随机激励下亚音速二维粘弹性壁板的全局动力学

doi:10.3901/JME.2023.23.105

机械工程学报 ›› 2023, Vol. 59 ›› Issue (23): 105-117.doi: 10.3901/JME.2023.23.105

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随机激励下亚音速二维粘弹性壁板的全局动力学

岳晓乐^1,2, 张慧康^1,2, 余钡^1,2, 张莹^1,2

1. 西北工业大学数学与统计学院西安 710129;
2. 西北工业大学空天领域复杂性科学教育部重点实验室西安 710129

收稿日期:2022-10-08 修回日期:2023-08-01 发布日期:2024-02-20
通讯作者: 张莹(通信作者)，女，1981年出生，博士，教授，博士研究生导师。主要研究方向为非线性随机动力学。E-mail：yingzhang@nwpu.edu.cn
作者简介:岳晓乐，男，1985年出生，博士，教授，博士研究生导师。主要研究方向为随机动力学全局分析。E-mail：xiaoleyue@nwpu.edu.cn
基金资助:
国家自然科学基金(12172284，12172286)和中央高校基本科研业务费专项资金资助项目。

Global Dynamics of Two-dimensional Viscoelastic Panels under Random Excitations in Subsonic Airflow

YUE Xiaole^1,2, ZHANG Huikang^1,2, YU Bei^1,2, ZHANG Ying^1,2

1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129;
2. MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi'an 710129

Received:2022-10-08 Revised:2023-08-01 Published:2024-02-20

摘要/Abstract

摘要： 飞行器或列车由于服役环境复杂，壁板结构往往受到多种激励作用，影响其正常使用与安全。为此，针对亚音速气流下粘弹性壁板在外激力、气动力和随机噪声联合作用下的全局动力学特性展开研究。通过全局分岔图，观测到了激变、逆倍周期分岔等一系列复杂的动力学行为，借助胞映射方法，获得了系统的吸引子、吸引域、鞍等全局信息，得到了系统响应演化过程中的瞬态与稳态概率密度函数。讨论了激励幅值和频率对壁板稳态响应的影响，发现确定性系统随着粘弹性参数和激励幅值的变化会呈现复杂的全局结构，揭示了激变现象的发生机制。随机激励下无论是瞬态还是稳态情形，系统随机响应的演化过程始终与确定性全局结构中的不稳定流形形状保持一致，激励幅值和频率的增加会导致稳态响应概率函数峰值的减小。研究结果对于壁板安全防护设计具有理论指导意义。

关键词: 粘弹性壁板, 胞映射方法, 全局动力学, 随机响应

Abstract: The service environment of the panel structure is complex, and it is often affected by a variety of excitations, affecting its normal use and safety. The viscoelastic panel system in subsonic airflow is taken as the research object, and its global dynamic characteristics under the combined action of external force, aerodynamic force and random noise is studied. Through the global bifurcation diagram, a series of complex dynamical behaviors such as crisis, inverse doubling bifurcation, etc., are observed in the system. The global properties such as the attractors, saddles and basins of attraction are obtained and the transient and steady-state probability density functions of the system response evolution process are solved by using the cell mapping method. The influence of excitation amplitude and frequency on the steady-state response of the panel is further discussed. It is found that the system in a determined situation presents complex global structures with the change of the excitation amplitude and viscoelastic parameters which further explains the mechanism of the crisis phenomenon. Whether transient or steady-state, the evolution direction of the stochastic response is always consistent with the unstable manifold shape of the deterministic system. Further, in the steady-state response of the structural system, the increase in the amplitude and frequency of the external excitation will lead to a decrease in the peak of the response probability density function. The research results have theoretical significance for the design of panel safety protection.

Key words: viscoelastic panel, cell mapping method, global dynamics, stochastic response

中图分类号:

O324

岳晓乐, 张慧康, 余钡, 张莹. 随机激励下亚音速二维粘弹性壁板的全局动力学[J]. 机械工程学报, 2023, 59(23): 105-117.

