【摘要】 采用Melnikov方法研究两端固定输流管道系统在基础简谐运动激励下发生混沌运动时系统参数需满足的解析条件,通过计算衡量受扰系统鞍点稳定流形和不稳定流形之间距离的Melnikov函数,确定基础激励振幅和平均流速与激励频率间的临界值关系,并与系统混沌运动的数值仿真进行对比分析。结果表明,Melnikov方法所确定的混沌运动临界参数值略小于数值仿真方法所观察的出现混沌运动时对应的临界参数值,使用该方法可有效预测系统混沌运动的发生,从而为工程应用提供理论依据。更多还原

【Abstract】 When a fluid conveying pipe fixed at two ends is excited by harmonic motion of the base and its chaotic motion occurs,the analytic conditions that its parameters should satisfy are studied by using Melnikov method.The critical relations between the base excitation amplitude or the mean fluid flow-rate and the base excitation frequency are obtained by solving Melnikov functions for the distance between stable and unstable manifolds of saddle points of the perturbed system.Based on comparison between the results from theoretic analysis and numerical simulation,it could be concluded that the critical values of the parameter determined by Milnikov method are a little bit smaller than those corresponding to the chaotic motion observed firstly in numerical simulation.The method proposed here can effectively predict the chaotic motion of the piping system and it provides a theoretical foundation for engineering application.更多还原