1/3 SUBHARMONIC RESPONSE OF DUFFING OSCILLATOR UNDER PERIODIC AND RANDOM EXCITATIONS
Abstract
The subharmonic response of one third order of Duffing oscillator under harmonic and random excitations is investigated for the first time by a technique combining the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function for Fokker-Planck equation. The averaged equations are linear zed so that the stationary density function of the approximate response can be found exactly by the technique of auxiliary function. The one third order subharmonic response obtained by the present technique is validated by numerical simulation. The significant contribution of this work is that it may lead to a new trend in investigating subharmonic oscillators in random nonlinear systems.
Supporting agencies: Работа выполнена при поддержке Национального Фонда развития и науки Вьетнама (NAFOSTED), Вьетнамского национального университета г. Хошимин (VNU-HCM) и гранта РФФИ № 14-08-00206.
About the Authors
N. D. Anh
Institute of Mechanics, Hanoi, Vietnam
Viet Nam
Viet Nam
Vilor Lavrentyevich Zakovorotny
Don State Technical University, Russia
Russian Federation
Russian Federation
D. N. Hao
University of Information Technology, HochiMinh City, Vietnam
Viet Nam
Viet Nam
N. Х. Chiem
University of Le Quy Don, Hanoi, Vietnam
Viet Nam
Viet Nam
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Review
For citations:
Anh N.D., Zakovorotny V.L., Hao D.N., Chiem N.Х. 1/3 SUBHARMONIC RESPONSE OF DUFFING OSCILLATOR UNDER PERIODIC AND RANDOM EXCITATIONS. Vestnik of Don State Technical University. 2014;14(4):39-49. https://doi.org/10.12737/6816
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