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IJMSD | 美国哈维穆德学院Philip D. Cha教授团队：设置多节点以抑制简谐激励下非均匀欧拉-伯努利梁振动

已有 1443 次阅读 2024-3-7 09:51 |个人分类:IJMSD|系统分类:论文交流

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动力吸振器已被广泛应用于结构振动的被动控制。相较于主动控制对能源、反馈控制设计和稳定性分析的依赖，动力吸振器因其简便性而受到青睐。节点指稳态响应位移为零的点。有学者提出将节点作为振动抑制的一种手段，并研究了此类节点诱导被动动力吸振器的计算整定和灵敏度分析，却鲜有讨论将节点诱导法应用于非均匀欧拉-伯努利梁的振动抑制。

鉴此，哈维穆德学院Philip D. Cha教授团队在前期研究的基础上，将均匀梁多节点振动抑制研究工作扩展到非均匀欧拉-伯努利梁，提出了一种基于有限元法(finite element method, FEM)和假设模态法(assumed modes method, AMM)的混合计算方法，使用调谐动力吸振器诱导多节点来实现受简谐激励、任意边界条件、非均匀欧拉-伯努利梁（梁厚度为定值而宽度变化）的振动抑制。其中，FEM用于对非均匀梁进行建模，AMM用于计算动力吸振器所需的附加力，而附加力则被用于后续动力吸振器调谐参数的计算。研究成果以"Alleviating vibrations along a harmonically driven nonuniform Euler–Bernoulli beam by imposing nodes"为题发表于《国际机械系统动力学学报(英文)》(International Journal of Mechanical System Dynamics, IJMSD)。该文通过对不同非均匀性、边界条件以及附着位置和节点位置的多个系统进行数值仿真计算，验证了该文方法减振的有效性。结果表明，该方法降低了分析复杂度，缩短了确定动力吸振器调谐参数的计算时间。此外，一旦在梁上产生了接近零位移的区域，就可以将额外的集总元件附加到该区域中，且它们将几乎保持静止。这一简便经济的方法对在非均匀梁上布置传感器具有指导意义。

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.

Keywords: vibration suppression, nonuniform beam, vibration absorber, finite element, enforcing nodes

DOI: 10.1002/msd2.12090

To Share: https://onlinelibrary.wiley.com/doi/10.1002/msd2.12090（点击链接直达原文）

To Cite: Baltan-Brunet M, Kopp F, Cha PD. Alleviating vibrations along a harmonically driven nonuniform Euler–Bernoulli beam by imposing nodes. Int J Mech Syst Dyn. 2023; 3(4): 345-359. doi:10.1002/msd2.12090

该文亮点

1.将现有通过诱导节点进行振动被动抑制的技术扩展到受简谐激励、任意边界条件的非均匀欧拉-伯努利梁上。

2.提出了一种运用有限元梁模型并使用假设模态法的高效混合计算方法，求解了动力吸振器诱导节点所需的附加力。

3.通过对多个系统的数值仿真计算验证了所提出减振方法的有效性。

Highlights

1. Existing techniques to suppress vibrations by inducing nodes are expanded to apply to harmonically forced, arbitrarily supported, nonuniform Euler–Bernoulli beams.

2. An efficient hybrid method is proposed to leverage a finite element beam model along with an equation derived using assumed mode method to solve for the needed restoring forces of vibration absorbers to induce nodes.

3. Numerical studies validate the approach in several systems.

作者简介

Melis Baltan-Brunet received her B.S. in Engineering from Harvey Mudd College, Claremont, CA, USA in 2023. She is currently a staff member at MIT Lincoln Laboratory in Lexington, Massachusetts, USA. Her current interests include hardware in the loop system analysis and testing.

Fionna Kopp received a B.S. degree in Engineering from Harvey Mudd College, Claremont, CA, USA in 2022. She is currently a Ph.D. student in Mechanical Engineering at the University of California Berkeley, Berkeley, CA, USA. Her current research interests include model predictive control and iterative learning control.

Philip D. Cha received his B.S. in Mechanical Engineering from Cornell University, and his M.S. and Ph.D. in Mechanical Engineering from the University of Michigan. His research interests include mechanical vibration, structural dynamics, vibration of combined systems, and vibration suppression using vibration absorbers.

期刊简介

IJMSD由来自18个国家的21位院士、17位国际学会主席、20位国际期刊主编等69位科学家和国际出版巨头美国Wiley出版社合作创办。主编为国际机械系统动力学学会(International Society of Mechanical System Dynamics, ISMSD)主席、中国科学院院士、南京理工大学芮筱亭院士，3位合作主编为加拿大工程院院士、欧洲科学院院士、加拿大麦吉尔大学Marco Amabili 院士，国际理论与应用力学联盟(International Union of Theoretical and Applied Mechanics, IUTAM)前司库、国际多体系统动力学协会(International Association for Multibody System Dynamics, IMSD)前主席、德国斯图加特大学Peter Eberhard 教授和美国工程院及科学院院士、欧洲科学院外籍院士、英国皇家学会外籍院士、中国科学院外籍院士、美国工程科学协会前主席、美国西北大学Yonggang Huang 院士。

IJMSD旨在用机械系统动力学科学与技术为现代装备设计、制造、试验、评估和使用全生命周期性能的提升提供先进的理论、软件、方法、器件、标准，为全球科学家和工程专家提供广泛的机械系统动力学国际交流平台。IJMSD强调从“系统”视角及系统级工具理解动力学，所涉及的机械系统不仅包括各种不同尺度的机械系统和结构，还包括具有多物理场/多学科特征的综合机械系统。

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