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

Hinke, Lars (2008) Modelling approaches for the low-frequency analysis of built-up structures with non-deterministic properties. University of Southampton, Institute of Sound and Vibration Research, Doctoral Thesis , 208pp.


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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.

Item Type: Thesis (Doctoral)
Subjects: T Technology > TJ Mechanical engineering and machinery
Q Science > QC Physics
Q Science > QA Mathematics > QA76 Computer software
Divisions : University Structure - Pre August 2011 > Institute of Sound and Vibration Research > Dynamics
ePrint ID: 63243
Accepted Date and Publication Date:
April 2008Made publicly available
Date Deposited: 24 Oct 2008
Last Modified: 27 Mar 2014 18:45

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