轴向加速度运动弦线横向振动的数值计算方法被引量：8

NUMERICAL SIMULATION OF THE TRANSVERSE VIBRATION OF AXIALLY ACCELERATING STRING

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摘要讨论轴向加速度运动弦线横向振动的数学模型、数值计算方法等问题。基于Coriolis加速度和Lagrangian应力公式 ,利用Newton第二定律导出轴向加速度运动弦线横向振动的动力学模型 ;通过线性变换将方程化为一阶无量纲的非线性微分方程组 ;并利用Crank Nicoson的中点离散技巧 ,给出运动方程的单步二阶差分方法 ;算法把对运动方程和本构方程分别离散 ,使之可以用于不同本构的运动弦线的数值仿真。且方法对线性问题绝对稳定 ,对非线性问题也有较好的稳定性。作为应用实例 ,利用该方法对一类加速度运动弦线的横向振动进行数值仿真 ,利用弹性弦线的守衡公式检验数值结果的精度 ,并利用给出的数值方法分析速度、加速度。 A mathematical model describing the transverse vibration of an axially accelerating strings is given. Based on Crank Nicoson's technique, and a new approach for the numerical simulation of the model is raised. The truncation error of the one step difference method reaches O (Δ t 2+Δ x 2 ) and of quite good stability condition. The numerical method can be used for elastic models as well as viscoelastic ones. As a numeric example, a special model of the transverse vibration of a moving string is given and its dynamical analysis is made. The effects of some parameters of the model acted on the string system, such as that of the axial velocity, the acceleration and the Young's modulus, are analyzed and showed in figures. A conservative quantity is used to check the results.

作者周洪刚朱凌郭乙木

机构地区浙江大学固体力学研究所

出处《机械强度》 CAS CSCD 北大核心 2004年第1期16-19,共4页 Journal of Mechanical Strength

关键词轴向加速度运动弦线横向振动数值仿真 Crank-Nicoson公式数学模型 Axially accelerating strings Transverse vibration Numerical simulation Crank-Nicoson's technique

分类号 O322 [理学—一般力学与力学基础] TB115 [理学—应用数学]

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