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

作　　者：邢誉峰[1] 李玉婷 王雨竹 XING Yufeng;LI Yuting;WANG Yuzhu(Institute of Solid Mechanics,Beihang University,Beijing 100083,China)

机构地区：[1]北京航空航天大学固体力学研究所,北京100083

出　　处：《力学与实践》2025年第1期195-200,共6页Mechanics in Engineering

基　　金：国家自然科学基金项目(12172023)资助。

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,这既限制了其应用,也难以与其他具有可控数值阻尼的方法如广义-α方法等进行比较。本文通过谱分析,利用ρ_(∞)(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-ρ_(∞)方法。在此基础上,构造与之对应的模拟系统,其解析解与Newmark-ρ_(∞)方法结果吻合。根据模拟系统解析解,可以从理论角度给出幅值衰减率和周期延长率的定义,这有助于明晰时间积分方法存在幅值误差和相位误差的机理,也可以为设计结构依赖型方法提供理论基础。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 the generalized–α method.According to the spectral analysis method,this article utilizesρ_∞,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-ρ_∞method with precisely controllable numerical damping.On this basis,the analog system corresponding to the Newmark-ρ_∞ method is constructed,and its analytical solutions agree with those of the Newmark-ρ_∞ method.In addition,according to the analytical solutions of the analog system,the amplitude decay rate and the period elongation rate can be defined in theory.This helps clarify the mechanism of the amplitude and phase errors of time integration methods,and also provide a theoretical basis for designing structure dependency time integration methods.

关 键 词：Newmark方法 可控数值阻尼 幅值衰减率 周期延长率 模拟系统 

分 类 号：O302[理学—力学]