Abstract
We revisit the two degrees of freedom model of the thin elastica presented by Cusumano and Moon (1995) [3]. We observe that for the corresponding experimental system (Cusumano and Moon, 1995 [3]), the ratio of the two natural frequencies of the system was ≈44 which can be considered to be of O(1/ε), where ε1. The presence of such a vast difference between the frequencies motivates the study of the system using the method of direct partition of motion (DPM), in conjunction with a rescaling of fast time in a manner that is inspired by the WKB method, similar to what was done in Sheheitli and Rand (to appear) [8]. Using this procedure, we obtain an approximate expression for the solutions corresponding to non-local modes of the type observed in the experiments (Cusumano and Moon, 1995 [2]). In addition, we show that these non-local modes will exist for energy values larger than a critical energy value that is expressed in terms of the parameters. The formal approximate solution is validated by comparison with numerical integration.
Original language | English (US) |
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Pages (from-to) | 99-107 |
Number of pages | 9 |
Journal | International Journal of Non-Linear Mechanics |
Volume | 47 |
Issue number | 4 |
DOIs | |
State | Published - May 2012 |
Externally published | Yes |
Keywords
- Bifurcation
- DPM
- Elastica
- Method of direct partition of motion
- Non-local modes
- WKB method