Abstract |
Nonlinear Transformation of Acoustic
Waves in Microinhomogeneous Media with Relaxation
V.E.Nazarov, V.Yu.Zaitsev,
I.Yu.Belyaeva (Institute of Applied Physics RAS, Nizhny Novgorod, Russia)
e-mail:
vyuzai@hydro.appl.sci-nnov.ru
A
nonlinear equation of state and the corresponding wave equation are derived in
the framework of a rheological model suggested for elastic media containing
defects with relaxation. The defects in the model are considered as highly
compliant visco-elastic inclusions that exhibit a nonlinear stress-strain
dependence. For real solids, these inclusions may model, for example, cracks,
intergrain contacts and other similar defects. The proposed model thus can be
applied to a wide class of microinhomogeneous materials (Earth rocks,
engineering materials, damaged metals, etc.), which are also called
"mesoscopic" solids. The derived equations, being a generalisation of
the KDV-Burgers equation conventional for nonlinear acoustics of homogeneous
media, consistently comprise the following material properties connected to the
presence of the defects: (i) the microstructure-induced absorption (including
near-constant Q-factor), (ii) the complementary dispersion of sound velocity,
(iii) increased magnitude of the "mesoscopic" elastic nonlinearity
and (iv) frequency dependence of the nonlinearity. To illustrate the
aforementioned manifestations of the material microstructure, a few basic
nonlinear effects (second and difference-frequency harmonics generation, and
self-demodulation of high-frequency pulses) are analyzed in the framework of
the derived equations. Main distinctions of the effects compared to the case of
"classical" lattice (atomic) nonlinearity of homogeneous solids are
pointed out. The work was supported by RFBR (grants No 01-05-64417,
02-02-16237).
Section
: 2