本文建立了弹性支撑的刚性管受到涡激激励的耦合动力学方程,提出了一种速度和加速度耦合的Van der Pol尾流振子模型,并分别研究了横流向单自由度涡激振动模型以及横流向与顺流向耦合的二自由度涡激振动模型。在单自由度涡激振动模型的...
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本文建立了弹性支撑的刚性管受到涡激激励的耦合动力学方程,提出了一种速度和加速度耦合的Van der Pol尾流振子模型,并分别研究了横流向单自由度涡激振动模型以及横流向与顺流向耦合的二自由度涡激振动模型。在单自由度涡激振动模型的研究中,我们首先利用同伦分析法对横流向单自由度涡激振动方程进行研究,得到了求解系统的近似稳态解的代数方程组。然后,研究了模型耦合参数和物理参数的变化对系统的响应频率和振幅的影响。根据参数影响分析,分别在低质量比(在水中)和高质量比(在空气中)选取了合适的系统参数所得的的结果能够与不同质量比下的实验研究结果吻合较好;并且发现当流体介质为水时,即质量比较低的情况下,加速度耦合系数相较于速度耦合系数取值较大,说明加速度耦合项的影响较大,而当流体介质为空气,质量比较高时,速度耦合系的影响会偏大。基于单自由度涡激振动模型的研究及所选取的模型参数,进一步研究了二自由度涡激振动模型中其它模型耦合参数的变化对系统响应的影响,并选取了合适的参数所得到的结果能够与实验结果相吻合。
In transport of micro or nanosized particles through a confined structure driven by thermal fluctuations and external forcing-a situation that arises commonly in a variety of fields in physical and biological sciences...
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In transport of micro or nanosized particles through a confined structure driven by thermal fluctuations and external forcing-a situation that arises commonly in a variety of fields in physical and biological sciences, efficient and controllable separation of particles of different sizes is an important but challenging problem. We study, numerically and analytically, the diffusion dynamics of Brownian particles through the biologically relevant setting of a spatially periodic structure, subject to static and temporally periodic forcing. Molecular dynamical simulations reveal that the mean velocity in general depends sensitively on the particle size. The phenomenon of current reversal is uncovered, where particles larger than or smaller than a critical size diffuse in exactly opposite directions. This striking behavior occurs in a wide range of the forcing amplitude and provides a mechanism to separate the Brownian particles of different sizes. Besides the forcing amplitude, other parametric quantities characterizing the forcing profile,such as the temporal asymmetry, can also be exploited to modulate or control the transport dynamics of particles of different sizes. To gain a theoretical understanding, we exploit the Fick-Jacobs approximation to obtain a one-dimensional description of the diffusion problem, which enables key quantities characterizing the diffusion process, such as the mean velocity, to be predicted. In the regime of weak forcing, a reasonable agreement between theory and numerics is achieved. Beyond the weakly forcing regime, the diffusion approximation breaks down, causing the theoretical predictions to deviate from the numerical results, into which we provide physical insights. Our findings have potential applications in optimizing transport in microfluidic devices or through biological channels.
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