操作员(生物学)
非线性系统
粘弹性
微分算子
一般化
状态变量
分数阶微积分
功能(生物学)
数学分析
数学
应用数学
物理
热力学
基因
生物
转录因子
抑制因子
进化生物学
量子力学
化学
生物化学
作者
Dov Ingman,J. Suzdalnitsky,Michael I. Zeifman
出处
期刊:Journal of Applied Mechanics
[ASME International]
日期:1999-04-09
卷期号:67 (2): 383-390
被引量:76
摘要
A dynamic integro-differential operator of variable order is suggested for a more adequate description of processes, which involve state dependent measures of elastic and inelastic material features. For any negative constant order this operator coincides with the well-known operator of fractional integration. The suggested operator is especially effective in cases with strong dependence of the behavior of the material on its present state—i.e., with pronounced nonlinearity. Its efficiency is demonstrated for cases of viscoelastic and elastoplastic spherical indentation into such materials (aluminum, vinyl) and into an elastic material (steel) used as a reference. Peculiarities in the behavior of the order function are observed in these applications, demonstrating the “physicality” of this function which characterizes the material state. Mathematical generalization of the fractional-order integration-differentiation in the sense of variability of the operator order, as well as definitions and techniques, are discussed. [S0021-8936(00)02102-4]
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