Tunable Highly-Nonlinear Acoustic Waves
and their coupling with Linear Elastic Media
Creators: name: Khatri, Devvrath
Publisher: name: Keck Institute for Space Studies
Year: 2010

description: This project aims at introducing and testing a new method of Non-Destructive Evaluation (NDE)
and Structural Health Monitoring (SHM) for materials and engineering systems, based on the
use of Highly Nonlinear Acoustic Waves (HNAWs). At a fundamental level the project aims at
understanding the interface behavior between linear and highly nonlinear media. The effects of
interface dynamics on the temporary localization of incident waves and their decomposition into
reflected waves are investigated.
We implemented a finite element model for HNAWs formation and propagation in granular chain
using commercially available software Abaqus. We validated our finite element model with the
theoretical work of static loading between two beads using Hertz’s law and for dynamic impact
loading for the formation and propagation of solitary wave in the chain of beads using Nesterenko’s
theory. We also compared our results with discrete particle model and corroborate the results with
experiments.
To use nonlinear actuator system for NDE/SHM applications purpose, we studied the losses in the
energy transmission as wave propagate in chain of spherical beads. We proposed a quantitativelyaccurate
extension of the Hertzian model encompassing realistic material dissipative effects in a
one-dimensional chain of granular materials. Using an optimization scheme, we computed the
relevant exponents and prefactors of the dissipative terms in the equations of motion. Using linear
Rayliegh damping we modeled the dissipation effects in the finite element simulations. We used the
root mean square deviation method to obtained the optimized mass proportional factor of damping.
The experimental results are found to be in good agreement with proposed model in terms of wave
amplitude and wave shape.
To understand the coupling of nonlinear media with adjacent linear elastic media, we studied
experimentally and numerically the effects of solitary waves interacting with different single- and
multi-layered media. We performed the theoretical analysis of the coupling based on the longwavelength
approximation in a one-dimensional chain of beads. The numerical predictions based
on discrete particle model and experimental results are in good agreement with the theoretical
analysis. In our study, we found a correlation between the properties of reflected waves from the
interface and the elastic modulus of adjacent linear elastic media. For elastic modulus value below
the critical limit, we monitored the generation of secondary reflected solitary waves at the interface
and found the dependence of them on the ratio of elastic modulus of adjacent media and of the
spherical particles.
In order to understand the coupling of nonlinear actuator system with the composite media for
NDE/SHM purpose, we further extended our study for the interaction of highly nonlinear acoustic
waves with double layered media. The results shows a correlation between the properties of primary
reflected waves with the inertia of the top layer and the dependence of properties of secondary
reflected solitary waves on the bottom layer. The results were found in good agreement with the
experimental finding.
The work done as part of this research enhances our understanding on the basic physics and
tunability of nonlinear media, and further establishes a theoretical and numerical foundation in the
applications of NDE/SHM in various areas.