Automated nonlinear parameter variation for vibration optimization of structures with friction

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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.