Nonlinear Responses of a String-Beam Coupled System with Four-Degrees-of-Freedom and Multiple Parametric excitations

The nonlinear dynamic responses of a string-beam coupled system subjected to harmonic external and parametric excitations are studied in this work in the case of 1:2 internal resonance between the modes of the beam and string. First, the nonlinear governing equations of motion for the string-beam coupled system are established. Then, the Galerkin's method is used to simplify the nonlinear governing equations to a set of ordinary differential equations with four-degrees-of-freedom. Utilizing the method of multiple scales, the eight-dimensional averaged equation is obtained. The case of 1:2 internal resonance between the modes of the beam and string — principal parametric resonance-1/2 subharmonic resonance for the beam and primary resonance for the string — is considered. Finally, nonlinear dynamic characteristics of the string-beam coupled system are studied through a numerical method based on the averaged equation. The phase portrait, Poincare map and power spectrum are plotted to demonstrate that the periodic and chaotic motions exist in the string-beam coupled system under certain conditions.

[1]  Gianni Royer-Carfagni,et al.  Parametric-resonance-induced cable vibrations in network cable-stayed bridges. A continuum approach , 2003 .

[2]  On the bifurcation of large amplitude solutions for a system of wave and beam equations , 2003 .

[3]  Z. Ding.  Nonlinear periodic oscillations in a suspension bridge system under periodic external aerodynamic forces , 2002 .

[4]  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 .

[5]  Graziano Leoni,et al.  Vibrations of beams prestressed by internal frictionless cables , 1999 .

[6]  G. Holubová,et al.  Initial-boundary value problem for the nonlinear string-beam system , 2003 .

[7]  Seid H. Pourtakdoust,et al.  Chaotic Analysis of Nonlinear Viscoelastic Panel Flutter in Supersonic Flow , 2003 .

[8]  Vincenzo Gattulli,et al.  Nonlinear interactions in the planar dynamics of cable-stayed beam , 2003 .

[9]  Paolo Clemente,et al.  Experimental modal analysis of the Garigliano cable-stayed bridge , 1998 .

[10]  Wei Zhang,et al.  Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom , 2006 .

[11]  Pao-Hsii Wang,et al.  Parametric studies on cable-stayed bridges , 1996 .

[12]  Z. Ding.  Multiple periodic oscillations in a nonlinear suspension bridge system , 2002 .

[13]  Jean W. Zu,et al.  Dynamic analysis of an optical fiber coupler in telecommunications , 2003 .

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

[15]  R.-F. Fung,et al.  DYNAMIC MODELLING AND VIBRATION ANALYSIS OF A FLEXIBLE CABLE-STAYED BEAM STRUCTURE , 2002 .

[16]  Vincenzo Gattulli,et al.  One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models , 2005 .

[17]  Wei Zhang,et al.  Multipulse Shilnikov orbits and Chaotic Dynamics for Nonlinear Nonplanar Motion of a Cantilever Beam , 2005, Int. J. Bifurc. Chaos.

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