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Using modal derivatives to determine the behaviour of mode shapes and natural frequencies during large deflections

Belt, M. van den (2017) Using modal derivatives to determine the behaviour of mode shapes and natural frequencies during large deflections.

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Abstract:In this paper, a method will be presented with which it is possible to determine how mode shapes and natural frequencies change during large elastic deflections. This is done by applying a model order reduction technique in the floating frame of reference. This model order reduction technique makes use of modal derivatives, which are corrections on the mode shapes. Modal derivatives take higher order terms of the strain energy into account and therefore the method can account for geometric nonlinearities and can thus be applied on large elastic deflections. Using modal derivatives, mode shapes and natural frequencies in any given configuration can be determined. It is also possible to determine mode shapes and natural frequencies by solving the eigenvalue problem of a beam in a certain configuration, but this method requires significantly more calculation time. By comparing the results obtained using modal derivatives to the results obtained by using the eigenvalue problem, the method is validated. This validation shows that modal derivatives can indeed be used to correctly describe the behaviour of the mode shapes and natural frequencies for large deflections. The method is applied on a three-dimensional beam element as well, showing coupling between bending and torsion modes.
Item Type:Essay (Master)
Faculty:ET: Engineering Technology
Subject:52 mechanical engineering
Programme:Mechanical Engineering MSc (60439)
Link to this item:http://purl.utwente.nl/essays/74400
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