Abstract

Nonlinear Effects of Plane Longitudinal Wave Propagation in Porous Materials

A.Pegushin (Nizhny Novgorod State University, Nizhny Novgorod, Russia); V.I.Erofeyev (Mechanical Engineering Research Institute of Russian Academy of Sciences, Nizhny Novgorod, Russia)

e-mail: pegushin@ru.ru

Several nonlinear effects of plane longitudinal wave propagation in dry porous medium are studied. The material is isotropic and elastic. The wavelength is assumed to be much greater than the distance between pores, and distance between the pores, in turn, is much greater than the radius of the pores. Pores are spherical, closed and pressure in them is neglected. The resultant mathematical model is nonlinear. The consequences of the existence of cavities are the dispersion of waves, the frequency-dependent damping, and an additional nonlinear effect (so-called porous nonlinearity). These factors manifest in different regimes. The influence of dispersion, dissipation, and nonlinearity on wave propagation can be estimated from the porosity of the material, the characteristic pore size, and the frequency of wave. The consequence of non-linearity is the generation of a wave of double frequency (super-harmonic). The dependence of basic parameters (velocity, amplitude) of super-harmonic waves on parameters of porous medium (porosity, pore size) is established. Theoretical study was performed for the plane stationary wave (particularly for the soliton of deformation) propagation in porous medium. Relations between the parameters of the wave (velocity, amplitude, frequency) and the parameters of the material have been established.

Section : 3