GLOBAL DYNAMICS OF PARAMETRICALLY EXCITED NONLINEAR REVERSIBLE-SYSTEMS WITH NONSEMISIMPLE 1 1 RESONANCE/

In this paper, we analytically investigate the global dynamics associa ted with the nonlinear reversible systems that exhibit Hopf bifurcatio n in the presence of one-to-one nonsemisimple internal resonance. The effect of periodic parametric excitations is examined on such systems near the principal subharmonic resonance in presence of dissipation. T he nonlinear and nonautonomous system is simplified considerably by re ducing it to the corresponding four-dimensional normal form. The norma l form associated with the reversible systems is obtained as a special case from the general normal form equations obtained in [N. Sri Namac hchivaya, M.M. Doyle, W.F. Langford and N. Evans, Normal form for gene ralized hopf bifurcation with non-semisimple 1:1 resonance, Z. Angew. Math. Phys. (ZAMP) 45 (1994) 312-335]. Under small perturbations arisi ng from parametric excitations and nonreversible dissipation, two mech anisms are identified in such systems that may lead to chaotic dynamic s. Explicit restrictions on the system parameters are obtained for bot h of these mechanisms which lead to this complex behavior. Finally, th e results are demonstrated through a two-degree-of-freedom model of a thin rectangular beam vibrating under the action of a pulsating follow er force.