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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Energy conservation in Newmark based time integration algorithms
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Energy conservation in Newmark based time integration algorithms

机译：基于Newmark的时间积分算法中的节能

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Energy balance equations are established for the Newmark time integration algorithm, and for the derived algorithms with algorithmic damping introduced via averaging, the so-called α-methods. The energy balance equations form a sequence applicable to: Newmark integration of the undamped equations of motion, an extended form including structural damping, and finally the generalized form including structural as well as algorithmic damping. In all three cases the expression for energy, appearing in the balance equation, is the mechanical energy plus some additional terms generated by the discretization by the algorithm. The magnitude and character of these terms as well as the associated damping terms are discussed in relation to energy conservation and stability of the algorithms. It is demonstrated that the additional terms in the energy lead to periodic fluctuations of the mechanical energy and are the cause of the phenomenon of response 'overshoot', previously observed empirically in the application of Newmark based algorithms to high-frequency components. It is also demonstrated that the stability limit of the explicit Newmark algorithm is reached, when the stiffness term in the algorithmic energy vanishes, and that energy fluctuations take place for integration intervals close to the stability limit.
机译：为Newmark时间积分算法以及为通过平均引入算法阻尼的推导算法（即所谓的α方法）建立了能量平衡方程。能量平衡方程形成一个序列，该序列适用于：无阻尼运动方程的Newmark积分，包括结构阻尼的扩展形式，最后包括结构阻尼和算法阻尼的广义形式。在这三种情况下，出现在平衡方程中的能量表达式都是机械能加上算法离散化生成的一些附加项。讨论了这些项的大小和特性以及相关的阻尼项，与算法的节能性和稳定性有关。事实证明，能量中的附加项会导致机械能的周期性波动，并且是响应“过冲”现象的原因，这种现象以前在基于Newmark的算法应用于高频分量的经验中得到了观察。还证明了，当算法能量中的刚度项消失时，达到了显式Newmark算法的稳定性极限，并且积分间隔接近稳定性极限时发生了能量波动。

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