Computing Natural Frequencies and Mode Shapes of an Axially Moving Non-Uniform Beam

A. Sinha
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引用次数: 2

Abstract

The partial differential equation of motion of an axially moving beam with spatially varying geometric, mass and material properties has been derived. Using the theory of linear time-varying systems, a general algorithm has been developed to compute natural frequencies, mode shapes, and the critical speed for stability. Numerical results from the new method are presented for beams with spatially varying rectangular cross sections with sinusoidal variation in thickness and sine-squared variation in width. They are also compared to those from the Galerkin method. It has been found that critical speed of the beam can be significantly reduced by non-uniformity in a beam’s cross section.
计算轴向运动非均匀梁的固有频率和模态振型
导出了具有空间变化几何、质量和材料特性的轴向运动梁的运动偏微分方程。利用线性时变系统的理论,开发了一种计算固有频率、模态振型和稳定临界速度的通用算法。本文给出了矩形截面为厚度为正弦变化、宽度为正弦平方变化的空间变化梁的数值结果。还将它们与伽辽金方法的结果进行了比较。研究发现,光束截面的不均匀性可以显著降低光束的临界速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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