Nonlinear elastic properties of a model one-dimensional granular unconsolidated structure

Abstract

The characteristic features of the propagation of finite-amplitude elastic waves in a model one-dimensional unconsolidated granular medium are investigated. The model medium is represented by a linear chain of 80 steel balls with a diameter of 6.5 mm each, this chain being preliminarily loaded with an external static force F. The elastic properties of the model are analyzed. The theoretical dependences of the coefficients of elasticity of the second, third, and fourth orders on the force F are obtained. The experimental setup is described. The results of studying the nonlinear effects, namely, the higher harmonic generation and the wave generation at combination frequencies, which accompany the acoustic wave propagation in the chain, are presented. For the chain of balls under study, a structural phase transition from the 1D structure to a 2D one is observed with an increase in the external compression force F applied to the balls. The results of the study are analyzed using the Hertz theory of contact interactions.