling indexes of their midline motions are 0.793 and 0.604, respectively. It is shown that the midline motions of Pholis Laeta contain a large proportion of travelling wave, while the midline motions of Rainbow trout contain a larger proportion of standing wave. These biological results verify the complex modal characteristics of the midline motions, and the complex modal characteristics have close relation to the dynamic properties of fish body and the swimming patterns.
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Key words:
- fish /
- swimming pattern /
- midline motions /
- complex modal decomposition /
- travelling index
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