Multipulse Chaotic Dynamics for Nonautonomous Nonlinear Systems and Application to a FGM Plate

The extended Melnikov method is improved to investigate the nonautonomous nonlinear dynamical system in Cartesian coordinate. The multipulse chaotic dynamics of a simply supported functionally graded materials (FGM) rectangular plate subjected to transversal and in-plane excitations is investigated in this paper for the first time. The formulas of the FGM rectangular plate are two-degree-of-freedom nonautonomous nonlinear system with coupling of nonlinear terms including several square and cubic terms. The extended Melnikov method is improved to enable us to analyze directly the nonautonomous nonlinear dynamical system of the simply-supported FGM rectangular plate. The results obtained here indicate that multipulse chaotic motions can occur in the simply-supported FGM rectangular plate. Numerical simulation is also employed to find the multipulse chaotic motions of the simply-supported FGM rectangular plate.

[1]  M. Yao,et al.  THEORIES OF MULTI-PULSE GLOBAL BIFURCATIONS FOR HIGH-DIMENSIONAL SYSTEMS AND APPLICATION TO CANTILEVER BEAM , 2008 .

[2]  M. Yao,et al.  Multi-pulse chaotic dynamics in non-planar motion of parametrically excited viscoelastic moving belt , 2012 .

[3]  Stephen Wiggins.  Global Bifurcations and Chaos: Analytical Methods , 1988 .

[4]  W. Zhang,et al.  Shilnikov-Type multipulse orbits and Chaotic Dynamics of a Parametrically and Externally excited Rectangular Thin Plate , 2007, Int. J. Bifurc. Chaos.

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

[6]  Wei Zhang,et al.  Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations , 2012 .

[7]  Yukinori Kobayashi,et al.  Nonlinear dynamic behaviors of clamped laminated shallow shells with one-to-one internal resonance , 2007 .

[8]  Yue Baozeng,et al.  Heteroclinic bifurcations in completely liquid-filled spacecraft with flexible appendage , 2007 .

[9]  Jie Yang,et al.  Periodic and Chaotic Motions of FGM thin Plate with Two Simply Supported Opposite and Two Free Edges , 2011, Int. J. Bifurc. Chaos.

[10]  W. Zhang,et al.  Nonlinear Responses of a String-Beam Coupled System with Four-Degrees-of-Freedom and Multiple Parametric excitations , 2009, Int. J. Bifurc. Chaos.

[11]  Weiqin Yu,et al.  Orbits homoclinic to resonances in a harmonically excited and undamped circular plate , 2010 .

[12]  J. N. Reddy,et al.  Three-dimensional thermomechanical deformations of functionally graded rectangular plates , 2001 .

[13]  Jan Awrejcewicz,et al.  Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods , 2012 .

[14]  Hui-Shen Shen,et al.  Nonlinear vibration and dynamic response of functionally graded plates in thermal environments , 2004 .

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

[16]  P. Xu,et al.  The Existence of Silnikov's Orbit in Four-dimensional Duffing's Systems , 2003 .

[17]  Christopher Jones,et al.  Geometric singular perturbation theory , 1995 .

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

[19]  Liqun Chen,et al.  BIFURCATIONS AND CHAOS OF AN AXIALLY MOVING PLATE UNDER EXTERNAL AND PARAMETRIC EXCITATIONS , 2012 .

[20]  K. M. Liew,et al.  Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates , 2003 .

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