Analytical analysis of the fundamental frequency of 2D gap resonance
CONG Longfei;TENG Bin;GOU Ying;State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology;
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.