Fractional mechanical model for the dynamics of non-local continuum

被引：0
作者：
Cottone, G. [1 ]
Paola, M. Di [1 ]
Zingales, M. [1 ]
机构：
[1] Dipartimento di Ingegneria Strutturale, Geotecnica University of Palermo, 90128, Palermo, Viale delle Scienze
来源：
Lecture Notes in Electrical Engineering | 2009年 / 11卷
关键词：
Fractional calculus; Modes of vibration and dynamics of non-local bar; Non-local elasticity; Power law attenuation function;
D O I：
10.1007/978-0-387-76483-2_33
中图分类号：
学科分类号：
摘要：
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. © 2009 Springer Science+Business Media LLC.
引用
收藏
页码：389 / 423
页数：34
相关论文
共 37 条
  • [1] Aifantis E.C., Gradient effects at macro micro and nano-scales, Journal of the Mechanical Behavior of Materials, 5, pp. 355-375, (1994)
  • [2] Aifantis E.C., Update on a class of gradient theories, Mechanics of Materials, 35, pp. 259-280, (2003)
  • [3] Atanackovic T.M., A model for the uniaxial isothermal deformation of viscoelastic body, Acta Mechanica, 159, pp. 77-86, (2002)
  • [4] Bazant Z.P., Belytschko T.B., Continuum theory for strain-softening, Journal of Engineering Mechanics, 110, pp. 1666-1692, (1984)
  • [5] Bazant Z.P., Jirasek M., Non-local integral formulations of plasticity and damage, Journal of Engineering Mechanics, 128, pp. 1129-1239, (2002)
  • [6] Benvenuti E., Borino G., Tralli A., A thermodynamically consistent non- local formulation of damaging materials, European Journal of Mechanics /A Solids, 21, pp. 535-553, (2002)
  • [7] Borino G., Failla B., Parrinello F., A Symmetric non-local damage theory, International Journal of Solids and Structures, 40, pp. 3621-3645, (2003)
  • [8] Carpinteri A., Chiaia B., Cornetti P., Static-kinematic duality and the principle of virtual work in the mechanics of fractal media, Computer Methods in Applied Mechanics and Engineering, 191, 1-2, pp. 3-19, (2001)
  • [9] Carpinteri A., Chiaia B., Cornetti P., A mesoscopic theory of damage and fracture in heterogeneous materials, Theoretical and Applied Fracture Mechanics, 41, 1-3, pp. 43-50, (2004)
  • [10] Carpinteri A., Chiaia B., Cornetti P., On the mechanics of quasi-brittle materials with a fractal microstructure, Engineering Fracture Mechanics, 70, 16, pp. 2321-2349, (2003)
1234