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Behavior of bifurcation and chaos in a forced oscillator(?)containing a square nonlinear term is investigated by using Mel’nikov method and digital computer simulations. 相似文献
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强非线性振动系统求解的两种解析方法 总被引:2,自引:0,他引:2
本文给出了拟保守系统的渐近解,该解是在非线性解的基础上的摄动解,因而可求解强非线性振动系统。文中利用此解研究了具有强非对称恢复力项的Liénard方程的极限环问题,给出了各种特殊情况下该方程的极限环幅值的计算公式,并讨论了非线性恢复力项对极限环的影响。此外,本文提出了一种改进的谐波平衡法,该方法是谐波平衡法与伽辽金方法结合的产物。 相似文献
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In this paper we extend Poincare’s nonlinear oscillation theory of discrete system tocontinuum mechanics.First we investigate the existence conditions of periodic solution forlinear continuum system in the states of resonance and non-resonance.By applying theresults of linear theory,we prove that the main conclusion of Poincare’s nonlinearoscillation theory can be extended to continuum mechanics.Besides,in this paper a newmethod is suggested to calculate the periodic solution in the states of both resonance andnonresonance by means of the direct perturbation of partial differential equation andweighted integration. 相似文献
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李骊 《应用数学和力学(英文版)》1982,3(4):541-547
In this paper, the differential system of second-order withvariable coefficients is studied. and some criteria of theboundedness and asymptotic behavior for solutions are given.Consider a system of differential equationsdx_1/dt=p_(11)(t)x_1 p_(12)(t)x_2dx_2/dt=p_(21)(t)x_1 p_(22)(t)x_2Now we studg the boundedness and asymptotic behavior of its so-lutions. In the case of Pij(t)being periodic functions. it wasinvestigated by Burdina; in the case of Pij(t) being arbitraryfunctions. it has not been investigated yet. Besides. the me-thod used by Burdina is only oppropriate for the former but notfor the latter case. In this paper we shall give a method whichis appropriate for both cases. 相似文献
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In this paper we give the relationship between Melnikov function and Poincare map, and a new proof for Melnikov's method. The advantage of our paper is to give a more explicit solution and to make Melnikov function for the subharmonics bifurcation and Melnikov function which the stable manifolds and unstable manifolds intersect transversely into a formula. 相似文献
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毛士忠(盐城师专): 读了你刊1982年第3卷第4期“二阶变系数微分方程组解的有界性与渐近性”一文后,感到其中有些地方值得商榷。具体意见如下: 1.文中开头提出的解的“有界性与渐近性” 从原文看似乎不够明确,不知指的是一切解的有界性、稳定性,还是零解的稳定性;指的是有限区间上的稳定性、还是按Lyapunov意义下的稳定性。因为对线性方程组来说“一切解在t≥t_0上的有界性等价于零解按Lyapunov意义下的稳定性”。但原文并未提及,因此不够明确。 相似文献