Tunable Highly-Nonlinear Acoustic Waves and their coupling with Linear Elastic Media

Abstract

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.

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