CUED Publications database

A comparison of worst-case predictions with experimental results for a locally nonlinear beam

Butlin, T (2014) A comparison of worst-case predictions with experimental results for a locally nonlinear beam. In: UNSPECIFIED pp. 2989-3004..

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There is an increasing need for efficient tools capable of predicting the nonlinear vibration response of complex structures. In many applications these nonlinearities are spatially localised: this can be exploited so that efficient linear methods are used to describe the dynamics of the majority of the structure, which reduces the size of the nonlinear problem. There are many examples of this class of system: oilwell drills with localised interactions with the borehole wall; turbine blades in contact with their casing structure; brake systems with a local non-linear frictional contact; and 'buzz, squeal and rattle' problems in the automotive industry. But in many cases the nonlinear law is poorly characterised, even to the extent that its functional form is not always known. This paper presents a recently developed method based on 'anti-optimisation' for handling this class of problem in a novel way. The method seeks a worst-case system response with respect to a chosen metric by considering the internal nonlinear force as an independent excitation to the linear system. Constraints are used to capture what is thought to be known about the nonlinearity without needing to specify a particular law. The approach is distinct from a traditional worst-case analysis in two ways: the unknowns of the anti-optimisation are the time histories of the nonlinear forcing (rather than parameters associated with a particular law); and the constraints provide a very flexible approach to specifying incomplete knowledge of the nonlinear relationship. Taking this approach allows target and constraint functions to be evaluated from the forced response of a linear system, so that each step of the optimisation process is an efficient computation. It is particularly well suited to locally nonlinear problems because only a few degrees of freedom are associated with the nonlinearity, which reduces the size of the optimisation problem. The method is applied to an impacting beam and predictions are compared with results from an experimental test rig. The beam was suspended by string to mimic free-free boundary conditions and driven sinusoidally at one end. A pair of end-stops constrained lateral motion at the opposite end. Some care has been taken in the design of the rig to reduce the effect of unwanted nonlinearities. Results have been obtained across a range of frequencies, amplitudes and contact conditions, and some initial comparisons with the worst-case predictions will be shown and discussed.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Divisions: Div C > Applied Mechanics
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:19
Last Modified: 10 Aug 2017 01:39