Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

Pan Bo; Tang Jingda; Tarumi Ryuichi; Shang Fulin; Wang Yanbo; Zhang Weijun; Zhang Xueyan

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Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

机译：三弦弦非线性自由振动的理论分析

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Here we present a theoretical analysis on the nonlinear free vibration of a tri-cross string system, which is an element of space net-antennas. We derived the governing equations from Hamilton's principle and obtained a linearized solution by the standard perturbation method. The semi-analytical solutions of the governing equations have not been provided referring to the solution of plate vibrating problem. This analysis revealed that natural frequencies of the tri-cross string depend on the vibration amplitude due to the geometrical nonlinearity in the constitutive equation. The geometric parameters, such as the diameters and the lengths of the constituent strings, also affect the frequency through the nonlinearity of the tri-cross string. The nonlinear natural frequency shows coupled characteristic; that is, the natural frequency of the tri-cross string varies with that of the constituent strings, but the contribution of each constituent string to the natural frequency is in different proportions.

机译：在这里，我们对三叉弦系统的非线性自由振动进行理论分析，三叉弦系统是空间网状天线的一个组成部分。我们从汉密尔顿原理推导了控制方程，并通过标准摄动法获得了线性化解。参考板振动问题的解决方案，尚未提供控制方程的半解析解。该分析表明，由于本构方程中的几何非线性，三叉弦的固有频率取决于振动幅度。几何参数，例如组成弦的直径和长度，也通过三叉弦的非线性影响频率。非线性固有频率表现出耦合特性。即，三叉弦的固有频率与构成弦的固有频率不同，但各构成弦对固有频率的贡献比例不同。

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来源
《Shock and vibration》 |2017年第7期|3935686.1-3935686.17|共17页
作者
Pan Bo; Tang Jingda; Tarumi Ryuichi; Shang Fulin; Wang Yanbo; Zhang Weijun; Zhang Xueyan;
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作者单位

XianThermal Power Res Inst Co Ltd Xian 710032 Shaanxi Peoples R China;

Xi An Jiao Tong Univ Dept Engn Mech State Key Lab Strength & Vibrat Mech Struct Xian 710049 Shaanxi Peoples R China;

Osaka Univ Dept Mech Engn Suita Osaka 5650871 Japan;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
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Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

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