李卓, 徐秉业. 粘弹性分数阶导数模型的有限元法[J]. 工程力学, 2001, 18(3): 40-44.
引用本文: 李卓, 徐秉业. 粘弹性分数阶导数模型的有限元法[J]. 工程力学, 2001, 18(3): 40-44.
LI Zhuo, XU Bing-ye. FINITE ELEMENT METHOD FOR VISCOELASTIC FRACTIONAL DERIVATIVE MODEL[J]. Engineering Mechanics, 2001, 18(3): 40-44.
Citation: LI Zhuo, XU Bing-ye. FINITE ELEMENT METHOD FOR VISCOELASTIC FRACTIONAL DERIVATIVE MODEL[J]. Engineering Mechanics, 2001, 18(3): 40-44.

粘弹性分数阶导数模型的有限元法

FINITE ELEMENT METHOD FOR VISCOELASTIC FRACTIONAL DERIVATIVE MODEL

  • 摘要: 本文给出了粘弹性分数阶导数模型的有限元格式,并用模态分析的方法进行了运动方程解耦。用Laplace变换及其反变换,解析地计算了解耦后单自由度系统的时域和频域响应。时域响应被分为极点部分和截断部分,它们分别代表短期内的衰减振动和长时间内的缓慢恢复效应。以一维杆件为例,对有限元算法和解析解做了对比,分析了响应精度与单元个数的关系。结果表明用有限元法计算的位移接近解析解,而要得到准确的高频加速度响应,则需要划分许多单元格。

     

    Abstract: The finite element method (FEM) for viscoelastic fractional derivative model is presented in this paper. The motion equations are uncoupled with modal analysis method. With Laplace transformation and inverse Laplace transformation, analytical solutions of time domain response and frequency domain response of single degrees-of-freedom are obtained. The time domain response consists of transient response and steady-state response which represent short period damping vibration and long period recovery response, respectively. Take a one-dimensional bar as example, the FEM solution is compared with the analytical one. It is shown that the FEM solution of displacement agrees with analytical one and more elements are required to acquire accurate results of acceleration response in high frequency domain.

     

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