Stability on finite time interval and time-dependent bifurcation analysis of Duffing's equations

The concept of stability on finite time interval is proposed and some stability theorems are established. The delayed bifurcation transition of Dufflng's equations with a time-dependent parameter is analyzed. Function is used to predict the bifurcation transition value. The sensitivity of the solutions to initial values and parameters is also studied.     

IUTAM“面向先进技术与工程设计的非线性动力学会议”概况

<正>2010年7月27日～30日,由国际理论与应用力学联合会(IUTAM)主办的"面向先进技术与工程设计的非线性动力学会议"在英国阿伯丁召开.会议由英国阿伯丁大学工学院M.Wiercigroch教授和意大利罗马大学工学院G.Rega教授担任主席,来自英国、德国、法国、意大利、荷兰、奥地利、西班牙、葡萄牙、丹麦、波兰、俄罗斯、乌克兰、以色列、中国、日本、印度、美国、加拿大和巴西等19个国家的75名学者出席了会议,52位学者做了学术报告,17位学者做了墙报交流.     

Nonlinear dynamics and vibration reduction of a dry friction oscillator with SMA restraints

The dynamic behaviors of a dry friction oscillator with shape memory alloy (SMA) are investigated. Motion equations of the system are formulated by the restoring force of the oscillator in terms of a polynomial constitutive model dependent mainly on the temperature. The vibration response of the system and the influence of the temperature are investigated. It is shown that chaotic motions can be observed and dramatically changed by temperature characteristics. Moreover, some sliding bifurcations are also discovered and influenced by the temperature. Compared with conventional dry friction elastic oscillators, the dry friction SMA oscillator presents much richer dynamic behavior caused by pseudo-elasticity, and vibration reduction can be achieved through the shape memory property of SMA restraints.     

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为了更好地发挥<力学进展>对力学研究的促进作用,编委会决定,选择有发展前景的若干力学研究方向组织专辑评述:即,每次围绕一个方向约请若干国内外知名专家从不同的角度撰写综述评论文章,集中于一期内发表,并提供较详细的重要参考文献,以便向读者展示该方向最新发展的全貌,从而达到开阔学术思想、启发探索兴趣、提供研究导向的目的.     

Non-existence of positive radial solutions for a class of quasilinear elliptic system

In this paper, our main purpose is to establish some nonexistence results of positive radial solutions to the quasilinear ordinary differential equation system. The main results of the present paper are new and extend the previously known results.     

Single rub-impacting periodic motions of a rigid constrained rotor system

This paper discusses the existence of single rub-impacting period-n motions for a kind of rotor systems with rigid constraints. The ranges of parameters for period-2 motions are also given. An example of this method is given.     

A station-keeping strategy for collinear libration point orbits

Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena. Since such periodic or quasi-periodic orbits are exponentially unstable, the station-keeping maneuver is needed. A station-keeping strategy which is found by an analytical method is presented to eradicate the dominant unstable component of the libration point trajectories. The inhibit force transforms the unstable component to a stable component. In this method, it is not necessary to determine a nominal orbit as a reference path.     

The analysis of the spectrum of Lyapunov exponents in a two-degree-of-freedom vibro-impact system

In the study of dynamical systems, the spectrum of Lyapunov exponents has been shown to be an efficient tool for analyzing periodic motions and chaos. So far, different calculating methods of Lyapunov exponents have been proposed. Recently, a new method using local mappings was given to compute the Lyapunov exponents in non-smooth dynamical systems. By the help of this method and the coordinates transformation proposed in this paper, we investigate a two-degree-of-freedom vibro-impact system with two components. For this concrete model, we construct the local mappings and the Poincaré mapping which are used to describe the algorithm for calculating the spectrum of Lyapunov exponents. The spectra of Lyapunov exponents for periodic motions and chaos are computed by the presented method. Moreover, the largest Lyapunov exponents are calculated in a large parameter range for the studied system. Numerical simulations show the success of the improved method in a kind of two-degree-of-freedom vibro-impact systems.