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Keywords: bifurcation
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Journal Articles
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2020, 15(4): 041003.
Paper No: CND-19-1266
Published Online: February 24, 2020
... to study the various responses of the system. The system is subjected to hard excitation and hence the subharmonic and superharmonic resonance conditions have been studied. The second-order method of multiple scales (MMS) has been used to find the response, stability, and bifurcations of the system...
Journal Articles
Article Type: Research-Article
J. Comput. Nonlinear Dynam. December 2019, 14(12): 121008.
Paper No: CND-18-1482
Published Online: October 24, 2019
... damping, and input power on bifurcation, and chaos properties of the system are analyzed. The numerical results indicate that the system performs a chaotic motion after several frequency jumps as the mesh frequency increases. When the backlash increases, the frequency region of double-side impact and...
Journal Articles
Article Type: Research-Article
J. Comput. Nonlinear Dynam. March 2015, 10(2): 021002.
Paper No: CND-13-1024
Published Online: March 1, 2015
.... , 12 ( 3 ), pp. 117 – 131 . 10.1007/s11220-011-0065-2 [27] Nayfeh , A. H. , and Balachandran , B. , 1995 , Applied Nonlinear Dynamics , Wiley-Interscience , New York . [28] Rao , S. S. , 2007 , Mechanical Vibrations , Wiley , New York . bifurcation microbeam...
Journal Articles
Article Type: Research-Article
J. Comput. Nonlinear Dynam. March 2015, 10(2): 021010.
Paper No: CND-13-1292
Published Online: March 1, 2015
...Hu Yuda; Hu Peng; Zhang Jinzhi (1) Bifurcation point set B 1 = { α 5 = 0 } ,   B 2 = { α 5 = 1 4 α 3 2 , α 3 < 0 } . (2) Hysteresis set H = { α 3 = 0...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. April 2012, 7(2): 021001.
Published Online: December 22, 2011
... structures are introduced to describe different periodic and chaotic motions. Analytical prediction of complex periodic motion of the ball in the periodically shaken impact pair is completed, and the corresponding stability and bifurcation analysis are also carried out. Numerical illustrations of periodic...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. January 2012, 7(1): 011006.
Published Online: August 15, 2011
... dynamically unstable, due to both e ff ects of friction and mode coupling. Furthermore, the amplitude of the vibration in the unstable region is determined through nonlinear analysis. The obtained results show that this unstable vibration is a bifurcation classified as a supercritical Hamiltonian-Hopf...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. October 2011, 6(4): 041014.
Published Online: June 14, 2011
... system is an archetypal model of modal interaction in stability theory representing a large class of structural problems. When the system displays coincident buckling loads, several post-buckling paths emerge from the bifurcation point (critical load) along the fundamental path. This leads to a complex...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. October 2011, 6(4): 041012.
Published Online: May 20, 2011
... function determines the stability of these equilibria, and bifurcation diagrams are constructed to demonstrate the co-existence of several equilibrium configurations of the vessel. To validate the results, a vessel of rectangular cross section was built. The results of the experiments agree well with the...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. October 2011, 6(4): 041009.
Published Online: April 14, 2011
...Wei Huang; Andrew J. Dick In this paper, a study of the characteristics of period-doubling bifurcations in the dynamic behavior of an atomic force microscope probe for off-resonance excitation is presented. Using a three-mode approximation and excitation at two-and-a-half times the fundamental...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. October 2011, 6(4): 041002.
Published Online: March 22, 2011
... semidiscretization method applied for the corresponding time-periodic delay system. Predictor-corrector method is developed to continue the periodic solutions as the bifurcation parameter, that is, the axial immersion is varied. It is observed that the influence of the state dependent delay on linear stability can...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. July 2011, 6(3): 031004.
Published Online: December 16, 2010
... settings. This paper argues for exploiting nonsmooth fold bifurcations in the design of ultrafast and robust, resettable, electromechanical limit switches. Specifically, the discussion emphasizes the dramatic changes in system response associated with the onset of near-grazing, low-velocity contact in...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. July 2011, 6(3): 031003.
Published Online: December 15, 2010
...-sliding bifurcations. 05 05 2009 23 08 2010 15 12 2010 15 12 2010 Keller , H. B. , 1977 , “ Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems ,” Applications of Bifurcation Theory , Academic Press , New York , pp...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. April 2011, 6(2): 021001.
Published Online: October 15, 2010
... calculating the frequency response curves that pitchfork bifurcation can occur followed by “localization phenomenon” for a specific excitation frequency range. During this range, sloshing occurs at different amplitudes in the two tanks, even if the dimensions of both tanks are identical. Furthermore, Hopf...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. January 2011, 6(1): 011014.
Published Online: October 7, 2010
... frequencies (two fast and one slow), which is amenable to a singular perturbation analysis. We then restrict the dynamics in neighborhoods of resonance manifolds and perform local bifurcation analysis of the forced subharmonic orbits. We find increased complexity in the dynamics as the frequency detuning...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. January 2011, 6(1): 011012.
Published Online: October 5, 2010
... the numerical results, the differences between the responses in single- and dual-pendulum systems are shown. A pitchfork bifurcation occurs followed by mode localization where both identical pendula vibrate at constant but different amplitudes. Hopf bifurcations occur, and then amplitude- and phase...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. January 2011, 6(1): 011010.
Published Online: October 4, 2010
..., “Experimental Continuation of Periodic Orbits Through a Fold,” Phys. Rev. Lett., 100(24), p. 244101) , a branch of periodic orbits is continued through a saddle-node bifurcation and along the associated branch of unstable periodic orbits using a modified time-delay controller. At each step in the continuation...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. January 2011, 6(1): 011005.
Published Online: September 28, 2010
...Jan Sieber; Bernd Krauskopf; David Wagg; Simon Neild; Alicia Gonzalez-Buelga We present an experimental procedure to track periodic orbits through a fold (saddle-node) bifurcation and demonstrate it with a parametrically excited pendulum experiment where the tracking parameter is the amplitude of...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. January 2011, 6(1): 011001.
Published Online: September 27, 2010
... second that visits a lower-well orbit and a two-well orbit. Bifurcation diagrams obtained by sweeping the ac voltage amplitudes and frequency are presented. Period doubling, reverse period doubling, and the one-well chaos through period doubling are observed in amplitude sweep. In frequency sweep, period...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. October 2010, 5(4): 041014.
Published Online: August 17, 2010
... the sensor. The gain and delay of the feedback signal are chosen such that the base excitations set the beam into stable limit-cycle oscillations as a result of a supercritical Hopf bifurcation of the trivial fixed points. The amplitude of these limit-cycles is shown to be ultrasensitive to parameter...
Journal Articles
Article Type: Research Papers
J. Comput. Nonlinear Dynam. October 2010, 5(4): 041012.
Published Online: August 12, 2010
... taking fractional order on system dynamics is investigated using phase diagram, bifurcation diagram and Poincaré map. The bifurcation diagram is introduced to exam the effect of excitation amplitude, frequency, and damping coefficient on the Duffing system with fractional order damping. The analysis...