弹性约束浅拱的内共振非线性模态

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (23) : 48-53.

论文

弹性约束浅拱的内共振非线性模态

曾有艺易壮鹏

作者信息 +

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

ZENG Youyi; YI Zhuangpeng

Author information +

文章历史 +

摘要

动力系统采用弹性约束时自振特性、非线性模态与采用理想边界时存在差异, 约束刚度值将改变各种非线性动力行为产生的参数域, 本文采用多尺度法进行直接摄动构造了一端竖向弹性约束浅拱在发生2:1内共振时的非线性模态。结果表明: 内共振非线性系统存在单模态运动和耦合模态运动; 弹性约束的存在及不同取值将导致不同的非对称线性模态、形函数及内共振激发条件; 不同约束刚度时非线性模态的时空效应呈现不同的动力形态。

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.

导出引用

曾有艺易壮鹏. 弹性约束浅拱的内共振非线性模态[J]. 振动与冲击, 2015, 34(23): 48-53

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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