水中封闭球壳湿模态的正交性及其应用研究

The Orthogonality of Wet Modes in a Closed Spherical Shell Immersed in Deep Water and Its Application in Dynamic Response Analysis

基于势流理论和弹性薄壳的Ｆｌüｇｇｅ方程，并利用液固交界面处的相容条件和自伴随微分算子特性，证明了水中封闭球壳自由振动时湿模态的两个正交关系．在此基础上，再对外激励下的响应进行湿模态展开，借助提出的这组正交关系，可使在湿模态空间中得到的运动方程解耦。

Based on the potential flow theory and Flügge equations of thin elastic shell, the two relationships of orthogonality of wet modes in coupled free vibrations of a closed spherical thin elastic shell immersed in deep water are proved, by using the interactive conditions of fluid/solid interfacial boundary and properties of self adjoint differential operator. We use the relationships to expand the shells response under external exciting in the wet modes space. The shells motion equations could be decoupled in the wet modes space. The equations can be solved to handle a number of single freedom equations.