| 分数算子描述的黏弹性体力学问题数值方法 |
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| 引用本文： | 张卫,徐华,清水信行. 分数算子描述的黏弹性体力学问题数值方法[J]. 力学学报, 2004, 36(5): 617-622. DOI: 10.6052/0459-1879-2004-5-2003-355 |
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| 作者姓名： | 张卫 徐华 清水信行 |
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| 作者单位： | 暨南大学应用力学研究所,广州,510632;西安交通大学现代设计及转子轴承系统教育部重点实验室,西安,710049;磐城明星大学机械工程系,日本,福岛 |
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| 基金项目： | 广东省自然科学基金(E010428)，教育部重点实验室访问学者基金(K123)资助项目.~~ |
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| 摘 要： | 讨论由黎曼-刘维尔 (Riemann-Liouville)分数导数描述的黏弹性体力学问题的数值方法. 该方法利用黎曼-刘维尔分数导数定义中核函数的特性，并结合被积函数在单步中的逼近以及Newmark型数值法，建立了分数导数计算公式. 算例表明，该算法具有收敛快、精度高、稳定性好和易于应用和改进的优点. 在对动态系统的瞬态响应分析和有限元分析格式中，算法都获得了满意的结果.
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| 关 键 词： | 分数导数 黏弹性 数值分析 Newmark数值法 |
| 修稿时间： | 2003-09-01 |
The numerical analysis formulation of the viscoelastic solid modeled by fractional operator |
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| Zhang Wei Xu Hua Nubuyuki ShimizuInstitute of Applied Mechanics,Jinan University,Guangzhou ,China The Laboratory of Modern Design and Rotor-Bearing System,Key Lab. of the Ministry of Education,Xi'an Jiao-tong University,Xi'an ,China Dept. of Mechanical Engineering,Iwaki Meisei University,Iwaki,Japan. The numerical analysis formulation of the viscoelastic solid modeled by fractional operator[J]. chinese journal of theoretical and applied mechanics, 2004, 36(5): 617-622. DOI: 10.6052/0459-1879-2004-5-2003-355 |
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| Authors: | Zhang Wei Xu Hua Nubuyuki ShimizuInstitute of Applied Mechanics Jinan University Guangzhou China The Laboratory of Modern Design Rotor-Bearing System Key Lab. of the Ministry of Education Xi'an Jiao-tong University Xi'an China Dept. of Mechanical Engineering Iwaki Meisei University Iwaki Japan |
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| Affiliation: | Zhang Wei Xu Hua Nubuyuki ShimizuInstitute of Applied Mechanics,Jinan University,Guangzhou 510632,China The Laboratory of Modern Design and Rotor-Bearing System,Key Lab. of the Ministry of Education,Xi'an Jiao-tong University,Xi'an 710049,China Dept. of Mechanical Engineering,Iwaki Meisei University,Iwaki,Japan |
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| Abstract: | The numerical method of mechanical problems for the viscoelastic solids with Riemann-Liouville fractional derivative model is presented in this paper. Instead of using finite Grunwald definition of fractional derivative to approximate the Riemann-Liouville's, this work has developed a numerical algorithm directly from Riemann-Liouville's definition by taking advantages of the features of its integrand kernel, assuming the approximating function for the integrand and making use of Newmark-type numerical methods. The numerical formulations are used to analyze the transient dynamic response for a viscoelastic oscillator and the finite element analysis procedures. The sample results show that the proposed method possesses the advantages of fast convergence, higher accuracy, higher stability and easy for application and further modification. |
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| Keywords: | fractional derivative viscoelasticity numerical method Newmark method |
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