The autoparametric 3:2 resonance in conservative systems
نویسنده
چکیده
In the resonance model, high-frequency quasi-periodic oscillations (QPOs) are supposed to be a consequence of nonlinear resonance between modes of oscillations occurring within the innermost parts of an accretion disk. Several models with a prescribed mode–mode interaction were proposed in order to explain the characteristic properties of the resonance in QPO sources. In this paper, we examine nonlinear oscillations of a system having two degrees of freedom and we show that this case could be particularly relevant for QPOs. We present a very convenient way how to study autoparametric resonances of a fully general system using the method of multiple scales. We concentrate to conservative systems and discuss their behavior near the 3:2 parametric resonance.
منابع مشابه
Post-critical Behavior of Three- dimensional Composite Beams Near the Autoparametric Resonance under Flapwise Excitation
The bifurcation analysis of a composite beam subjected to harmonic flapwise base excitation is studied when the ratio of flapwise and chordwise internal resonances is 1:2. Results are obtained by the numerical solution of modulation equations. Chracteristics of the response are investigated in terms of time history, phase portraits diagrams and bifurcation diagram of poincare maps. It is observ...
متن کاملRotary bistable and Parametrically Excited Vibration Energy Harvesting
Parametric resonance is a type of nonlinear vibration phenomenon [1], [2] induced from the periodic modulation of at least one of the system parameters and has the potential to exhibit interesting higher order nonlinear behaviour [3]. Parametrically excited vibration energy harvesters have been previously shown to enhance both the power amplitude [4] and the frequency bandwidth [5] when compare...
متن کاملRandom Vibration of a Nonlinear Autoparametric System
A noisy autoparametric system exhibiting 1:2 resonance is studied as a random perturbation of a fourdimensional Hamiltonian system. The problem involves three time scales. Nonstandard stochastic averaging technique is rigorously developed, application of which results in a lower-dimensional description of the system. Probability density of the limiting process is obtained using FEM methods. The...
متن کاملDynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension
This paper presents vibration analysis of an autoparametric pendulum-like mechanism subjected to harmonic excitation. To improve dynamics and control motions, a new suspension composed of a semiactive magnetorheological damper and a nonlinear spring is applied. The influence of essential parameters such as the nonlinear damping or stiffness on vibration, near the main parametric resonance regio...
متن کاملCoexistence Phenomenon in Autoparametric Excitation of Two Degree of Freedom Systems
Coexistence phenomenon refers to the absence of expected tongues of instability in parametrically excited systems. In this paper we obtain sufficient conditions for coexistence to occur in the generalized Ince equation: (1 + a1 cos t+ a2 cos 2t) v̈ +(b1 sin t+ b2 sin 2t) v̇ +(δ + c1 cos t+ c2 cos 2t) v = 0 The results are applied to the stability of motion of a nonlinear normal mode, the x-mode, ...
متن کامل