邢誉峰, 李玉婷, 王雨竹. 具有可控数值阻尼的Newmark-ρ方法及模拟系统. 力学与实践, xxxx, x(x): 1-6. doi: 10.6052/1000-0879-24-141
引用本文: 邢誉峰, 李玉婷, 王雨竹. 具有可控数值阻尼的Newmark-ρ方法及模拟系统. 力学与实践, xxxx, x(x): 1-6. doi: 10.6052/1000-0879-24-141
Xing Yufeng, Li Yuting, Wang Yuzhu. Newmark-ρ method with controllable numerical damping and analog system. Mechanics in Engineering, xxxx, x(x): 1-6. doi: 10.6052/1000-0879-24-141
Citation: Xing Yufeng, Li Yuting, Wang Yuzhu. Newmark-ρ method with controllable numerical damping and analog system. Mechanics in Engineering, xxxx, x(x): 1-6. doi: 10.6052/1000-0879-24-141

具有可控数值阻尼的Newmark-ρ方法及模拟系统

NEWMARK-ρ METHOD WITH CONTROLLABLE NUMERICAL DAMPING AND ANALOG SYSTEM

  • 摘要: Newmark方法是多数现代时间积分方法发展的基石。虽然经典Newmark方法有数值阻尼,但不能对其进行精确控制,这既限制了其引用,也难以与其他具有可控数值阻尼的方法如广义- \alpha 方法等进行比较。本文通过谱分析,利用 \rho _\infty (与无穷大频率对应的谱半径)表示Newmark方法中的两个自由参数,形成数值阻尼精确可控的单参数Newmark- \rho _\infty 方法。在此基础上,构造与之对应的模拟系统,其解析解与Newmark- \rho _\infty 方法结果之间的差别可以忽略,此外,还给出幅值衰减率的新定义,这都有助于明晰时间积分方法存在误差的机理,也可以为设计结构依赖型方法提供理论基础。

     

    Abstract: The Newmark method is a cornerstone of the development of most modern time integration methods. Although the classical Newmark method has numerical damping, it cannot be precisely controlled, which limits its applicability and makes it difficult to compare with other methods with controllable numerical damping, such as generalized – α method. According to the spectral analysis method, this article utilizes \rho _\infty , which is the spectral radius corresponding to the infinite frequency, to represent the two free parameters in the Newmark method, generating the one-parameter Newmark- \rho _\infty with precisely controllable numerical damping. On this basis, the analog system corresponding to the Newmark- \rho _\infty method is constructed, and the differences of its analytical solutions with those of the Newmark- \rho _\infty method are negligible, In addition, the amplitude decay rate is redefined. All of these help clarify the mechanism of cumulative errors of time integration methods, and can also provide a theoretical basis for designing structure dependency time integration methods.

     

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