Nonlinear modulation of SH waves in an incompressible hyperelastic plate |
| |
Authors: | Semra Ahmetolan Mevlut Teymur |
| |
Institution: | (1) Department of Mathematics, Faculty of Sciences and Letters, Istanbul Technical University, TR-34469 Maslak, Istanbul, Turkey |
| |
Abstract: | Propagation of nonlinear shear horizontal (SH) waves in a homogeneous, isotropic and incompressible elastic plate of uniform
thickness is considered. The constituent material of the plate is assumed to be generalized neo-Hookean. By employing a perturbation
method and balancing the weak nonlinearity and dispersion in the analysis, it is shown that the nonlinear modulation of waves
is governed asymptotically by a nonlinear Schr?dinger (NLS) equation. Then the effect of nonlinearity on the propagation characteristics
of asymptotic waves is discussed on the basis of this equation. It is found that, irrespective of the plate thickness, the
wave number and the mode number, when the plate material is softening in shear then the nonlinear plane periodic waves are
unstable under infinitesimal perturbations and therefore the bright (envelope) solitary SH waves will exist and propagate
in such a plate. But if the plate material is hardening in shear in this case nonlinear plane periodic waves are stable and
only the dark solitary SH waves may exist. |
| |
Keywords: | Nonlinear elasticity nonlinear waves solitary waves perturbation methods |
本文献已被 SpringerLink 等数据库收录! |
|