YUE Xiaole, ZHANG Huikang, YU Bei, ZHANG Ying. Global Dynamics of Two-dimensional Viscoelastic Panels under Random Excitations in Subsonic Airflow[J]. Journal of Mechanical Engineering, 2023, 59(23): 105-117.

参考文献

[1] DOWELL E H，VOSS H M. Theoretical and experimental panel flutter studies in the Mach number range 1.0 to 5.0[J]. AIAA Journal，1965，3(12):2292-2304.
[2] IBRAHIM R A，ORONO P O. Stochastic non-linear flutter of a panel subjected to random in-plane forces[J]. International Journal of Non-linear Mechanics，1991，26(6):867-883.
[3] VAICAITIS R，DOWELL E H，VENTRES C S. Nonlinear panel response by a Monte Carlo approach[J]. AIAA Journal，1974，12(5):685-691.
[4] LI Peng，YANG Yiren，XU Wei，et al. Stochastic analysis of a nonlinear forced panel in subsonic flow with random pressure fluctuations[J]. Journal of Applied Mechanics，2013，80(4):041005.
[5] PARANDVAR H，FARID M. Nonlinear reduced order modeling of functionally graded plates subjected to random load in thermal environment[J]. Composite Structures，2015，126:174-183.
[6] FAZELZADEH S A，POURTAKDOUST S H，ASSADIAN N. Stochastic analysis of two dimensional nonlinear panels with structural damping under random excitation[J]. Aerospace Science and Technology，2006，10(3):192-198.
[7] GUO Xinyun，LEE Y Y，MEI C. Non-linear random response of laminated composite shallow shells using finite element modal method[J]. International Journal for Numerical Methods in Engineering，2006，67(10):1467-1489.
[8] ZHOU Kai，LIN Zhenkun，HUANG Xiuchang，et al. Vibration and sound radiation analysis of temperature-dependent porous functionally graded material plates with general boundary conditions[J]. Applied Acoustics，2019，154:236-250.
[9] KUPFERMAN R，PAVLIOTIS G A，STUART A M. Itô versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise[J]. Physical Review E，2004，70(3):036120.
[10] 杨智春，刘丽媛，王晓晨. 高超声速飞行器受热壁板的气动弹性声振分析[J]. 航空学报，2016，37(12):3578-3587. YANG Zhichun，LIU Liyuan，WANG Xiaochen. Analysis of aeroelastic vibro-acoustic response foe heated panel of hypersonic vehicle[J]. Acta Aeronautica et Astronautica Sinica，2016，37(12):3578-3587.
[11] BARZYKIN A V，SEKI K，SHIBATA F. Periodically driven linear system with multiplicative colored noise[J]. Physical Review E，1998，57(6):6555.
[12] MAJEE P，GOSWAMI G，BAG B C. Colored non-Gaussian noise induced resonant activation[J]. Chemical Physics Letters，2005，416(4-6):256-260.
[13] SHI Tingting，XU Xuemei，SUN Kehui，et al. Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback[J]. Chinese Physics B，2020，29(5):050501.
[14] HUANG Yong，LIU Xianbin. Stochastic stability of viscoelastic system under non-Gaussian colored noise excitation[J]. Science China Physics，Mechanics and Astronomy，2012，55(3):483-492.
[15] FUENTES M A，WIO H S，TORAL R. Effective Markovian approximation for non-Gaussian noises: a path integral approach[J]. Physica A: Statistical Mechanics and its Applications，2002，303(1-2):91-104.
[16] BOUZAT S，WIO H S. New aspects on current enhancement in Brownian motors driven by non-Gaussian noises[J]. Physica A: Statistical Mechanics and its Applications，2005，351(1):69-78.
