Simultaneous resonances involving two mode shapes of parametrically-excited rectangular plates

Nguyen, Hai

doi:10.1016/j.jsv.2013.04.010

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…Substituting (14) into the 1 -order equations in (13a) and (13b) leads to the differential equations, which can be written as a six-dimensional dynamical system by separating real and imaginary parts as where (⋅) stands for the derivation with respect to 1 , 1 = 1 1 − 1 − 3 + 4 , and…”

Section: Nonlinear Dynamic Equationsmentioning

confidence: 99%

“…Established a continuum beam model for the nonlinear vibration of rotor-bearing system. Nguyen [14] and Hegazy [15] presented the nonlinear resonances involving two mode shapes of thin plates. It has been shown that when a parametric resonance is excited in the presence of an internal resonance, the coincidence of these two types of resonances will give rise to the simultaneous resonances.…”

Section: Introductionmentioning

confidence: 99%

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The Combined Internal and Principal Parametric Resonances on Continuum Stator System of Asynchronous Machine

Zhang²

2014

Shock and Vibration

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With the increasing requirement of quiet electrical machines in the civil and defense industry, it is very significant and necessary to predict the vibration and noise characteristics of stator and rotor in the early conceptual phase. Therefore, the combined internal and principal parametric resonances of a stator system excited by radial electromagnetic force are presented in this paper. The stator structure is modeled as a continuum double-shell system which is loaded by a varying distributed electromagnetic load. The nonlinear dynamic equations are derived and solved by the method of multiple scales. The influences of mechanical and electromagnetic parameters on resonance characteristics are illustrated by the frequency-response curves. Furthermore, the Runge-Kutta method is adopted to numerically analyze steady-state response for the further understanding of the resonance characteristics with different parameters.

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Section: Nonlinear Dynamic Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Combined Internal and Principal Parametric Resonances on Continuum Stator System of Asynchronous Machine

Zhang²

2014

Shock and Vibration

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“…Nayfeh et al [26,27] and Lifshitz et al [28] studied parametrically excited multidegree-of-freedom systems with different nonlinearities, while Perkins et al [29] illustrated the beneficial effects that noise can produce on the responses of an array of coupled nonlinear oscillators externally excited. However, few studies have been devoted to simultaneous resonances [30][31][32], and they are mostly limited to single or few degree-of-freedom systems.…”

Section: Introductionmentioning

confidence: 99%

Collective dynamics of periodic nonlinear oscillators under simultaneous parametric and external excitations

et al. 2015

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The collective dynamics of a periodic structure of coupled Duffing-Van Der Pol oscillators is investigated under simultaneous external and parametric excitations. An analytico-computational model based on a perturbation technique, combined with standing wave decomposition and the asymptotic numerical method is developed for a finite number of coupled oscillators. The frequency responses and the basins of attraction are analyzed for the case of small arrays, demonstrating the importance of the multimode solutions and the robustness of their attractors. This model can be exploited to design periodic structure-based smart systems with high performance, by taking advantage of the multi-modes induced by the collective dynamics.

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“…Parametric resonance PR is the state of oscillating instability which can arise under periodic disturbance of a parameter of the structure, for example, under periodic variation of the pendulum length or the tensile force in a beam, plate or a flexible screen (Parszewski, 1992; Virgin, 2007). The problem of the parametric resonance in mechanical systems is studied by numerous researches and development centres (Başar et al, 1987;Bąk et al, 2013;de Silva, 2005;Hagedorn and Koval, 1971;Michalczyk, 1995;Nguyen, 2013;Osiński, 1985;Parszewski, 1982;Slepyan, 2013, 2014). The parametric resonance phenomenon has been known since 19th century.…”

Section: Introductionmentioning

confidence: 99%

The Experimental Investigation Of The Screen Operation In The Parametric Resonance Conditions

Bąk

Noga

Stachowicz

2015

Acta Mechanica Et Automatica

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In this paper the experimental studies of the screen working in the parametric resonance condition are discussed. The investigations are conducted for laboratory parametric resonance screen. The measuring test is performed for four cases of tension force values. The full sheet metal instead of the sieve is used. For each considered case the natural frequency of the plate and the parameter modulation frequency are determined. The achieved results are presented and discussed. It is shown that the highest sieve plate amplitude is obtained when the parameter modulation frequency is two times larger than natural frequency of the sieve plate. This parametric resonance vibration was observed only for tension force equal to 4000 N because of the rotational speed limits of electrical vibratos.

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Simultaneous resonances involving two mode shapes of parametrically-excited rectangular plates

Cited by 5 publications

References 15 publications

The Combined Internal and Principal Parametric Resonances on Continuum Stator System of Asynchronous Machine

The Combined Internal and Principal Parametric Resonances on Continuum Stator System of Asynchronous Machine

Collective dynamics of periodic nonlinear oscillators under simultaneous parametric and external excitations

The Experimental Investigation Of The Screen Operation In The Parametric Resonance Conditions

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