论文标题
具有非线性频率依赖性的有限元模型的时间集成
Time integration of finite element models with nonlinear frequency dependencies
论文作者
论文摘要
声音和振动的分析通常在频域中进行，这意味着稳态行为和时谐激发的假设。但是，外部激发可能是短暂的，而不是时间谐波，需要时间域分析。在频域中，仍然描述了某些材料特性，例如\通常用于阻尼处理的某些材料特性，这会使模拟时间复杂化。在本文中，我们提出了一种具有非线性频率依赖性的有限元模型线性化的方法。线性化依赖于通过AAA方法对有限元矩阵的合理近似。我们介绍了扩展的AAA方法，该方法是经典的AAA，结合了第二个多项式项，以捕获模型的二阶行为。添加了一个过滤步骤，用于卸下不稳定的极点。
The analysis of sound and vibrations is often performed in the frequency domain, implying the assumption of steady-state behaviour and time-harmonic excitation. External excitations, however, may be transient rather than time-harmonic, requiring time-domain analysis. Some material properties, e.g.\ often used to represent for damping treatments, are still described in the frequency domain, which complicates simulation in time. In this paper, we present a method for the linearization of finite element models with nonlinear frequency dependencies. The linearization relies on the rational approximation of the finite element matrices by the AAA method. We introduce the Extended AAA method, which is classical AAA combined with a degree two polynomial term to capture the second order behaviour of the models. A filtering step is added for removing unstable poles.
