Number: Mech 21/90
Author(s): VALDEK, U
Title: Asymptotics of 3D wave motion by evolution equations in nonlinear elastic media with memory. 13 p.
Language: English
ABSTRACT. The evolution equation approach has been widely used in dynamics
of liquids and gases. In dynamics of solids such an asymptotic description
is less used, but several problems are rather well analysed. For example,
one- dimensional longitudinal waves in solids have been described by the
Burgers equation, which takes into account dissipation according to the
Voigt model /1/. In the case of relaxing media, the evolution equation
is, generally speaking, of integro-differential type. The two-dimensional
evolution equation of longitudinal waves has also been derived and
analysed /2,3/. The corresponding two-dimensional mathematical models of
shear waves in solids are much more complicated /4,5/. As to
three-dimensional wave motion then only cases with simplified asymptions
are known /6/. In this paper three-dimensional longitudinal and shear
waves are investigated on a rather general basis. A special modified
constitutive equation of the continuous nonlinear viscoelastic medium is
being used /7/. In contrast to the usual models, this constitutive
equation permits to explain better the physical meaning of kernel
functions, which describe viscous properties of the medium.