二维狭缝内波动基频共振频率的解析分析

Analytical analysis of the fundamental frequency of 2D gap resonance

针对波浪作用下二维狭缝内水体波动问题,通过无量纲化的Laplace方程对狭缝内水体波动形式进行简化,将狭缝内水体波动问题转化为波浪对单浮体的作用问题。应用线性势流理论讨论了波浪作用下狭缝内水体共振的机理,利用特征函数展开方法对狭缝内水体波动的共振频率进行了计算与分析。计算结果在狭缝宽度较小时,与基于线性势流理论的半解析方法、比例边界元方法、渐进匹配方法以及简化分析的结果相比,具有相同的变化趋势和数值;在狭缝宽度趋于0时,得到相同的共振频率渐进表达式。在狭缝宽度较大时,在趋势和数值上均与基于线性势流理论的半解析方法的结果吻合,与渐进匹配方法以及简化分析的结果变化趋势相同,数值上有差异。结果表明,该方法可以更广泛地应用于二维狭缝内波动基频共振频率的求解。

To solve the problem of the oscillation inside the narrow 2D gap caused by wave,simplification is made by use of the non-dimensional Laplace equation and the problem is converted into a problem of wave action on a single floating body. The linear potential theory is applied to reveal the mechanism of water resonance inside a gap and the gap resonance frequency was computed by the eigenfunction expansion method. When the gap is narrow,the results match well in tendency and value with the results got by the semi-analytical method,scaled boundary finite element method,asymptotic matching method based on the linear potential theory and the results with simplification,all methods have the same asymptotic presentation of the resonance frequency when the wide of the gap tends to zero. When the gap is wider,the results also match well in change tendency and value with the results got by the semi-analytical method based on the linear potential theory. However,the results have the same tendency as asymptotic matching method based on the linear potential theory and the results with simplification,but have different values. The results showed that the current method could be more widely used in the calculation of the fundamental frequency of 2D gap resonance.