Semi-Implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics With Hysteresis

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL Journal of Computational and Nonlinear Dynamics Pub Date : 2023-03-20 DOI:10.1115/1.4057042
Bidhayak Goswami, Anindya Chatterjee
{"title":"Semi-Implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics With Hysteresis","authors":"Bidhayak Goswami, Anindya Chatterjee","doi":"10.1115/1.4057042","DOIUrl":null,"url":null,"abstract":"Abstract Structural damping is often empirically rate-independent wherein the dissipative part of the stress depends on the history of deformation but not its rate of change. Hysteresis models are popular for rate-independent dissipation; and a popular hysteresis model is the Bouc-Wen model. If such hysteretic dissipation is incorporated in a refined finite element model, then the model involves the usual structural dynamics equations along with nonlinear nonsmooth ordinary differential equations for a large number of internal hysteretic states at Gauss points used within the virtual work calculation. For such systems, numerical integration is difficult due to both the distributed nonanalytic nonlinearity of hysteresis as well as large natural frequencies in the finite element model. Here, we offer two contributions. First, we present a simple semi-implicit integration approach where the structural part is handled implicitly based on the work of Piché, while the hysteretic part is handled explicitly. A cantilever beam example is solved in detail using high mesh refinement. Convergence is good for lower damping and a smoother hysteresis loop. For a less smooth hysteresis loop and/or higher damping, convergence is noted to be roughly linear on average. Encouragingly, the time-step needed for stability is much larger than the time period of the highest natural frequency of the structural model. Subsequently, data from several simulations conducted using the above semi-implicit method are used to construct reduced order models of the system, where the structural dynamics is projected onto a few modes and the number of hysteretic states is reduced significantly as well. Convergence studies of error against the number of retained hysteretic states show very good results.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"439 1","pages":"0"},"PeriodicalIF":1.9000,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4057042","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract Structural damping is often empirically rate-independent wherein the dissipative part of the stress depends on the history of deformation but not its rate of change. Hysteresis models are popular for rate-independent dissipation; and a popular hysteresis model is the Bouc-Wen model. If such hysteretic dissipation is incorporated in a refined finite element model, then the model involves the usual structural dynamics equations along with nonlinear nonsmooth ordinary differential equations for a large number of internal hysteretic states at Gauss points used within the virtual work calculation. For such systems, numerical integration is difficult due to both the distributed nonanalytic nonlinearity of hysteresis as well as large natural frequencies in the finite element model. Here, we offer two contributions. First, we present a simple semi-implicit integration approach where the structural part is handled implicitly based on the work of Piché, while the hysteretic part is handled explicitly. A cantilever beam example is solved in detail using high mesh refinement. Convergence is good for lower damping and a smoother hysteresis loop. For a less smooth hysteresis loop and/or higher damping, convergence is noted to be roughly linear on average. Encouragingly, the time-step needed for stability is much larger than the time period of the highest natural frequency of the structural model. Subsequently, data from several simulations conducted using the above semi-implicit method are used to construct reduced order models of the system, where the structural dynamics is projected onto a few modes and the number of hysteretic states is reduced significantly as well. Convergence studies of error against the number of retained hysteretic states show very good results.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
结构动力学中的半隐式积分与数据驱动模型降阶
结构阻尼通常是经验速率无关的,其中应力的耗散部分取决于变形的历史,而不是其变化率。迟滞模型是与速率无关的耗散的常用模型;一个流行的迟滞模型是Bouc-Wen模型。如果将这种滞回耗散纳入一个精细的有限元模型中,则该模型包含了通常的结构动力学方程以及用于虚功计算的高斯点处大量内部滞回状态的非线性非光滑常微分方程。对于这类系统,由于其迟滞分布的非解析非线性和有限元模型中较大的固有频率,使得数值积分变得困难。在这里,我们提供两个贡献。首先,我们提出了一种简单的半隐式集成方法,其中结构部分基于pich的工作被隐式处理,而滞后部分被显式处理。采用高网格细化方法对悬臂梁实例进行了详细求解。收敛有利于较低的阻尼和较平滑的滞回线。对于不太光滑的迟滞回路和/或较高的阻尼,收敛性平均大致为线性。令人鼓舞的是,稳定所需的时间步长远大于结构模型最高固有频率的时间周期。随后,利用上述半隐式方法进行的多次仿真数据构建了系统的降阶模型,其中结构动力学被投影到几个模态上,并且显著减少了滞后状态的数量。对误差对保留滞回态数目的收敛性研究显示出很好的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
期刊最新文献
Energy Transfer and Dissipation in Combined-Stiffness Nonlinear Energy Sink Systems Synchronization of a Class of Nonlinear Systems With and Without Uncertainty Using State Feedback and Extended Kalman Filter Based Control Scheme Optimal Control of Mechanical Systems Based On Path-Fitted Variational Integrators Motor Bearing Fault Diagnosis in an Industrial Robot Under Complex Variable Speed Conditions A Computational Conformal Geometry Approach to Calculate the Large Deformations of Plates/shells with Arbitrary Shapes
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1