Automated nonlinear parameter variation for vibration optimization of structures with friction

对于非线性振动问题，已知有各种数值方法来预测周期激励下的稳态振动行为。因此，即使在工业应用中，例如在具有摩擦接触的透平机械中，设计过程也是可能的。然而，稳健设计的计算量可能会随着可变参数的数量和离散等级的增加而迅速增加。在这里，通常很容易达到经济参数研究的极限。在本项目的范围内，设计过程将被描述为一个优化问题，并实现自动化，以便针对特定参数集执行较少的非线性计算。优化算法必须适应非线性结构振动问题的特殊要求，从而可以在一般的非线性优化中同时调整可变参数。首先讨论了在已有的求解非线性振动问题的方法中，关于适当的代价函数和数值挑战的必要问题。随后，研究了实现低维非线性系统的非线性优化的结构。还讨论了结果的呈现以供用户检查。通过一个面向应用的摩擦接触算例，扩展了非线性结构振动问题典型模型的自动优化过程，最后给出了一个面向工业的透平机械领域的算例。计算结果可分别与常规优化参数集进行比较和验证，从而为自动化优化技术的工业化开发提供参考。

For nonlinear vibration problems, various numerical methods are known to predict a steady-state vibration behavior under periodic excitation. Thus, a design process is possible even in industrial applications, for example in turbomachinery with frictional contacts. However, the computational effort for a robust design can quickly increase with the number and discrete gradation of variable parameters. Here, the limits of an economic parameter study are often easily reached. Within the scope of this project, the design process is to be formulated as an optimization problem and automated, so that less nonlinear calculations have to be performed for specific parameter sets. With the help of optimization algorithms, which have to be adapted to the special requirements of nonlinear structural vibration problems, variable parameters can thus be adjusted simultaneously in a general nonlinear optimization. The necessary questions concerning suitable cost functions as well as numerical challenges in established methods for solving nonlinear vibration problems are addressed at the beginning. Subsequently, the structures for nonlinear optimization for implementation are investigated on low-dimensional nonlinear systems. The presentation of results for inspection by the user is also discussed. With the help of an application-oriented example with frictional contact, the process of automated optimization is extended for typical models of nonlinear structural vibration problems, before an industry-oriented example from the field of turbomachinery is treated at the end. The results can be compared with conventionally optimized parameter sets and validated, respectively, so that an industrial exploitation of the automated optimization can get discussed as well.