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131.
There exist a sufficient condition for the existence of at least one periodic solution for a type of second order autonomous ordinary differential equations. The correctness of the condition has been pointed out by Schauder's fixed point theorem. In order to indicate the validity of the assumptions made, two illustrative examples, showing its application in the nonlinear vibration and relaxation oscillation are presented. 相似文献
132.
Noureddine Mehidi 《Meccanica》2007,42(4):403-407
We first approximate the solutions of the nonautonomous oscillating suspension point pendulum equation by the solutions of
a second order autonomous differential equation. Using the strict monotonicity of the periodic solutions of the approximating
equation, we prove the existence of a large number of subharmonic periodic solutions of the plane pendulum when its point
of suspension is excited parametrically. 相似文献
133.
Li Li 《Nonlinear dynamics》1996,9(3):223-247
In this paper a new method for solving for the periodic solution (limit cycle) of a strongly nonlinear system is suggested. Using this method not only the existence, stability and number of periodic solutions can be decided, but at the same time the approximate expressions for these periodic solutions can also be obtained. The proof of this method is given as well.The project is supported by the National Natural Science Foundation of China. 相似文献
134.
Rain-wind-induced vibrations of a simple oscillator 总被引:1,自引:0,他引:1
A.H.P. van der Burgh 《International Journal of Non》2004,39(1):93-100
In this paper a relatively simple mechanical oscillator which may be used to study rain-wind-induced vibrations of stay cables of cable-stayed bridges is considered. In recent publications, mention is made of vibrations of (inclined) stay cables which are excited by a wind field containing rain drops. The rain drops that hit the cables generate a rivulet on the surface of the cable. The presence of flowing water on the cable changes the cross section of the cable experienced by the wind field. A symmetric flow pattern around the cable with circular cross section may become asymmetric due to the presence of the rivulet and may consequently induce a lift force as a mechanism for vibration. During the motion of the cable the position of rivulet(s) may vary as the motion of the cable induces an additional varying aerodynamic force perpendicular to the direction of the wind field. It seems not too easy to model this phenomenon, several author state that there is no model available yet.The idea to model this problem is to consider a horizontal cylinder supported by springs in such a way that only one degree of freedom, i.e. vertical vibration is possible. We consider a ridge on the surface of the cylinder parallel to the axis of the cylinder. Additionally, let the cylinder with ridge be able to oscillate, with small amplitude, around the axis such that the oscillations are excited by an external force.It may be clear that the small amplitude oscillations of the cylinder and hence of the ridge induce a varying lift and drag force. In this approach it is assumed that the motion of the ridge models the dynamics of the rivulet(s) on the cable. By using a quasi-steady approach to model the aerodynamic forces, one arrives at a non-linear second-order equation displaying three different kinds of excitation mechanisms: self-excitation, parametric excitation and ordinary forcing. The first results of the analysis of the equation of motion show that even in a linear approximation for certain values of the parameters involved, stable periodic motions are possible. In the relevant cases where in linear approximation unstable periodic motions are found, results of an analysis of the non-linear equation are presented. 相似文献
135.
136.
在化学专业英语的学习过程中,学生最早接触的是元素周期表。本文对一些元素的英文名称采用解读式的教学方法,通过将元素的英文名称同著名科学家、特定地理名称、太阳系中的星球以及神话中的人物相关联,使元素的英文名称不再枯燥乏味,而变得生动形象,这一过程可以使学生更好地体验学习的乐趣。 相似文献
137.
We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature. 相似文献
138.
139.
Periodic Solutions of Delay Differential Equations with a Small Parameter: Existence,Stability and Asymptotic Expansion 总被引:1,自引:0,他引:1
Chunhua?Ou Jianhong?WuEmail author 《Journal of Dynamics and Differential Equations》2004,16(3):605-628
We consider a scalar delay differential equation with a small parameter, and employ Walthers method to obtain a result on the existence and stability of a slowly oscillatory periodic solution that represents a refinement of the estimate for the Lipschitz constant of a returning map. We also develop a matching method and obtain asymptotic expansions of the slowly oscillatory periodic solution and its minimal period.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthdayAMS subject classifications: 34K15; 34K20; 34C25. 相似文献
140.