Alleviating vibrations along a harmonically driven nonuniform Euler–Bernoulli beam by imposing nodes

Melis Baltan-Brunet, Fionna Kopp, Philip D. Cha
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Abstract

A passive approach is developed to quench excess vibration along a harmonically driven, arbitrarily supported, nonuniform Euler–Bernoulli beam with constant thickness (height) and varying width. Vibration suppression is achieved by attaching properly tuned vibration absorbers to enforce nodes, or points of zero vibration, along the beam. An efficient hybrid method is proposed whereby the finite element method is used to model the nonuniform beams, and a formulation based on the assumed modes method is used to determine the required attachment force supplied by each absorber to induce the desired nodes. Knowing the attachment forces needed to induce nodes, design plots are generated for the absorber parameters as a function of the tolerable vibration amplitude for each absorber mass. When the node locations are judiciously chosen, it is possible to dramatically suppress the vibration along a selected region of the beam. As such, sensitive instruments can be placed in this region and will remain nearly stationary. Numerical studies illustrate the application to several systems with various types of nonuniformity, boundary conditions, and attachment and node locations; these examples validate the proposed method to passively control excess vibration by inducing nodes on nonuniform beams subjected to harmonic excitations.
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通过施加节点缓解谐波驱动非均匀欧拉-伯努利梁的振动
本研究开发了一种被动方法,用于抑制具有恒定厚度(高度)和变化宽度的谐波驱动、任意支撑、非均匀欧拉-伯努利梁的过量振动。通过在梁的强制节点或零振动点上安装适当调谐的振动吸收器来实现振动抑制。本文提出了一种高效的混合方法,即使用有限元法对不均匀梁进行建模,并使用基于假定模态法的公式来确定每个吸振器为诱导所需的节点而提供的所需附着力。了解了诱导节点所需的附着力后,就可以生成吸收器参数与每个吸收器质量的可容忍振动振幅的函数关系设计图。如果节点位置选择得当,就有可能显著抑制横梁选定区域的振动。因此,敏感仪器可以放置在该区域,并几乎保持静止。数值研究说明了几种具有不同类型不均匀性、边界条件、附件和节点位置的系统的应用情况;这些例子验证了所提出的通过在受谐波激励的不均匀梁上诱导节点来被动控制多余振动的方法。
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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