Resonant non-linear vibrations in continuous systems—I. Undamped case

Ablowitz, Mark J.; Aşkar, Attila; Çakmak, A. Ş.; Engin, Hasan

doi:10.1016/0020-7462(79)90011-8

Cited by 9 publications

(7 citation statements)

References 3 publications

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“…The method of multiple scales [1,2] is used to detemine a uniform first-order expansion of the solution of equations (2.16)-(2.18). To this end, we express the solution as the sum of a static component and a dynamic component; that is, u(x,t) = bx + v(x,t) w = 0…”

Section: Methods Of Solutionmentioning

confidence: 99%

Non-linear response of a fluid valve

Nayfeh

Bouguerra

1990

International Journal of Non-Linear Mechanics

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Section: Methods Of Solutionmentioning

confidence: 99%

Non-linear response of a fluid valve

Nayfeh

Bouguerra

1990

International Journal of Non-Linear Mechanics

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“…It was shown in [37][38][39] that this system is chaotic for α = 1 with the parameter values a = b = 0.35, c = 0.3 and d = 0.2. Using nonlinear coupling feedback functions, system (9) is coupled as follows:…”

Section: Numerical Resultsmentioning

confidence: 99%

Phase synchronization in fractional differential chaotic systems

Erjaee

Momani

2008

Physics Letters A

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“…The above nonlinear boundary-value problem for ~ is solved by a perturbation procedure, similar to that of Ablowitz et al [1], using characteristic variables of the wave equation. We begin by assuming the expansion…”

Section: Perturbation Analysismentioning

confidence: 99%

Long Nonlinear Water Waves in a Channel Near a Cut‐off Frequency

Kantzios

Akylas

1988

Stud Appl Math

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A theoretical study is made of the free-surface flow induced by a wavemaker, performing torsional oscillations about a vertical axis, in a shallow rectangular channel near a cut-off frequency. Exactly at cut-off, linearized water-wave theory predicts a temporally unbounded response due to a resonance phenomenon. It is shown, through a perturbation analysis using characteristic variables, that the nonlinear response is governed by a forced Kadomtsev-Petviashvili (KP) equation with periodic boundary conditions across the channel. This nonlinear initial-boundary-value problem is investigated analytically and numerically. When surface-tension effects are negligible, the nonlinear response reaches a steady state and exhibits jump phenomena. On the other hand, in the high-surfacetension regime, no steady state is obtained. These results are discussed in connection with similar forced wave phenomena studied previously in a deepwater channel and related laboratory experiments.

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Resonant non-linear vibrations in continuous systems—I. Undamped case

Cited by 9 publications

References 3 publications

Non-linear response of a fluid valve

Non-linear response of a fluid valve

Phase synchronization in fractional differential chaotic systems

Long Nonlinear Water Waves in a Channel Near a Cut‐off Frequency

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