充液系统中液体晃动的全局分岔和混沌
Global Bifurcation and Chaos of Liquid Sloshing in Liquid-Filled System
DOI: 10.12677/OJAV.2018.62004, PDF,    国家自然科学基金支持
作者: 曹俊灵*：天津大学力学系，天津;天津市联大通讯发展有限公司，天津；钟 顺：天津市联大通讯发展有限公司，天津
关键词: 充液系统；同宿轨道；混沌阈值；Liquid-Filled System； Homoclinic Orbits； Chaotic Threshold
摘要: 本文以在各类工程中广泛应用的充液系统为研究对象，建立了柱形储液箱中液体晃动模态的非线性动力学方程组。通过积分，得到了该类系统的同宿轨道的解析表达式，并利用Melnikov方法对此系统的全局动力学行为进行分析，计算出系统在扰动条件下进入混沌的阈值，表明此类系统在受到较大扰动时，将发生全局分岔和混沌现象。同时，文中给出的算例证明了理论分析结果的正确性。
Abstract: The nonlinear governing equations of the liquid sloshing modals in cylindrical storage tank are established. Through integration, the analytical expressions of the homoclinic orbits of this kind of system are got. Using the Melnikov method, the global dynamical behaviors are analyzed. The threshold of the chaotic motion is calculated, which shows that there exists global bifurcation and chaos when the system is subjected to greater disturbance. Meanwhile, numerical simulations are also given, which confirm the analytical results.
文章引用：曹俊灵, 钟顺. 充液系统中液体晃动的全局分岔和混沌[J]. 声学与振动, 2018, 6(2): 29-35. https://doi.org/10.12677/OJAV.2018.62004

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