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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >Nonlinear sloshing and passage through resonance in a shallow water tank
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Nonlinear sloshing and passage through resonance in a shallow water tank

机译：浅水箱中的非线性晃动和通过共振通过

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This paper is concerned with the effect of slowly changing the length of a tank on the nonlinear standing waves (free vibrations) and resonant forced oscillations of shallow water in the tank. The analysis begins with the Boussinesq equations. These are reduced to a nonlinear differential-difference equation for the slow variation of a Riemann invariant on one end. Then a multiple scale expansion yields a KdV equation with slowly changing coefficients for the standing wave problem, which is reduced to a KdV equation with a variable dispersion coefficient. The effect of changing the tank length on the number of solitons in the tank is investigated through numerical solutions of the variable coefficient KdV equation. A KdV equation which is "periodically" forced and slowly detuned results for the passage through resonance problem. Then the amplitude-frequency curves for the fundamental resonance and the first overtone are given numerically, as well as solutions corresponding to multiple equilibria. The evolution between multiple equilibria is also examined.
机译：本文关注的是缓慢改变水箱长度对非线性驻波（自由振动）和水箱中浅水共振强迫振动的影响。分析从Boussinesq方程开始。将它们简化为非线性微分差分方程，以解决一端黎曼不变量缓慢变化的问题。然后，倍数展开产生一个具有缓慢变化的驻波问题系数的KdV方程，将其简化为具有可变色散系数的KdV方程。通过变系数KdV方程的数值解，研究了改变罐长对罐中孤子数的影响。 KdV方程会“周期性地”被强迫缓慢地失谐，从而通过共振问题。然后数值给出了基本共振和第一泛音的振幅-频率曲线，以及对应于多重平衡的解。还检查了多个平衡之间的演变。

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