强非线性振动系统求解的两种解析方法

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。     

THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENTS

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.     

CHAOTIC BEHAVIOR OF A NONLINEAR OSCILLATOR

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.     

求解完全强非线性自治系统周期解及其稳定性的三变量迭代法

本文提出用广义位移x,基波幅值变化率da/dt=A(a)和系统频率ω(a)进行迭代的一种解析方法——三变量迭代法,求解一般的二阶完全强非线性自治系统的周期解及其稳定性。通过若干实例计算,表明了该方法行之有效。     

EXTENSION OF POINCARE’S NONLINEAR OSCILLATION THEORY TO CONTINUUM MECHANICS(I)—BASIC THEORY AND METHOD

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.     

双质量非线性共振筛的一种分析方法与实验研究

本文应用非线性振动理论,对振动输送的带料计算提出一种直接的理论分析方法。以双质量非线性共振筛为例,计算了带料时的共振曲线,讨论了物料的质量和冲击力对槽体振动的影响。     

具有间隙的动力系统的极限环

本文研究了系统ｘ＋ｆ（ｘ）＋ｇ（ｘ）＝０的极限环的存在性，其中ｇ（ｘ）有两个间断点并且不满足ｇ（ｘ）·ｘ＞０（ｘ≠０）．还引进［２，３］中定义的Филиппов解的概念，利用Филиппов解的整体存在性和普遍唯一性定理解决方程的解的存在唯一性问题，得到了几个极限环存在性定理     

Jacobi因子在稳定性理论中的应用

本文利用Jacobi因子的性质,得出一些有关定常系统、非定常系统以及极限环的不稳定定理。     

MELNIKOV FUNCTION AND POINCAR(?) MAP

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.     

强非线性系统的频闪法

本文给出了求强非线性系统周期解的频闪法,并给出了该方法的数学证明。