Nonlinear resonance in stretched strings with viscous damping

Anand, G. V. (1966) Nonlinear resonance in stretched strings with viscous damping Journal of the Acoustical Society of America, 40 (6). pp. 1517-1528. ISSN 0001-4966

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The phenomena of amplitude jumps and nonplanar oscillations, which are characteristic features of non-linear resonance in stretched strings, have been studied in detail, taking the effect of damping into account. Expressions for the resonance frequency and amplitude, and the frequencies and amplitudes at which the jumps occur, have been obtained; and it has been shown that the resonance frequency is not a constant of the system but increases with the driving force. Finally, it is established that, in the presence of damping, (1) nonplanar oscillations exist only if the driving force φ exceeds a certain critical value, φu; (2) over a small interval of the driving force φj'; >φ> φw the nature of the downward jump is qualitatively different from the (normal) downward jump occurring for values of φ greater than φj'; (3) if φ, lies in the interval φw > φ > φj, jump phenomenon is exhibited even though the oscillations are planar at all frequencies; and (4), if φ < φj, the response is essentially linear in character. In Appendix A, it has been established that, if φ > φw, upward jump in amplitude is always accompanied by a transition to nonplanar motion unless the damping is very heavy.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
ID Code:89740
Deposited On:30 Apr 2012 14:50
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