Efficient analysis of modifications in dynamic systems
Embargo Date
2024-01-16
OA Version
Citation
Abstract
Structural modifications may need to be made to a system during the design phase, thus changing the finite element model that describes the system. Analyzing a finite element model may provide information on the natural frequencies of the system, or its response as a result of being forced. These characteristics are important to understand when designing a system; however, for large systems these analyses are computationally expensive. If many modifications are analyzed, repeating the analysis every time becomes prohibitive. Perturbations are considered smaller structural modifications and methods exist to predict responses for the perturbed system using results from the nominal system. These methods are quicker than repeating the entire analysis.
There are two major reasons a system may be structurally modified. The first is to determine an optimal solution by testing different options. An optimal solution may avoid certain natural frequencies near a known forcing frequency or minimize the overall vibration of the system. The second is when there is an uncertain parameter in the system, and the goal is to determine the mean and variance of a response metric, such as a spatially averaged response. To determine statistics for a response the uncertain parameter is typically sampled many times and the system is analyzed for each sample. Then, statistics may be calculated from the results. Every time the uncertain parameter is sampled, it may be considered a perturbation. Three different methods are developed in this research to evaluate perturbations, for harmonically forced systems.
The first method uses the Neumanns series to accelerate generalized polynomial chaos expansions, in order to predict the mean and variance of a frequency response function for a system with an uncertain parameter. The second method uses a scalar expression to approximate perturbed natural frequencies from a nominal eigenvalue analysis. This expression is derived by breaking the system into groups of element sets whose properties are uniformly perturbed. The third method predicts perturbed displacement vectors by breaking the model into sets to speed up existing methods, including the Condensation and Bickford Methods.