Dynamic behavior of a circular shaft with geometrical nonlinearity and constant spin, subjected to periodic axial load is investigated. The case of parametric combination resonance is studied. Extension of shaft center line is the source of nonlinearity. The shaft has gyroscopic effect and rotary inertia but shear deformation is neglected. The equations of motion are derived by extended Hamilto...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...

in this paper, chaotic motion analysis and its control for a non-planar non-linear cantilever beam with axial and lateral parametric excitation in the free end is accomplished. this is a new method for control of chaotic motion of a non-linear planar beam. in this survey, internal resonance of the beam is 2:1 and the initial resonance is in the outside of plane and it is assumed a sub-resonance...

in this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. the governing equation represented motion is solved by the method of multiple scales. considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. numerical results indicate the effects of fractional damping on stability.

We discuss topological transitions during parametric resonance in the gauge sector of electroweak theory. It is shown that the resonance leads to separation of topological indices of the gauge and Higgs fields, resulting in topological transitions of non-sphaleron nature.

We study parametric resonant decay of inflaton field with emphasis on its physical meaning. We show that the parametric resonance is indeed an induced process, which means that the more numbers of produced particles, the more inflaton field decays. We also consider the dissipative effects of produced particles and find that the dissipation reduces the resonant decay rate of inflaton field.