Multi-pulse orbits and chaotic dynamics in a nonlinear forced dynamics of suspended cables

The global bifurcations in mode of a nonlinear forced dynamics of suspended cables are investigated with the case of the 1:1 internal resonance. After determining the equations of motion in a suitable form, the energy phase method proposed by Haller and Wiggins is employed to show the existence of the Silnikov-type multi-pulse orbits homoclinic to certain invariant sets for the two cases of Hamiltonian and dissipative perturbation. Furthermore, some complex chaos behaviors are revealed for this class of systems.

[1]  Gregor Kovačič,et al.  A Melnikov Method for Homoclinic Orbits with Many Pulses , 1998 .

[2]  Tasso J. Kaper,et al.  MULTI-BUMP ORBITS HOMOCLINIC TO RESONANCE BANDS , 1996 .

[3]  N. Namachchivaya,et al.  Pipes conveying pulsating fluid near a 0:1 resonance: Local bifurcations , 2005 .

[4]  Giuseppe Rega,et al.  The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables , 2007 .

[5]  Z. C. Feng,et al.  Global bifurcations in the motion of parametrically excited thin plates , 1993 .

[6]  Stephen Wiggins,et al.  On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with brokenO(2) symmetry , 1993 .

[7]  George Haller,et al.  Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schro¨dinger equation , 1995 .

[8]  Z. C. Feng,et al.  Global Bifurcations in Parametrically Excited Systems with Zero-to-One Internal Resonance , 2000 .

[9]  Stephen Wiggins,et al.  Global Bifurcations and Chaos , 1988 .

[10]  George Haller,et al.  N-pulse homoclinic orbits in perturbations of resonant hamiltonian systems , 1995 .

[11]  Giuseppe Rega,et al.  Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables , 2008 .

[12]  B. Ravindra,et al.  Low-dimensional chaotic response of axially accelerating continuum in the supercritical regime , 1998 .

[13]  G. Kovačič,et al.  Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation , 1992 .

[14]  Giuseppe Rega,et al.  Space-time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables , 2008 .

[15]  M. Yao,et al.  Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt , 2006 .

[16]  M. Yao,et al.  Global Bifurcations and Chaotic Dynamics in Nonlinear Nonplanar Oscillations of a Parametrically Excited Cantilever Beam , 2005 .

[17]  S. Wiggins,et al.  Orbits homoclinic to resonances: the Hamiltonian case , 1993 .

[18]  B. Tabarrok,et al.  Melnikov's method for rigid bodies subject to small perturbation torques , 1996, Archive of Applied Mechanics.