Andreas Hohl

Dynamic analysis of three-dimensional structures is common practice in industry to optimize products and in research to gain insights on the influence of parameters. The complexity differs based on the linearity or nonlinearity of the underlying problem, the type of excitation, e.g., forced or self-excitation, and the number of degrees of freedom that need to be examined. Reduced order models and optimized numerical methods are used to optimize the time and computational power needed to gain a certain insight. This article focusses on a specific class of problems where the modes of the structure do not or do not significantly change through the (damping) device or force that is added to the structure. Herein, lumped mass models are commonly used for analysis of the dynamic response of the system. In the article, it is highlighted that lumped mass models can give quantitative insight but modally reduced models allow a direct optimization of the problems with respect to the physical degree of freedom that, for example, is subject to self-excitation or dampened. The benefit of modal minimal models and its limitations are shown and discussed for different linear and nonlinear dynamic problems.

Deep drilling operations are primarily used to produce oil, gas, and geothermal heat from reservoirs in the earth’s crust. Today’s drilling technology allows to drill holes up to several thousand feet of true vertical depth and through long horizontal reservoir sections. A drill string, built of thread-connected components, is used to transfer mechanical energy from a drill rig at

In turbomachinery applications bladed disks are subjected to high dynamic loads due to fluctuating gas forces. Dynamic excitation can result in high vibration amplitudes which can lead to high cycle fatigue (HCF) failures. Herein, the blades are almost identical but differ due to wear or small manufacturing tolerances. Especially, after regeneration and repair procedures the properties of the blades can differ with a high variance. These deviations of the blade properties can lead to a localization of the vibrational energy in single blades and even higher risk of HCF. A recently developed substructure model with a combination of the Hurty transformation or Component Mode Synthesis (CMS) and the so called Wave Based Substructuring (WBS) is used to obtain a Reduced Order Model (ROM) with a reasonable low number of degrees of freedom. The CMS of the disk can be calculated with one cyclic disk segment of the underlying finite element model. The WBS is used to describe the numerous coupling degrees of freedom between the disk and the blades with a truncated set of waves. The orthogonal waves are derived by a Singular Value Decomposition or a QR decomposition from the coupling nodes normal modes calculated by a cyclic modal analysis of the full structure. The blade eigenvalues of the clamped blade can be mistuned individually under consideration of the variance as well as the correlation between the different eigenvalues of the blades. Monte-Carlo-Simulations are performed to calculate the effect of these parameters on the forced response of a mistuned bladed disk for blade dominated modes. Furthermore, Monte-Carlo-Simulations and a constraint optimization approach is used to calculate the worst and best case blade patterns for specific blade patterns and blade patterns with distributed blade properties.