随机扰动下粘弹性旋转悬臂梁的非线性动力分析

IF 4.9 2区 工程技术 Q1 ACOUSTICS
Xudong Gu , Shuai Li , Bingxin Zhao , Zichen Deng
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引用次数: 0

摘要

旋转梁的动态特性对具有旋转部件的设备的性能有很大的影响,如航天器的柔性线、汽轮机和直升机的旋翼。非线性变形与粘弹性材料的耦合将导致包含积分的非线性粘弹性项,这在以往的研究中被忽视。与传统研究不同,本文研究了随机激励下旋转粘弹性悬臂梁的非线性动力学问题。通过对建模过程中的非线性变形、旋转效应和粘弹性本构进行积分,建立了新的非线性动力学方程,并采用假设模态法将其转化为粘弹性项积分的非线性随机微分方程。采用数值模拟和随机线性化方法对旋转悬臂梁的多模态响应进行了分析,结果表明,主模态振动主导了旋转悬臂梁的动力响应。因此,提出了一种基于随机平均法的理论方法来推导主模态的近似响应。由非线性变形和粘弹性耦合产生的非线性粘弹性项转化为振幅相关修正阻尼和保守力的组合。通过求解Fokker-Planck-Kolmogorov (FPK)方程得到解析响应。最后,综合分析了激励强度、阻尼比、旋转角速度和粘弹性参数对系统响应的影响。理论预测与数值模拟的高度一致性验证了所提分析方法的有效性,有助于深入理解粘弹性旋转梁的动力特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonlinear dynamic analysis of a viscoelastic rotating cantilever beam under stochastic perturbation
The dynamic characteristics of rotating beams significantly affect the performance of equipment with rotating components, such as flexible wires of spacecrafts, steam turbines and helicopter rotors. The coupling of nonlinear deformation and viscoelastic materials will lead to integral-containing nonlinear viscoelastic terms, which have been overlooked in previous studies. Departing from conventional studies, this paper investigated the nonlinear dynamics of a rotating viscoelastic cantilever beam under stochastic excitation. A new nonlinear dynamic equation is established by integrating nonlinear deformation, rotation effect, and viscoelastic constitution in the modeling process, which is transformed into a set of nonlinear stochastic differential equations with integral viscoelastic terms using the assumed mode method. Numerical simulations and stochastic linearization method are used to analyze the multimodal response of the rotating cantilever beam, in which the results showed that the primary mode vibration dominates the dynamic response. Thus, a theoretical method based on stochastic averaging method is proposed to derive the approximate responses of the primary mode. The nonlinear viscoelastic terms resulting from the coupling of nonlinear deformation and viscoelasticity are converted into a combination of the amplitude-dependent modified damping and conservative forces. Analytical responses are obtained by solving the Fokker-Planck-Kolmogorov (FPK) equation. Finally, the impacts of excitation intensity, damping ratio, rotational angular velocity and viscoelastic parameters on the system response are comprehensively analyzed. The high consistency between the theoretical predictions and numerical simulations validates the effectiveness of the proposed analytical method, which facilitates a deeper understanding the dynamic behavior of viscoelastic rotating beams.
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来源期刊
Journal of Sound and Vibration
Journal of Sound and Vibration 工程技术-工程:机械
CiteScore
9.10
自引率
10.60%
发文量
551
审稿时长
69 days
期刊介绍: The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application. JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.
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