Affiliation:
1. Department of Theoretical Mechanics, Voronezh State University of Architecture and Civil Engineering, Voronezh 394006, Russia
Abstract
The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10years 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.
Reference337 articles.
1. Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids;Rossikhin;Appl. Mech. Rev.
2. Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics;Mainardi
3. The Influence of Damping on Waves and Vibrations;Gaul;Mech. Syst. Signal Process.
4. Fractional Calculus Approach to Dynamic Problems of Viscoelastic Materials;Shimizu;JSME Int. J., Ser. C
5. A Survey of Fractional Calculus for Structural Dynamics Applications;French
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