A NEW MULTI-PULSE CHAOTIC MOTION FOR PARAMETRICALLY EXCITED VISCOELASTIC AXIALLY MOVING STRING

摘要

In this paper, the Shilnikov type multi-pulse orbits and chaotic dynamics of parametrically excited viscoelastic moving string are studied in detail. Using Kelvin-type viscoelastic constitutive law, the equation of motion for viscoelastic moving string with the external damping and parametric excitation is given. The four-dimensional averaged equation under primary parametric resonance is obtained by directly using the method of multiple scales and Galerkin's approach to the partial differential governing equation of viscoelastic moving string. The Shilnikov type multi-pulse chaotic motions of viscoelastic moving string are also found by using numerical simulation. A new phenomenon on the multi-pulse jumping orbits and a new strange attractor are observed from three-dimensional phase space for the first time.