依据哈密顿原理获得了三交叉弦结构非线性自由振动的运动方程，并应用摄动法推导了自振频率下的一阶摄动解。相较于传统的单根弦线非线性振动运动方程多采用单三角级数，三交叉弦结构首次采用三重三角级数解法并成功获取一阶摄动解。通过分析表明，非线性自振频率的解析解除了具有典型的非线性特性，还体现了各个子结构参数变化对整体结构自振频率的影响，即存在子结构间的耦合特性。结果表明，整个结构与局部子结构在子结构自身因参数发生改变时，变化幅度之间不是线性关系，且整体结构小于子结构自身因参数改变的变化幅度。
Abstract
Abstract:Theoretical analysis on the nonlinear free vibration of a tri-cross string system was presented in this work, which is an element of space net-antennas.The governing equations were derived from the Hamilton’s principle and a linearized solution was obtained by the standard perturbation method.The semi-analytical solutions of the governing equations has not been provided referring to the solution of the plate vibrating problem.This analysis reveals that natural frequencies of the tri-cross string depend on the vibration amplitude due to 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, i.e. 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.
关键词
三交叉弦 /
非线性 /
解析解 /
摄动方法
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Key words
tri-cross string /
nonlinearity /
perturbation method /
coupling effect
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