Parametric attenuation and amplification of acoustic signals in the media with hysteretic quadratic nonlinearity

It is demonstrated that in a mesoscopic material with quadratic hysteretic nonlinearity a weak acoustic signal is initially attenuated in the field of a strong pump wave propagating in the same direction as the signal and is initially amplified in the field of a strong pump wave propagating in the o pposite direction. The attenuation of a signal in the field of a strong sta nding pump wave is predicted. Consequently the subharmonic route to chaos o bserved in elastic nonlinear resonators does not seem to be favorable in re sonance bars composed of mesoscopic materials (such as rocks, soil, concret e or damaged atomic materials). Theoretical predictions are in agreement wi th the available experimental data. (C) 2000 Elsevier Science B.V. All righ ts reserved.