Stability of a Shallow Arch with One End Moving at Constant Speed
Resource
International Journal of Non-Linear Mechanics,,41,706715.
International Journal of Non-Linear Mechanics 41: 706-715
Journal
International Journal of Non-Linear Mechanics
Journal Issue
Non-Linear
Pages
706-715
Date Issued
2006
Date
2006
Author(s)
Lin, Jian-San
Abstract
In this paper we consider a shallow arch with rise parameter h, free of lateral loading, but subject to prescribed end motion e with constant speed c. Attention is focused on finding out whether dynamic snap-through will occur. Quasi-static analysis is first performed to identify all equilibrium configurations and their stability properties when e and h are specified. If the arch is stretched quasi-statically, it will be straightened up and no snap-through will occur. However, when the speed c is not negligible it is possible for the arch to snap to the other side dynamically. Careful analysis shows that the only possible situation when dynamic snap-through may occur is h > 3 sqrt(6) and sqrt(frac(8, 3)) h - 4 < e < frac(2, 9) h2 - 4. In this case, to prevent dynamic snap-through to occur the end speed c must not exceed a critical speed, which is a function of e and h. The minimum critical stretching speed is found to be 25.9 for all possible combinations of e and h. © 2006 Elsevier Ltd. All rights reserved.
Subjects
Dynamic stability; End motion; Energy barrier; Shallow arch
Other Subjects
Dynamics; Equations of motion; Numerical methods; Parameter estimation; Stability; Dynamic stability; End motion; Energy barrier; Shallow arch; Arches
Type
journal article
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