[17] 肖艳平，杨翊仁，叶献辉. 边界松驰对壁板颤振响应的影响分析[J]. 工程力学，2012，29(11):40-45. XIAO Yanping，YANG Yiren，YE Xianhui. Flutter analysis of panel with boundary conditions relaxation[J]. Engineering Mechanic，2012，29(11):40-45.
[18] 张云峰，刘占生. 粘弹壁板颤振的非线性动力特性[J]. 推进技术，2007，28(1):103-107. ZHANG Yunfeng，LIU Zhansheng. Nonlinear dynamic analysis of viscoelastic panel flutter[J]. Journal of Propulsion Technology，2007，28(1):103-107.
[19] TANG Huaiping，LI Peng，YANG Yiren. Chaos suppression of a subsonic panel with geometric nonlinearity based on Melnikov’s method[J]. International Journal of Dynamics and Control，2014，2(3):395-403.
[20] 李鹏，杨翊仁，鲁丽. 外激励作用下亚音速二维壁板的复杂响应研究[J]. 计算力学学报，2011，28(6):864-871. LI Peng，YANG Yiren，LU Li. Complicated response analysis of two-dimensional thin panel in subsonic flow with external excitation[J]. Chinese Journal of Computation Mechanics，2011，28(6):864-871.
[21] YOUNESIAN D，NOROUZI H. Chaos prediction in nonlinear viscoelastic plates subjected to subsonic flow and external load using extended Melnikov's method[J]. Nonlinear Dynamics，2016，84(3):1163-1179.
[22] BOLOTIN V V，GRISHKO A A，KOUNADIS A N，et al. Non-linear panel flutter in remote post-critical domains[J]. International Journal of Non-Linear Mechanics，1998，33(5):753-764.
[23] 刘少文，李鹏，杨翊仁. 亚音速气流中曲壁板的分岔研究[J]. 四川理工学院学报，2016，29(5):57-62. LIU Shaowen，LI Peng，YANG Yiren. Bifurcation analysis of curved plate in subsonic flow[J]. Journal of Sichuan University Science and Engineering，2016，29(5):57-62.
[24] HSU C S. A theory of cell-to-cell mapping dynamical systems[J]. Journal of Applied Mechanics，1980，47(4):931-939.
[25] 贺群，徐伟，李爽，等. 图胞映射的一种改进方法[J]. 物理学报，2008，57(2):743-748. HE Qun，XU Wei，LI Shuang，et al. A modified diagraph cell mapping method[J]. Acta Physica Sinica，2008，57(2):743-748.
[26] 洪灵，徐健学. 一类新的边界激变现象:混沌的边界激变[J]. 物理学报，2001，50(4):612-618. HONG Ling，XU Jianxue. A method of point mapping under cell reference for global analysis of nonlinear dynamical systems[J]. Acta Physica Sinica，2001，50(4):612-618.
[27] JIANG Jun，XU Jianxue. A new type of boundary crises:chaotic boundary crisis[J]. Physics Letters A，1994，188(2):137-145.
[28] YUE Xiaole，XU Wei，ZHANG Ying. Global bifurcation analysis of Rayleigh–Duffing oscillator through the composite cell coordinate system method[J]. Nonlinear Dynamics，2012，69(1-2):437-457.
[29] YUE Xiaole，XIANG Yilin，ZHANG Ying，et al. Global analysis of stochastic bifurcation in shape memory alloy supporter with the extended composite cell coordinate system method[J]. Chaos，2021，31(1):013133.
[30] SUN J Q，HSU C S. The generalized cell mapping method in nonlinear random vibration based upon short-time Gaussian approximation[J]. Journal of Applied Mechanics，1990，57(4):1018-1025.
[31] YUE Xiaole，YU Bei，LI Yongge，et al. Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise[J]. Chaos，Solitons and Fractals，2022，155:111744.
[32] BAURA A，SEN M K，GOSWAMI G，et al. Colored non-Gaussian noise driven open systems: Generalization of Kramers’ theory with a unified approach[J]. The Journal of Chemical Physics，2011，134(4): 044126.

随机激励下亚音速二维粘弹性壁板的全局动力学

Global Dynamics of Two-dimensional Viscoelastic Panels under Random Excitations in Subsonic Airflow

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