{"title":"随机扰动下粘弹性旋转悬臂梁的非线性动力分析","authors":"Xudong Gu , Shuai Li , Bingxin Zhao , Zichen Deng","doi":"10.1016/j.jsv.2025.119428","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":17233,"journal":{"name":"Journal of Sound and Vibration","volume":"619 ","pages":"Article 119428"},"PeriodicalIF":4.9000,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear dynamic analysis of a viscoelastic rotating cantilever beam under stochastic perturbation\",\"authors\":\"Xudong Gu , Shuai Li , Bingxin Zhao , Zichen Deng\",\"doi\":\"10.1016/j.jsv.2025.119428\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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.</div></div>\",\"PeriodicalId\":17233,\"journal\":{\"name\":\"Journal of Sound and Vibration\",\"volume\":\"619 \",\"pages\":\"Article 119428\"},\"PeriodicalIF\":4.9000,\"publicationDate\":\"2025-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Sound and Vibration\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022460X25005012\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Sound and Vibration","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022460X25005012","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ACOUSTICS","Score":null,"Total":0}
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.
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.