本文利用高精度的Boussinesq方程建立数值模型，并结合实验手段，深入分析了矩形水箱内部浅水晃荡运动的载荷特性。研究结果显示，当无因次外部激励频率接近液体固有频率时，晃荡运动与载荷时历曲线表现出相似的非线性特征，随着激励频率的增加，呈现出多种不同的形式。通过对载荷时历曲线进行傅里叶分析，得到了不同外部激励频率下载荷的频域分布特征。基于晃荡载荷与自由液面波高频响曲线的相似性以及载荷特性的分析结果，建立了晃荡载荷的近似计算方法。该方法在不同水深及激励幅值下表现出优良的泛化性能，能够修正共振状态下线性近似对壁面载荷的过高估计，使跳跃频率处误差减少了50%以上。利用所提出的近似方法能够在已知波高的情况下快速估计壁面载荷，为工程设计提供技术支持。
Abstract
This study utilizes a high-precision Boussinesq equation to establish a numerical model, combined with experimental methods, to deeply analyze the load characteristics of shallow water sloshing motion within a rectangular tank. The research results indicate that when the dimensionless external excitation frequency approaches the natural frequency of the liquid, the sloshing motion and load time history curves exhibit similar nonlinear characteristics. As the excitation frequency increases, various different forms emerge. By performing Fourier analysis on the load time history curves, the frequency domain distribution characteristics of the load under different external excitation frequencies were obtained. Based on the similarity between the sloshing load and the high-frequency response curve of the free liquid surface wave height, as well as the analysis results of the load characteristics, an approximate method of the sloshing load was established. This approach demonstrates excellent generalization performance under different water depths and excitation amplitudes, reducing the overestimation of wall loads by linear approximations in resonance states, with errors at jump frequencies reduced by more than 50%. The proposed approximate model can quickly estimate wall loads under known wave heights, providing a theoretical basis for engineering design.
关键词
浅水晃荡 /
载荷特性 /
近似方法 /
模型实验
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Key words
shallow water sloshing /
load characteristics /
approximation methods /
model experiments
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参考文献
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