Nonlinear Normal Modes Associated With Internal Resonance for Elastically Constrained Shallow Arch

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (23) : 48-53.

ZENG Youyi; YI Zhuangpeng

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Abstract

When dynamic system is elastically constrained the natural vibrations and nonlinear normal modes are different from that for ideal boundary conditions, and the constrain stiffness values will change the parametric region of various nonlinear dynamics. The nonlinear normal modes of a shallow arch with one end vertically elastically constrained in case of two-to-one internal resonance are constructed by using the multi-scale method and direct perturbation in this paper. The research results show that the internal resonant nonlinear system has both single-mode motion and couple-mode motion. Also, the existence and various values of elastic constraint lead to different asymmetric linear modes, shape functions and internal resonance activation conditions. Moreover, the space-time effects of nonlinear normal modes with different constraint stiffness display different dynamic configurations.

Key words

elastically constrained / shallow arch / nonlinear normal modes / 2:1 internal resonance / multi-scale method.

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ZENG Youyi; YI Zhuangpeng. Nonlinear Normal Modes Associated With Internal Resonance for Elastically Constrained Shallow Arch[J]. Journal of Vibration and Shock, 2015, 34(23): 48-53

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