Abstract
The implementation of both vibration source characterisation and sub-structure coupling/decoupling procedures rely on the complete description of a coupling interface, that is, the inclusion of coupling forces in all significant degrees of freedom (DoFs). However, it is not straight-forward to establish which DoFs are required in the description. E.g. is it necessary to include moments and/or in-plane forces? This is an important question as an incomplete description will lead to an erroneous representation of the dynamics. However, there are currently no methods of quantifying the completeness of an interface description. In this paper an experimental procedure is described for the assessment of interface completeness. Based on the theoretical blocking of DoF subsets, a relation is presented that allows for the contribution of an unknown DoF to be established. Further, a coherence style criterion is proposed to estimate the completeness of a given interface description. This criterion may be used to check whether sufficient coupling DoFs have been included in both source characterisation and sub-structure coupling/decoupling procedures. Numerical and experimental examples are provided to illustrate the concept.
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Notes
- 1.
Although we will refer to the proposed quantity as a criterion, given its definition, the authors are undecided as to whether ‘coefficient’ may be a more appropriate term.
- 2.
Whilst a complete interface description is required from a theoretical basis, it is often the case that their exists a subset of DoFs that are of particular importance, and themselves provide a satisfactory description of the interface. In such a case the remaining DoFs may not need to be accounted for.
- 3.
The blocked force \(\mathbf {\tilde {\bar {f}}_{c_i}}\) represents the reaction forces due to a source that is blocked in c i DoFs but unrestrained in the remaining c j DoFs. It is therefore by definition a blocked force, albeit not the true blocked force.
- 4.
A similar problem is encountered in the application of sub-structure coupling and decoupling procedures. The neglect of coupling interface DoFs results in an erroneous representation of the assembly/substructure dynamics.
- 5.
Although not discussed in any further detail here, for |c j | = 1, Eq. 14.13 may be considered the velocity at b due to the contribution of a single path, i.e. whilst all other paths are blocked. This is a similar concept to that used by Margans [17] in the formulation of the GTDT TPA procedure [18].
- 6.
Consequently, \(\mathbf {Y_{ba}^{({c_j})}} = 0\) since the DoF subset c j does not exist.
- 7.
Alternatively, if one considers Eq. 14.14, a complete interface description would block entirely the coupling interface, resulting in a velocity of 0 at the remote source DoFs b.
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This work was funded through the EPSRC Research Grant EP/P005489/1, Design by Science.
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Meggitt, J.W.R., Moorhouse, A.T., Elliott, A.S. (2018). On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for ‘Completeness’. In: Linderholt, A., Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-74654-8_14
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