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On Nonlocal Surface Elasticity and Propagation of Surface Anti-Plane Waves

  • Victor A. Eremeyev
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 46)

Abstract

We discuss the nonlocal model of surface elasticity that is the model with surface energy density which depends on first and higher gradients of displacements. To demonstrate the peculiarities of the model we consider the propagation of anti-plane surface waves in an elastic halfspace with the surface energy. Using the least action principle we derive the governing equations for the problem. Analyzing the anti-plane deformations we obtain the dispersion relation and analyze its dependence on surface elastic moduli and on the order of considered gradients.

Keywords

Anti-plane waves Surface elasticity Strain gradient elasticity Surface waves Nth-order strain gradient elasticity 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia
  2. 2.Faculty of Mechanical Engineering and AvionicsRzeszów University of TechnologyRzesz ówPoland

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