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Principal response of van der pol-duffing oscillator under combined deterministic and random parametric excitation
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In this article, the principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated, and the behavior, stability and bifurcation of steady state response are studied.Abstract:
The principal resonance of Van der Pol-Duffing oscillator to combined deterministic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.read more
Citations
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Journal ArticleDOI
Forced nonlinear oscillator in a fractal space
TL;DR: In this paper , a fractal-differential model for nonlinear vibration system in fractal space is presented, and the stability criterion for the equation under consideration is obtained by using the linearized stability theory in the autonomous arrangement.
Journal ArticleDOI
Stationary response of strongly non-linear oscillator with fractional derivative damping under bounded noise excitation
F. Hu,Lincong Chen,W. Q. Zhu +2 more
TL;DR: In this paper, a stochastic averaging method for strongly nonlinear oscillators with lightly fractional derivative damping of order α (0 <α≤1) subject to bounded noise excitations is proposed by using the generalized harmonic function.
Journal ArticleDOI
Dynamic responses of axially moving viscoelastic beam under a randomly disordered periodic excitation
TL;DR: In this paper, the first-order and second-order steady-state moments of axially moving viscoelastic beam subject to a randomly disordered periodic excitation were derived based on the largest Lyapunov exponent.
Journal ArticleDOI
Principal parametric resonances of a slender cantilever beam subject to axial narrow-band random excitation of its base
TL;DR: In this paper, the non-linear integro-differential equations of motion for a slender cantilever beam subject to axial narrow-band random excitation are investigated, and the method of multiple scales is used to determine a uniform first-order expansion of the solution of equations.
Journal ArticleDOI
Responses of strongly non-linear oscillator parametrically excited by random narrow-band noise
TL;DR: The principal response of a strongly Van der Pol-Duffing oscillator subjected to parametric random narrow-band excitation is investigated and the excellent agreement between theoretical results and numerical ones can be found immediately.
References
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Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Journal ArticleDOI
Response statistics of non-linear systems to combined deterministic and random excitations
A. H. Nayfeh,S.J. Serhan +1 more
TL;DR: In this paper, a second-order closure method is presented for determining the response of non-linear systems to random excitations, where the excitation is taken to be the sum of a deterministic harmonic component and a random component.
Journal ArticleDOI
Invariant measures and Lyapunov exponents for generalized parameter fluctuations
TL;DR: In this article, the authors follow Khasminskii's concept to separate a stationary solution part by introducing polar coordinates and calculate the associated Lyapunov exponents according to Oseledec's multiplicative ergodic theorem.