TY - JOUR

T1 - Nonlinear interaction of co-directional shear horizontal waves in a two-layered elastic medium

AU - Ahmetolan, Semra

AU - Demirci, Ali

N1 - Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The nonlinear interaction of co-directional shear horizontal (SH) waves propagating in a two-layered plate of uniform thickness is considered. It is assumed that the constituent materials of both layers are nonlinear, homogeneous, isotropic and incompressible elastic and having different mechanical properties. It is also assumed that between the linear shear velocities of the top layer, c1, and the bottom layer, c2, the inequality c1< c2 is valid. For the existence of a SH wave, the phase velocity of the wave, c, must satisfy either the inequality c1< c2≤ c or the one c1< c≤ c2 and here the problem is examined under the second condition. By employing an asymptotic perturbation method and balancing the weak nonlinearity and dispersion in the analysis, it is shown that the first order slowly varying amplitudes of interacting waves are governed asymptotically by a coupled nonlinear Schrödinger (CNLS) equations. Then the effects of nonlinearity of the materials and the ratio of layers’ thickness on the linear instabilities of solutions of the CNLS equations and the existence of solitary wave solutions of the CNLS are examined.

AB - The nonlinear interaction of co-directional shear horizontal (SH) waves propagating in a two-layered plate of uniform thickness is considered. It is assumed that the constituent materials of both layers are nonlinear, homogeneous, isotropic and incompressible elastic and having different mechanical properties. It is also assumed that between the linear shear velocities of the top layer, c1, and the bottom layer, c2, the inequality c1< c2 is valid. For the existence of a SH wave, the phase velocity of the wave, c, must satisfy either the inequality c1< c2≤ c or the one c1< c≤ c2 and here the problem is examined under the second condition. By employing an asymptotic perturbation method and balancing the weak nonlinearity and dispersion in the analysis, it is shown that the first order slowly varying amplitudes of interacting waves are governed asymptotically by a coupled nonlinear Schrödinger (CNLS) equations. Then the effects of nonlinearity of the materials and the ratio of layers’ thickness on the linear instabilities of solutions of the CNLS equations and the existence of solitary wave solutions of the CNLS are examined.

KW - Nonlinear elasticity

KW - Nonlinear waves

KW - Perturbation methods

KW - Solitary waves

UR - http://www.scopus.com/inward/record.url?scp=85055084124&partnerID=8YFLogxK

U2 - 10.1007/s00033-018-1033-7

DO - 10.1007/s00033-018-1033-7

M3 - Article

AN - SCOPUS:85055084124

SN - 0044-2275

VL - 69

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 6

M1 - 140

ER -