Abstract
Recent advances in the design and construction of large inflatable/rigidizable space structures and potential new applications of such structures have produced a demand for better analysis and computational tools to deal with the new class of structures. Understanding stability and damping properties of truss systems composed of these materials is central to the successful operation of future systems. In this paper, we consider a mathematical model for an assembly of two elastic beams connected to a joint through legs. The dynamic joint model is composed of two rigid bodies (the joint-legs) with an internal moment. In an ideal design all struts and joints will have identical material and geometric properties. In this case we previously established exponential stability of the beam-joint system. However, in order to apply theoretical stability estimates to realistic systems one must deal with the case where the individual truss components are not identical and still be able to analyze damping. We consider a problem of this type where one beam is assumed to have a small Kelvin-Voigt damping parameter and the second beam has no damping. In this case, we prove that the component system is only polynomially damped even if additional rotational damping is assumed in the joint.
Original language | English (US) |
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Pages (from-to) | 1236-1246 |
Number of pages | 11 |
Journal | Mathematical and Computer Modelling |
Volume | 46 |
Issue number | 9-10 |
DOIs | |
State | Published - Nov 2007 |
Bibliographical note
Funding Information:This work was supported by DARPA/SPO, NASA LaRC and the National Institute of Aerospace under grant VT-03-1, 2535.
Keywords
- Beam
- Damping
- Polynomial decay rate
- Semigroup