瑞雷阻尼与显式积分算法的阻尼稳定性
首发时间:2014-07-09
摘要:在瑞雷阻尼假定下,采用理论分析与数值模拟方法,研究了多自由度体系显式直接积分算法的大阻尼或数学阻尼稳定性问题。研究对象主要为两种典型的条件稳定显式算法,LL和BW算法;但为了比较与控制显式算法的精度,又增加了无条件稳定的PJ算法作为补充研究对象。在精度与PJ算法一致,以及模型体系最高与最低模态频率之比为100或更大前提下,取得的主要研究结果为:BW算法的阻尼稳定性显著优于LL算法;对于相同的常用无量纲积分步长,BW算法较之LL算法的阻尼稳定区间可以延拓达千倍以上;对于相同的常用介质阻尼比,BW算法与LL算法的稳定阈值 之比,随阻尼比的增加而增加,最高亦达千倍以上。本文的阶段研究结果表明:继续深入研究BW算法的阻尼稳定性以及相关问题,对于推动显式算法在大型复杂体系动力分析中的广泛应用,具有重要的理论意义和实用价值。
关键词: 瑞雷阻尼 显式积分算法 数学阻尼比 无量纲积分步长 阻尼稳定性
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Reilly damping and the damping stability of the explicit integral algorithm
Abstract:Under the Raleigh damping assumption, by using the methods of theoretical analysis and numerical simulation, it is studied that the high or mathematics damping stability of conditionally stable explicit integration algorithm named LL and BW on the multi-degree of freedom system. But in order to compare and control the accuracy of explicit algorithm, the PJ algorithm of unconditional stability is added as a supplemental object. Under the condition that the accuracy of algorithm are the basically same and the ratio between maximum and minimum model frequency for the system is 100 or higher, the main achievements are: the damping stability of BW algorithm is much better than LL algorithm; For the same dimensionless integration step often used, the damping stability interval of BW algorithm can be 1000 times more than LL algorithm; For the same damping ratio of medium often used, the ratio of stable threshold between BW and LL that increase with the increasing of damping ratio can be more than 1000 times. The results of the essay show that the further study of the damping stability and related problems of the BW algorithm have a significant meaning and value for promoting the wide application of explicit algorithm in dynamic analysis of large complex system.
Keywords: rayleigh damping explicit integration algorithm mathematics damping ratio dimensionless integration step damping stability
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