|
Abstract |
Nonlinear Acoustic Waves in Micropolar
and Granular Media
I.S.Pavlov, S.A.Lisina, A.I.Potapov
(Mechanical Engineering Research Institute of Russian Academy of Sciences,
Nizhny Novgorod, Russia)
e-mail:
apotapov@sandy.ru
Oscillations
of the chain of dumb-bell-shaped particles [Potapov A.I., Pavlov I.S., Maugin
G.A. Nonlinear wave interactions in 1D crystals with complex lattice. Wave
Motion. 1999. V.29. P. 297-312] and particles of rectangular shape [Lisina
S.A., Potapov A.I., Nesterenko V.F. Nonlinear granular medium with rotations of
the particles. One-dimensional model. Phys. Acoust. 2001. V47. N5. P.666-674]
are considered. Such systems simulate dynamics of micropolar and granular
media. Nonlinear differential equations describing propagation and interaction
of longitudinal, transversal, and rotational waves have been obtained. Linear
parts of these equations are invariants with respect to a shape and sizes of
the particles. The analytical relationship between micromodel parameters and
material constants of a medium has been found that enables one to determine the
last ones due to acoustic experiments.
In the low-frequency approximation the rotational wave does not
propagate, and the summand with a quadratic nonlinearity appears in the
equation for a transverse wave. This fact enables to explain the generation of
the second shear harmonics that is observed in solids and relate its
characteristics with structure parameters of the medium. The last property
enables one to obtain additional data about the medium microstructure. The
effect of localization of transverse and rotational waves in a half-space and
in a layer of finite width is discussed when the powerful longitudinal wave
acts upon them. The research described
in this paper was made possible by RFBR (grants 01-01-00386 and 00-02-16582).
Section
: 2