NONLINEAR DYNAMIC STABILITY OF A MOVING STRING BY HAMILTONIAN FORMULATION

✍ Scribed by Rong-Fong Fung; Jeng-Sheng Huang; Jau-Yang Yeh

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 562 KB
• Volume: 66
• Category: Article
• ISSN: 0045-7949
• DOI: 10.1016/s0045-7949(97)00104-1

✦ Synopsis

AbstractÐIn this paper, the stability behavior of an axially moving string is examined in the presence of parametric and combination resonances. The Galerkin discretization utilizing stationary string eigenfunctions is used to transform the partial dierential equation governing transverse response into a set of coupled ordinary dierential equations. Hamiltonian formulation and averaging method are used to yield a set of autonomous equations. The conditions of parametric and summed resonances are obtained over speci®c ranges between the natural and exciting frequencies. Explicit results of the stability boundaries for the ®rst and secondary principal parametric and the ®rst summation resonances and the bifurcation paths of the nontrivial amplitudes are obtained.