Acoustic detection and nonlinear response of granular materials under vertical vibrations

Owing to their efficient penetration into elastic media, the measurement of sound waves can provide a sensitive probe of both the structural and mechanical properties of the materials through which they propagate. In this work, we first investigate the transversal and longitudinal wave velocities in granular assemblies composed of glass beads under uniaxial load by the time-of-flight method. Then the ratio G/B, (G is the shear modulus and B is the bulk modulus) as a function of pressure is analyzed, based on the theory of classical elasticity. Experimental results show that, with the pressure increasing from 10 to 100 kPa, i) the velocity of longitudinal wave (c(L)) is obviously faster than that of transversal one (c(T)) in the granular system(the ratio c(L)/c(T) is about 1.6), and the c(L) and c(T) of the system show power law scaling, i.e. c(L) proportional to p(0.3817), c(T) proportional to p(0.2809); ii) the ratio G/B decreases in the low pressure range for glass beads packing, i.e. G/B proportional to p(-0.4539). It is found that the power-law exponent of G/B with pressure is very close to -1/2 (the prediction in 2015 Phys. Rev. Lett. 114 035502), suggesting that the granular system lies in glass L state within the pressure range in our experiment. Furthermore, the fast Fourier transform method is used to study the variation of acoustic attenuation and nonlinear characteristics in granular materials. Our results reveal that the acoustic attenuation coefficient (alpha) and the ratio of the second harmonic amplitude (mu(2 omega)) to the square of fundamental amplitude (mu(1 omega)) at the receiving end in the granular system, mu(2 omega)/mu(2)(1 omega), both decrease in power law with the increase of pressure, i.e. alpha proportional to p(-0.1879), mu(2 omega)/mu(2)(1 omega) proportional to p(-0.866) respectively.