This study deals with the computation of parameterized reduced order models for hydroelastic vibrations of interior fluid–structure systems with a free surface. The main parameter is the weight of the liquid acting on the structure, which allows static and dynamic simulations for different liquid heights in a tank. Both the structure and the liquid domains are mapped in reference configurations, which constituted a first originality of the paper. The second originality of the proposed approach consists in using projections on an eigenmode basis associated with the use of an adapted SVD in order to compute the eigenfrequencies of the coupled problem. In particular, we show that the proposed approach allows to construct reduced order model involving a small number of matrices through a decomposition of linearized reduced operators in terms of separated parameters functions. Convergence analysis of numerical results is discussed showing the efficiency of the method.

本研究涉及计算具有自由表面的内部流体结构系统的水弹性振动的参数化降阶模型。主要参数是作用在结构上的液体重量，它允许对罐中不同液体高度进行静态和动态模拟。结构和液体域都映射到参考配置中，这是本文的第一个独创性。所提出方法的第二个独创性在于使用与使用自适应 SVD 相关的特征模式基础上的投影为了计算耦合问题的特征频率。特别是，我们表明，所提出的方法允许通过根据分离参数函数分解线性化约简算子来构建涉及少量矩阵的降阶模型。讨论了数值结果的收敛性分析，显示了该方法的效率。