Fractional mechanical model for the dynamics of non-local continuum

Fractional mechanical model for the dynamics of non-local continuum
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非局部连续体动力学的分数阶力学模型

DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Zingales
M. Zingales
中科院分区：
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文献类型：
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作者：
G. Cottone;M. Paola;M. Zingales

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在本章中，分数阶微积分被用来解释物质粒子之间的长程相互作用。凝聚力已被假定为衰减与绝对距离的逆幂律产生，作为限制的情况下，一个普通的，分数阶微分方程。结果表明，所提出的数学公式是一个离散的，点弹簧模型，包括非局部的相互作用，由非相邻的粒子与线性弹簧的距离衰减刚度。与模型相关的边界条件与众所周知的运动学和静态约束相结合，并且它们不会出现发散行为。进行了动力学分析，研究了非局部系统的模态振型和固有频率。
In this chapter, fractional calculus has been used to account for long-range interactions between material particles. Cohesive forces have been assumed decaying with inverse power law of the absolute distance that yields, as limiting case, an ordinary, fractional differential equation. It is shown that the proposed mathematical formulation is related to a discrete, point-spring model that includes non-local interactions by non-adjacent particles with linear springs with distance-decaying stiffness. Boundary conditions associated to the model coalesce with the well-known kinematic and static constraints and they do not run into divergent behavior. Dynamic analysis has been conducted and both model shapes and natural frequency of the non-local systems are then studied.