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首页> 外文期刊>Journal of Applied Mechanics and Technical Physics >Accurate investigation of lateral vibrations of a quintic nonlinear beam on an elastic foundation: Using an exact formulation of the beam curvature
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Accurate investigation of lateral vibrations of a quintic nonlinear beam on an elastic foundation: Using an exact formulation of the beam curvature

机译：精确研究五阶非线性梁在弹性地基上的横向振动：使用梁曲率的精确公式

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摘要

This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode, which, in turn, yields the natural frequency of the system. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above-mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.
机译：本文获得了具有五次非线性的弹性基础上的梁振动的新公式，包括梁曲率的精确表达式。为了实现梁结构的正确设计，必须认识到梁如何以其横向模式振动，从而产生系统的固有频率。在这个方向上，采用了一种强大的分析方法，称为参数扩展方法，以获得频率-振幅关系的精确解。清楚地表明，级数展开的第一项足以产生上述系统的高度精确的近似值。最后，通过与数值计算的比较来评估本分析程序的准确性。

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