Modelling approaches for the low-frequency analysis of built-up structures with non-deterministic properties

Abstract

Virtual simulations of the behaviour of mechanical systems are of widespread use in academia and industry. Mechanical structures are often analysed using the finite element method, where deterministic models with one particular set of physical parameters are employed. However, the underlying assumption that the input data is precisely known is in general not valid, because there are uncertainties about the parameters, often until the last stage of the design cycle and even when the product is in service. Furthermore, every manufacturing process naturally introduces some product variability, which is inevitable. These effects can be compensated for by the application of safety factors. However, with the increasing requirements towards product performance, the effects of non-deterministic properties are of growing concern and advanced methods are needed that properly take them into account. In this context, it is often more important to predict the variation in the response than attempt to further improve the accuracy of a deterministic model. A number of viable methods to take non-deterministic properties into account already exist, but their computational efficiency and applicability have to be increased. In this thesis, a framework for the non-deterministic analysis of built-up structures using component mode synthesis (CMS) is presented. It is shown how several coordinate systems in CMS can be used advantageously for the quantification and propagation of non-deterministic data. A specific approach, based on considering the variation in component natural frequencies only, is introduced and its efficiency and accuracy investigated. The application of perturbational relations for uncertainty propagation in CMS is discussed. The framework of CMS is also used to combine qualitatively different uncertain data and the inclusion of experimental data is addressed. Overall, CMS methods can be used to reduce the numerical costs, improve the applicability of the approaches and also gain some physical insight for a structural dynamic problem with non-deterministic properties. Furthermore, several contributions are made to simulation methods that are usually applied in connection with the CMS approach. Different concepts for non-deterministic modal superposition are presented, which can be used to estimate the variation in frequency response functions from uncertain modal data. The application of the Line-Sampling simulation method, as an advanced Monte Carlo approach, to structural dynamic problems is shown. Finally, the modelling of spatial variations in components using random fields and the implementation in existing finite element models are addressed. Numerical examples are presented throughout.

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ORCID for B.R. Mace: orcid.org/0000-0003-3312-4918

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