Nonlinear modulation of Love waves in a compressible hyperelastic layered half space

Nonlinear modulation of SH waves in an incompressible hyperelastic plate

“…Such a material is called generalized neo-Hookean and the wave motion described above which is an anti-plane shear motion that can exist in the plate in the absence of body forces acting in the plane (X,Y ). As pointed out in some other investigations involving anti-plane shear motions in non-linear elastic media [10,13], in general, without any restrictions on stress constitutive equations an anti-plane shear motion can not be maintained in the media without body forces acting in the plane perpendicular to the polarization direction. Although in this work a plate made of generalized neo-Hookean material is considered, a parallel analysis can be performed for isotropic compressible or incompressible materials under certain restrictions as done in certain related problems [10,13].…”

“…By employing the asymptotic perturbation methods previously used in the fields of fluid mechanics, plasma physics, etc., investigating the propagation of weakly nonlinear waves [6][7][8], several problems related with the propagation of nonlinear dispersive elastic waves are examined [9][10][11][12][13][14][15][16][17][18]. In these works as a balance between nonlinearity and dispersion various scalar nonlinear evolution equations, which were obtained previously in the above mentioned fields, have been derived to describe the wave motions asymptotically.…”

Propagation of surface SH waves on a half space covered by a nonlinear thin layer

“…This fact has not been taken into account in the works done by Kalyanasundaram (1981), Bataille and Lund (1982). Later in Teymur (1988), the propagation of nonlinear Love waves in a half space covered by a layer of uniform finite thickness having different mechanical properties, is considered. The materials of the layer and the half space are both assumed to be homogeneous, isotropic and compressible hyper-elastic.…”

“…Ahmetolan & Teymur, 2007;Bataille & Lund, 1982;Demiray, 2008;Destrade, Gilchrist, & Saccomandi, 2010a;Destrade, Gilchrist, & Ogden, 2010b;Destrade, Goriely, & Saccomandi, 2011;Destrade & Saccomandi, 2005;Destrade & Saccomandi, 2006;Fu, 1996;Kalyanasundaram, 1981; http://dx.doi.org/10.1016/j.ijengsci.2014.08.005 0020-7225/Ó 2014 Elsevier Ltd. All rights reserved. 1991; Mayer, Parker, & Maradudin, 1992;Maugin, Hadouaj, & Malomed, 1992;Porubov & Samsonov, 1995;Soerensen, Christiansen, & Lomdahl, 1984;Teymur, 1988;Teymur, 1996;Teymur, 2007). For an extensive review of most of these works we refer to Parker and Maugin (1988), Maugin (1994), Parker (1994), Samsonov (1994), Mayer (1995), Norris (1998), Porubov (2003).…”

“…Later in Maugin and Hadouaj (1991), the problem is examined when the nonlinear substrate covered by a linear elastic interface of mathematically vanishing thickness. The equation of motion of the substrate approximated by a nonlinear equation having a third order nonlinearity as in Teymur (1988). The analysis is simplified by use of a linear thin film approximation which converts a two medium problem by one for a half space with a modified boundary condition on the top surface.…”