Abstract
A Boundary Condition Challenge Problem was released in May 2017 by Sandia National Laboratories and Kansas City’s National Security Campus (KCNSC). The challenge problem is intended to facilitate collaborative research on methods used for laboratory shock and vibration testing of aerospace components. Specifically, the challenge problem presents a test bed structure consisting of two sub-systems and an applied shock loading. The goal is to replicate the environment observed on one of the sub-systems when it is attached to a different sub-system in a laboratory testing environment.
Meanwhile, transfer path analysis (TPA) tools have been available for several decades. TPA techniques are used extensively for noise, vibration and harshness (NVH) engineering in the automotive industry. The techniques provide insight into the vibration transmission of a source excitation to a receiving structure. By re-framing the boundary condition problem into the TPA framework, it becomes clear that TPA tools are directly applicable to the boundary condition challenge problem.
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- 1.
The responses can also be written in terms of subsystem admittances with \( {\mathbf{u}}_{\mathbf{3}}=\left[{\mathbf{Y}}_{\mathbf{3}\mathbf{2}}^{\mathbf{B}}{\left({\mathbf{Y}}_{\mathbf{22}}^{\mathbf{A}}+{\mathbf{Y}}_{\mathbf{22}}^{\mathbf{B}}\right)}^{-\mathbf{1}}{\mathbf{Y}}_{\mathbf{21}}^{\mathbf{A}}\right]{\mathbf{f}}_{\mathbf{1}} \).
- 2.
The interface forces can also be written in terms of subsystem admittances with \( {\mathbf{g}}_{\mathbf{2}}={\left({\mathbf{Y}}_{\mathbf{2}\mathbf{2}}^{\mathbf{A}}+{\mathbf{Y}}_{\mathbf{2}\mathbf{2}}^{\mathbf{B}}\right)}^{-\mathbf{1}}{\mathbf{Y}}_{\mathbf{2}\mathbf{2}}^{\mathbf{A}}{\mathbf{f}}_{\mathbf{2}}^{\mathbf{eq}} \).
Abbreviations
- DoF:
-
Degree of freedom
- FRF:
-
Frequency response function
- u:
-
Dynamic displacements/rotations
- f:
-
Applied forces/moments
- g:
-
Interface forces/moments
- Y:
-
Admittance FRF matrix
- ⋆AB :
-
Pertaining to the assembled system
- ⋆A;⋆B :
-
Pertaining to the active/passive component
- ⋆1 :
-
Source excitation DoF
- ⋆2 :
-
Interface DoF
- ⋆⋆3 :
-
Receiver DoF
- ⋆4 :
-
Indicator DoF
- ⋆ps :
-
Pseudo-force DoF
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Harvie, J.M., van der Seijs, M. (2020). Application of Transfer Path Analysis Techniques to the Boundary Condition Challenge Problem. In: Walber, C., Walter, P., Seidlitz, S. (eds) Sensors and Instrumentation, Aircraft/Aerospace, Energy Harvesting & Dynamic Environments Testing, Volume 7. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-12676-6_15
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