Visualization of solitary waves via laser Doppler vibrometry for heavy impurity identification in a granular chain

Abstract

We study the propagation of highly nonlinear solitary waves in a one-dimensional granular chain composed of homogeneous spherical particles that includes a heavy impurity. We experimentally investigate the transmission and backscattering behavior of solitary waves in the region of the impurity by using a laser Doppler vibrometer. To assess the sensitivity of solitary waves to various impurity masses, this non-contact measurement technique is complemented by a conventional contact measurement method based on an instrumented sensor particle. By leveraging these two schemes, we find that the travelling time and attenuation of backscattered solitary waves are highly sensitive to the location and mass of an inserted impurity. The experimental results are found to be in satisfactory agreement with the numerical results obtained from a discrete element model and the theoretical predictions based on nonlinear wave dynamics and classical contact theory. This study demonstrates that laser Doppler vibrometry can be an efficient tool to visualize highly nonlinear wave propagation in granular media. With a view towards potential applications, highly nonlinear solitary waves can be employed as nondestructive probing signals to identify heavy impurities embedded in ordered granular architectures.