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首页> 外文期刊>International journal of non-linear mechanics >Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation
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Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation

机译：非线性弹性基础引导的轴向加速弦的参数振动和稳定性

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摘要

Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation are studied analytically. The axial speed, as the source of parametric vibrations, is assumed to involve a mean speed, along with small harmonic variations. The method of multiple scales is applied to the governing non-linear equation of motion and then the natural frequencies and mode shape equations of the system are derived using the equation of order one, and satisfying the compatibility conditions. Using the equation of order epsilon, the solvability conditions are obtained for three distinct cases of axial acceleration frequency. For all cases, the stability areas of system are constructed analytically. Finally, some numerical simulations are presented to highlight the effects of system parameters on vibration, natural frequencies, frequency-response curves, stability, and bifurcation points of the system.
机译：对非线性弹性基础引导的轴向加速弦的参数振动和稳定性进行了分析研究。假定作为参数振动源的轴向速度包括平均速度以及小的谐波变化。将多尺度方法应用于控制非线性运动方程，然后使用一阶方程并满足相容条件，推导系统的固有频率和模态形状方程。使用阶ε方程，可以得出三种不同情况下轴向加速度频率的可解条件。在所有情况下，系统的稳定性区域都是通过分析构造的。最后，通过一些数值模拟来突出系统参数对振动，固有频率，频率响应曲线，稳定性和系统的分叉点的影响。

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