Atlas: Non-linear vibrations of tensioned string having a non-ideal mid-support and variable velocity by Hakan BOYACI*

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Mathematical Problems in Engineering, Aerospace and Sciences
June 25-27, 2008
University of Genoa, Italy
Genoa, Italy

Organizers
General Organizer and Chair: Seenith Sivasundaram, USA; Local organizer and Chair: Marcello Sanguineti, Italy

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Non-linear vibrations of tensioned string having a non-ideal mid-support and variable velocity
by
Hakan BOYACI*
Celal Bayar Univ., Dept. Mechanical Engineering, 45140 Muradiye-Manisa, Turkey
Coauthors: Ali YURDDAS, Erdogan OZKAYA

-Abstract-

In this study, the effects of non-ideal mid-support on non-linear transverse vibrations of highly tensioned axially moving string with variable velocity are investigated. The string is on fixed supports and the immovable end conditions result in extension of the string during vibration and hence introduce further non-linear terms to the equation of motion. The mid-support is a non-ideal flexible support allowing little deflections and possesing spring characteristics. The velocity is assumed to be a harmonic function varying about a mean velocity. The equation of motion is derived by using Hamilton Principle and solved analytically by direct application of the Method of Multiple Scales (a perturbation technique). Principal parametric resonance cases are investigated in detail. Non-linear frequencies are derived depending on amplitude.

Date received: April 28, 2008