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Antiplane Surface Wave Propagation Within the Stress Gradient Surface Elasticity

  • Victor A. EremeyevEmail author
Chapter
Part of the Mathematics of Planet Earth book series (MPE, volume 6)

Abstract

We discuss a new class of antiplane surface waves in an elastic half space with surface stresses. Here we consider a surface elasticity within stress gradient model , that is when the surface stresses relate to surface strains through an integral constitutive dependence. For antiplane motions the problem is reduced to the wave equation with nonclassical dynamic boundary condition. The dispersion relation is derived.

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Notes

Acknowledgements

The author gratefully thanks the Reviewer for the helpful constructive comments and recommendations.

The author acknowledges financial support from the Russian Science Foundation under the grant “Methods of microstructural nonlinear analysis, wave dynamics and mechanics of composites for research and design of modern metamaterials and elements of structures made on its base” (No 15-19-10008-P).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland
  2. 2.Southern Federal UniversityRostov on DonRussia
  3. 3.Southern Scientific Center of RASRostov on DonRussia

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