Self-Excited System Vibrations With Parametric and External Excitations

Szabelski, Kazimierz; Warmiński, Jerzy

doi:10.1006/jsvi.1995.0547

Cited by 60 publications

(41 citation statements)

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“…In the Fig. 8 we can see behaviour of the system similar to that of one degree of freedom model presented in the introduction and papers [ 17], [ 19]. External force acting together with parametric and self-excitation changes classical resonance curve of the considered model.…”

Section: Numerical Calculationssupporting

confidence: 52%

“…Substituting solution (17) and taking into account the derivatives definitions (19), (20), after grouping terms with respect to ε order we get a set of differential equations in successive perturbation orders 0 ε -order…”

Section: Analytical Solutions Of Self Parametrically and Externally mentioning

confidence: 99%

“…The dynamics of such a system was investigated in papers [ 18], [ 19]. The nonlinear damping was there assumed as the Rayleigh's nonlinear function ( ) 0.01…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Warmiński

2010

Nonlinear Dyn

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Section: Numerical Calculationssupporting

confidence: 52%

Section: Analytical Solutions Of Self Parametrically and Externally mentioning

confidence: 99%

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Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Warmiński

2010

Nonlinear Dyn

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“…Synchronization of limit cycle oscillators by parametric excitation (2 f 0 laser modulation in our experiment͒ is the subject of recent theoretical research, 14,15 indicating the possibility for chaotic behavior. A theoretical model was recently proposed for mechanical neurocomputing based on synchronized MEMS oscillators.…”

Section: Form Approved Omb No 0704-0188mentioning

confidence: 94%

Frequency entrainment for micromechanical oscillator

Zalalutdinov

Aubin

Pandey

et al. 2003

Applied Physics Letters

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We demonstrate synchronization of laser-induced self-sustained vibrations of radio-frequency micromechanical resonators by applying a small pilot signal either as an inertial drive at the natural frequency of the resonator or by modulating the stiffness of the oscillator at double the natural frequency. By sweeping the pilot signal frequency, we demonstrate that the entrainment zone is hysteretic and can be as wide as 4% of the natural frequency of the resonator, 400 times the 1/Q ϳ10 Ϫ4 half-width of the resonant peak. Possible applications are discussed based on the wide range of frequency tuning and the power gain provided by the large amplitude of self-oscillations ͑controlled by a small pilot signal͒.

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“…Szabelski and Warmiński [27] investigated a nonlinear oscillator driven by parametric and external forcing, whilst the ratio of forcing frequencies is a rational number. On the other hand, Yagazaki and co-workers [28] analysed the dynamics of an oscillator subject to parametric and external excitations, whilst the ratio of forcing frequencies is an irrational number, but including also a weakly cubic nonlinear component.…”

Section: Extended Mathieu Equation: Inclusion Of Two Parametric Forcimentioning

confidence: 99%

Dynamics of a Parametrically Excited System with Two Forcing Terms

Sofroniou

Bishop

2014

Mathematics

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Motivated by the dynamics of a trimaran, an investigation of the dynamic behaviour of a double forcing parametrically excited system is carried out. Initially, we provide an outline of the stability regions, both numerically and analytically, for the undamped linear, extended version of the Mathieu equation. This paper then examines the anticipated form of response of our proposed nonlinear damped double forcing system, where periodic and quasiperiodic routes to chaos are graphically demonstrated and compared with the case of the single vertically-driven pendulum.

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Self-Excited System Vibrations With Parametric and External Excitations

Cited by 60 publications

References 0 publications

Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Frequency entrainment for micromechanical oscillator

Dynamics of a Parametrically Excited System with Two Forcing Terms

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