Random vibration of the point-driven portal and multi-bay planar frames

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-01-01 DOI:10.1016/j.probengmech.2024.103588
Richard Bachoo , Isaac Elishakoff
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Abstract

In this study, an analytical model is presented to determine the random response of point-driven portal and multi-bay planar frame structures. Coupling effects between bending and longitudinal deformations are taken into account, with the Timoshenko-Ehrenfest beam theory being applied to model the bending deformations. With the excitation taken as band-limited white noise, expressions are derived for the mean square displacements and velocities in terms of the autocorrelation and cross-correlation components. The influence of modal cross-correlations on the overall response is shown to be dependent on the number of bays. For a lightly damped single-bay frame, the natural frequencies are generally well separated and the modal cross-correlations are small. In this situation, the velocity response displays a near symmetric distribution about the center point of the frame. Moreover, narrow zones of intensified response begin emerging as the number of responding modes increases. For frames having two or more bays, the contribution of modal cross-correlations is larger due to the increased occurrence of clusters of natural frequencies. In such cases, modal cross-correlations introduce asymmetry into the overall response distribution of the frame. Additionally, the drive-point velocity of the multi-bay frame can be severely underestimated if modal cross-correlations are ignored. The study also investigates the influence of increased damping on the response characteristics.

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点驱动门式和多榀平面框架的随机振动
本研究提出了一个分析模型,用于确定点驱动门式结构和多榀平面框架结构的随机响应。该模型考虑了弯曲变形和纵向变形之间的耦合效应,并采用 Timoshenko-Ehrenfest 梁理论对弯曲变形进行建模。将激励作为带限白噪声,得出了自相关和交叉相关分量的均方位移和速度表达式。模态交叉相关对整体响应的影响与舱室数量有关。对于轻阻尼单梁框架,自然频率通常分离得很好,模态交叉相关也很小。在这种情况下,速度响应近似于围绕框架中心点的对称分布。此外,随着响应模态数量的增加,开始出现响应增强的狭窄区域。对于有两个或两个以上托架的框架,由于固有频率群的出现增加,模态交叉相关性的贡献更大。在这种情况下,模态交叉相关会给框架的整体响应分布带来不对称。此外,如果忽略模态交叉相关性,多榀框架的驱动点速度会被严重低估。研究还探讨了增加阻尼对响应特性的影响。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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