分析具有接触非线性的系统的非线性法向模态的混合连续框架

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL
Shih-Chun Huang, Meng-Hsuan Tien
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引用次数: 0

摘要

对具有接触间隙和预应力的结构系统的模态特性进行预测是一项计算挑战,因为片断线性刚度引起的非线性使得高效线性模态分析技术无法使用。获取这些结构系统的非线性法向模态(NNMs)的最常用方法是一个数值框架,它集成了数值积分、射击法和伪弧长延续方案。这种数值延续框架(NCF)通过迭代数值计算来计算 NNMs;因此,复杂非线性系统(尤其是片断线性系统)非线性模态分析的计算成本会随着模型规模的增大而变得过于昂贵。本研究提出了一种结合分析和数值方法的混合延续框架 (HCF),以高效计算具有接触边界的系统的非线性模态。这一新的混合框架利用半解析方法来进行迭代拍摄程序,从而大大减轻了数值延续的计算负担。我们在带有接触元素的弹簧-质量振荡器上演示了所提出的方法,并用传统的数值延续框架计算得到的NNMs验证了所提出方法得到的NNMs。使用所提出的框架计算系统的模态特性速度明显加快。此外,还确定并讨论了片线性系统的模态特性,包括内部共振和 NNM 曲线的急转弯。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Hybrid Continuation Framework for Analyzing Nonlinear Normal Modes of Systems With Contact Nonlinearity
The prediction of the modal properties of structural systems with contact clearances and prestress presents a computational challenge, as the nonlinearity induced by piecewise-linear stiffness eliminates the use of efficient linear modal analysis techniques. The most common approach to obtaining the nonlinear normal modes (NNMs) of these structural systems is a numerical framework that integrates numerical integration, the shooting method, and the pseudo-arc-length continuation scheme. This numerical continuation framework (NCF) computes NNMs through iterative numerical calculations; thus, the computational cost of the nonlinear modal analysis of complex nonlinear systems, particularly piecewise-linear systems, becomes prohibitively expensive as the model size increases. In this study, a hybrid continuation framework (HCF) combining analytic and numerical methods is proposed to enable efficient computations of NNMs for systems with contact boundaries. This new hybrid framework utilizes a semi-analytic method to conduct the iterative shooting procedure; thus, the computational burden of the numerical continuation can be significantly reduced. The proposed method is demonstrated on spring-mass oscillators with contact elements, and the NNMs obtained using the proposed method are validated by those computed using the traditional numerical continuation framework. The modal properties of the systems can be computed using the proposed framework with significant speed-up. Furthermore, the modal properties, including internal resonance and sharp turning in NNM curves, of the piecewise-linear systems are identified and discussed.
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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.
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