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首页> 外文期刊>International journal of non-linear mechanics >Computational and numerical analysis of a nonlinear mechanical system with bounded delay
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Computational and numerical analysis of a nonlinear mechanical system with bounded delay

机译：时滞非线性机械系统的计算与数值分析

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Modern structures are increasingly resistant and complex. In many cases, such systems are modeled by numerical approximations methods, due to its complexities. In the study of vibration levels in the response of a system is important to consider issues like reliability and efficient design, since that such vibrations are undesirable phenomena that may cause damage, failure, and sometimes destruction of machines and structures. In this paper we investigated a modeling strategy of nonlinear system with damping, subject the time delayed. From models widely used in literature and with the help of numerical simulations a nonlinear damped system with two degree-of-freedom is analyzed. The system is constituted of a primary mass attached to the ground by a spring and damping with linear or nonlinear characteristics (primary system), and the secondary mass attached to the primary system by a spring and damping with linear or nonlinear characteristics (secondary system). It is well known that time delayed systems, due to its own nature, has singular behavior in its dynamics and that such singularities propagate over the time. Based on this, the main concerns of the present paper is to analyze the stability of a delayed system with two degree of freedom by means of the techniques development in [1] (Hu andWang, 2002). We also obtain the solution using the integration of equations of motions performing a Fourth Order Runge-Kutta Method. The behavior of a nonlinear main system with nonlinear secondary system will be investigated to many cases of resonances. In this case, various time delayed values are used to confirm its influence on the attenuation of vibrations, but, unfortunately, also the increase of nonlinearity (instable responses) of the system in question is observed.
机译：现代结构越来越具有抵抗性和复杂性。在许多情况下，由于其复杂性，此类系统通过数值逼近方法进行建模。在研究系统响应中的振动水平时，重要的是要考虑诸如可靠性和高效设计之类的问题，因为这种振动是不希望出现的现象，可能会导致机器和结构的损坏，故障甚至毁坏。在本文中，我们研究了带有时滞的带有阻尼的非线性系统的建模策略。从文献中广泛使用的模型并借助数值模拟，分析了具有两个自由度的非线性阻尼系统。该系统由具有线性或非线性特征的弹簧和阻尼的初级质量（初级系统）和具有线性或非线性特征的弹簧和阻尼的次级质量（二级系统）组成。 。众所周知，时滞系统由于其自身的性质，其动力学具有奇异行为，并且这种奇异性会随时间传播。基于此，本文主要关注的是通过[1]中的技术发展来分析具有两个自由度的时滞系统的稳定性（Hu and Wang，2002）。我们还使用执行四阶Runge-Kutta方法的运动方程积分来获得解决方案。非线性主系统与非线性次系统的行为将在许多共振情况下进行研究。在这种情况下，可以使用各种时间延迟值来确认其对振动衰减的影响，但不幸的是，还可以观察到所讨论系统的非线性（不稳定响应）增加。

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