Abstract A mathematical model for predicting the vibrations of ice-shelves based on linear elasticity for the ice-shelf motion and potential flow for the fluid motion is developed. No simplifying assumptions such as the thinness of the ice-shelf or the shallowness of the fluid are made. The ice-shelf is modelled as a two-dimensional elastic body of an arbitrary geometry under plane-strain conditions. The model is solved using a coupled finite element method incorporating an integral equation boundary condition to represent the radiation of energy in the infinite fluid. The solution is validated by comparison with thin-beam theory and by checking energy conservation. Using the analyticity of the resulting linear system, we show that the finite element solution can be extended to the complex plane using interpolation of the linear system. This analytic extension shows that the system response is governed by a series of singularities in the complex plane. The method is illustrated through time-domain simulations as well as results in the frequency domain.

中文翻译：

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冰架波浪强迫的耦合流体弹性模型

摘要 建立了基于冰架运动线弹性和流体运动势流预测冰架振动的数学模型。没有做出简化的假设，例如冰架的薄度或流体的浅度。冰架被建模为平面应变条件下任意几何形状的二维弹性体。该模型使用耦合有限元方法求解，该方法结合了积分方程边界条件来表示无限流体中的能量辐射。通过与薄梁理论比较和检查能量守恒来验证该解决方案。使用所得线性系统的解析性，我们表明可以使用线性系统的插值将有限元解扩展到复平面。这种解析扩展表明系统响应受复平面中的一系列奇点控制。该方法通过时域仿真以及频域中的结果进行说明。