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黏弹性材料本构方程的广义分数阶单元网络表述及其广义解 被引量：10

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摘要 提出广义分数阶单元网络,取消了Schiessel等人所提出的分数阶单元法对参数的限制,增加了“协调方程”,将模型解的构造扩充到广义函数空间,使其包含更多的具有明显物理意义的解.应用并发展了离散求逆Laplace变换的方法,给出了模型方程的广义解.讨论了广义分数阶单元网络Zener,Poyinting-Thomson模型.结果表明,有关黏弹性材料本构方程前人所得的经典整数阶和分数阶单参数模型的所有结果均可作为本文的特例而被包括.
作者 徐明瑜 谭文长
机构地区 山东大学数学与系统科学学院生物医学工程研究中心 北京大学力学与工程科学系
出处 《中国科学（A辑）》 CSCD 北大核心 2002年第8期673-681,共9页 Science in China(Series A)
基金 教育部博士点专项科研基金 国家自然科学基金(批准号:10002003) 高等学校骨干教师基金资助项目
关键词 黏弹性材料 本构方程 广义分数阶单元网络 分数阶微积分 广义解 逆Laplace变换 协调方程
分类号 O345 [理学—固体力学]
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参考文献16

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二级参考文献13

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中国科学（A辑）
2002年 第8期

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