Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results

被引：516
作者：
Rossikhin, Yuriy A. [1 ]
Shitikova, Marina V. [1 ]
机构：
[1] Voronezh State Univ Architecture & Civil Engn, Dept Theoret Mech, Voronezh 394006, Russia
来源：
APPLIED MECHANICS REVIEWS | 2010年 / 63卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
fractional integrodifferentiation; free vibrations of viscoelastic systems with finite and infinite number degrees of freedom; impact response; FINITE-ELEMENT FORMULATION; DERIVATIVE VISCOELASTIC MODEL; NONLINEAR STOCHASTIC-SYSTEM; DAMPED VIBRATIONS; CONSTITUTIVE-EQUATIONS; TIME-DOMAIN; DIFFERENTIAL-EQUATIONS; SEISMIC MITIGATION; STRESS-RELAXATION; NUMERICAL SCHEME;
D O I：
10.1115/1.4000563
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics. This review involves the papers dealing with study of dynamic behavior of linear and nonlinear 1DOF systems, systems with two and more DOFs, as well as linear and nonlinear systems with an infinite number of degrees of freedom: vibrations of rods, beams, plates, shells, suspension combined systems, and multilayered systems. Impact response of viscoelastic rods and plates is considered as well. The results obtained in the field are critically estimated in the light of the present view of the place and role of the fractional calculus in engineering problems and practice. This articles reviews 337 papers and involves 27 figures. [DOI: 10.1115/1.4000563]
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收藏
页码：1 / 52
页数：52
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