Two-to-one internal resonances in continuous systems with arbitrary quadratic nonlinearities

被引：0

作者：

Pakdemirli, M ^{[1
]}

Özkaya, E

机构：

[1] Celal Bayar Univ, Dept Mech Engn, TR-45140 Manisa, Turkey

[2] King Fahd Univ Petr & Minerals, Dept Mech Engn, Dhahran 31261, Saudi Arabia

来源：

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING | 2004年 / 29卷 / 1C期

关键词：

vibrations; continuous systems; internal resonances;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Vibrations of a general continuous system with arbitrary quadratic nonlinearities are considered. The nonlinearities are expressed in terms of arbitrary quadratic operators. The two-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a specific problem.

引用

页码：99 / 112

页数：14

共 50 条

[41] Application of reconstitution multiple scale asymptotics for a two-to-one internal resonance in Magnetic Resonance Force Microscopy
Hacker, E.
Gottlieb, O.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2017, 94 : 174 - 199
[42] Self-excited oscillators with asymmetric nonlinearities and one-to-two internal resonance
Aristotle Univ, Thessaloniki, Greece
Nonlinear Dyn, 4 (325-346):
[43] Self-excited oscillators with asymmetric nonlinearities and one-to-two internal resonance
Verros, G
Natsiavas, S
NONLINEAR DYNAMICS, 1998, 17 (04) : 325 - 346
[44] Self-Excited Oscillators with Asymmetric Nonlinearities and One-to-Two Internal Resonance
G. Verros
S. Natsiavas
Nonlinear Dynamics, 1998, 17 : 325 - 346
[45] Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities
Abe, Akira
MATHEMATICAL PROBLEMS IN ENGINEERING, 2010, 2010
[46] A general solution procedure for the forced vibrations of a system with cubic nonlinearities: Three-to-one internal resonances with external excitation
Ozhan, B. Burak
Pakdemirli, Mehmet
JOURNAL OF SOUND AND VIBRATION, 2010, 329 (13) : 2603 - 2615
[47] Perturbation analysis in parametrically excited two-degree-of-freedom systems with quadratic and cubic nonlinearities
S. B. Li
W. Zhang
L. J. Gao
Nonlinear Dynamics, 2013, 71 : 175 - 185
[48] Perturbation analysis in parametrically excited two-degree-of-freedom systems with quadratic and cubic nonlinearities
Li, S. B.
Zhang, W.
Gao, L. J.
NONLINEAR DYNAMICS, 2013, 71 (1-2) : 175 - 185
[49] Three-to-one internal resonances in a general cubic non-linear continuous system
Pakdemirli, M
Özkaya, E
JOURNAL OF SOUND AND VIBRATION, 2003, 268 (03) : 543 - 553
[50] S = −1 resonances in two meson-one baryon systems
K. P. Khemchandani
A. Martínez Torres
E. Oset
Few-Body Systems, 2008, 44 : 145 - 147

← 1 2 3 4 5 →