Singular Characteristics of Nonlinear Normal Modes in a Two Degrees of Freedom Asymmetric System With Cubic Nonlinearities

XU Jian; LU Qi-shao; HUANG Ke-lei

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(8): 869-878

XU Jian, LU Qi-shao, HUANG Ke-lei. Singular Characteristics of Nonlinear Normal Modes in a Two Degrees of Freedom Asymmetric System With Cubic Nonlinearities[J]. Applied Mathematics and Mechanics, 2001, 22(8): 869-878.

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Singular Characteristics of Nonlinear Normal Modes in a Two Degrees of Freedom Asymmetric System With Cubic Nonlinearities

1.
Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, P R China;
2.
Department of Applied Mathematics, Peking University of Aeronautics and Astronautics, Beijing 100083, P R China

Received Date: 1999-09-27
Rev Recd Date: 2001-03-20
Publish Date: 2001-08-15

Abstract

Abstract

Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied,based on the invariant space in nonlinear normal modes and perturbation technique.Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerates.For non-resonances,it is analytically presented that a single-mode motion and localization of vibrations occur in the system,and the degree of localization relates not only to the coupling stiffness between oscillators,but also to the asymmetric parameter.The parametric threshold value of localization is analytically given.For 11 resonance,there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying.The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.
- asymmetric system,
- nonlinear normal mode,
- localization of vibration,
- bifurcation of normal mode,
- nonlinear dynamics

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References(16)

References

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