Nonlinear phenomenon in one-dimensional model of granular unconsolidated medium

Abstract

Here are represented the results of studying of nonlinear acoustic phenomenon in 1-D model unconsolidated granular medium. The medium was modeled as a system composed of identical steel spheres with the same radius, placed in a tube. Nonlinear acoustic effects in structures with the contact interaction are described by Hertz law.Investigation of nonlinear properties of the system was carried out using the spectral method. We experimentally investigated characteristics of the second and the third acoustic harmonics generation. The deformation of the spheres e during the experiment changed as we applied different static external force. Elastic nonlinearity of the system of spheres decreased with static strain e increasing. Analysis of the experimental results showed that if spheres experience elastic deformation, the amplitude of the second harmonic is proportional to 1/e, and the amplitude of the third harmonic is proportional to 1/e^2. These results are in agreement with theoretical analysis based on Hertz theory. However, the presence of dispersion in the radius of spheres leads to a drastic increase of the amplitudes of harmonics in a number of experiments when strain e of the system was equal to 2*10-5 - 3*10-5.We present a discussion of the results of the experiment.