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Keywords: Fixed Point Theory
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Journal Articles

Parametric Instability in a Taut String With a Periodically Moving Boundary

K. Wu, W. D. Zhu
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research-Article
J. Appl. Mech. June 2014, 81(6): 061002.
Paper No: JAM-13-1345
https://doi.org/10.1115/1.4026181
Published Online: January 30, 2014
... are analytically obtained using the wave solution and the fixed point theory, and period- i ( i > 1 ) parametric instability regions are numerically calculated using bifurcation diagrams. If the periodic boundary movement profile of the string satisfies certain condition, only period-1 parametric...
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Topics: Finite difference methods, String, Waves
Journal Articles

Dynamic Stability of a Class of Second-Order Distributed Structural Systems With Sinusoidally Varying Velocities

W. D. Zhu, K. Wu
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research-Article
J. Appl. Mech. November 2013, 80(6): 061008.
Paper No: JAM-12-1429
https://doi.org/10.1115/1.4023638
Published Online: August 19, 2013
... relative to the string, are obtained using the wave solution and the fixed point theory without spatially discretizing the governing partial differential equation. There are five nontrivial cases that involve different combinations of string and boundary motions: (I) a translating string...
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Topics: String, Waves
Journal Articles

Dynamic Stability of a Translating String With a Sinusoidally Varying Velocity

W. D. Zhu, X. K. Song, N. A. Zheng
Journal: Journal of Applied Mechanics
Publisher: ASME
Article Type: Research Papers
J. Appl. Mech. November 2011, 78(6): 061021.
https://doi.org/10.1115/1.4003908
Published Online: September 15, 2011
... velocity. A novel method based on the wave solutions and the fixed point theory is developed to analyze the instability phenomenon. The phase functions of the wave solutions corresponding to the phases of the sinusoidal part of the translation velocity, when an infinitesimal wave arrives at the left...
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Topics: String, Waves, Bifurcation, Displacement, Reflection