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

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

Highly nonlinear solitary waves in chains of ellipsoidal particles

We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated

Coupling of Highly Nonlinear Waves with Linear Elastic Media

This paper reports a fundamental study of the coupling between highly nonlinear waves, generated in a one dimensional granular chain of particles, with linear elastic media, for the development of a new Non Destructive Evaluation and Structural Health Monitoring (NDE/SHM) paradigm. We design and use novel acoustic actuators to excite compact highly nonlinear solitary waves in a one-dimensional linear elastic rod and investigate the pulse propagation across the interface. To model the actuator and rod system we use Finite Element Analysis (Abaqus) and obtain excellent agreement between the experimental observations and the numerical results. We also study the response of the system to the presence of defects (cracks) in the steel rod, by comparing the wave propagation properties in pristine and cracked test objects. The obtained results encourage the use of highly nonlinear waves as an effective tool for developing a new, viable NDE/SHM method

Highly nonlinear waves' sensor technology for highway infrastructures

This paper describes preliminary results towards the development of an innovative NDE/SHM scheme for material characterization and defect detection based on the generation of highly nonlinear solitary waves (HNSWs). HNSWs are stress waves that can form and travel in highly nonlinear systems (i.e. granular, layered, fibrous or porous materials) with a finite spatial dimension independent on the wave amplitude. Compared to conventional linear waves, the generation of HNSWs does not rely on the use of electronic equipment (such as an arbitrary function generator) and on the response of piezoelectric crystals or other transduction mechanism. HNSWs possess unique tunable properties that provide a complete control over tailoring: 1) the choice of the wave's width (spatial size) for defects investigation, 2) the composition of the excited train of waves (i.e. number and separation of the waves used for testing), and 3) their amplitude and velocity. HNSWs are excited onto concrete samples and steel rebar. The first pilot study of this ongoing effort between Caltech and the University of Pittsburgh is presented

Highly nonlinear waves' sensor technology for highway infrastructures

This paper describes preliminary results towards the development of an innovative NDE/SHM scheme for material characterization and defect detection based on the generation of highly nonlinear solitary waves (HNSWs). HNSWs are stress waves that can form and travel in highly nonlinear systems (i.e. granular, layered, fibrous or porous materials) with a finite spatial dimension independent on the wave amplitude. Compared to conventional linear waves, the generation of HNSWs does not rely on the use of electronic equipment (such as an arbitrary function generator) and on the response of piezoelectric crystals or other transduction mechanism. HNSWs possess unique tunable properties that provide a complete control over tailoring: 1) the choice of the wave's width (spatial size) for defects investigation, 2) the composition of the excited train of waves (i.e. number and separation of the waves used for testing), and 3) their amplitude and velocity. HNSWs are excited onto concrete samples and steel rebar. The first pilot study of this ongoing effort between Caltech and the University of Pittsburgh is presented

Coupling of Highly Nonlinear Waves with Linear Elastic Media

This paper reports a fundamental study of the coupling between highly nonlinear waves, generated in a one dimensional granular chain of particles, with linear elastic media, for the development of a new Non Destructive Evaluation and Structural Health Monitoring (NDE/SHM) paradigm. We design and use novel acoustic actuators to excite compact highly nonlinear solitary waves in a one-dimensional linear elastic rod and investigate the pulse propagation across the interface. To model the actuator and rod system we use Finite Element Analysis (Abaqus) and obtain excellent agreement between the experimental observations and the numerical results. We also study the response of the system to the presence of defects (cracks) in the steel rod, by comparing the wave propagation properties in pristine and cracked test objects. The obtained results encourage the use of highly nonlinear waves as an effective tool for developing a new, viable NDE/SHM method

Interaction of highly nonlinear solitary waves with linear elastic media

We study the interaction of highly nonlinear solitary waves in granular crystals, with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of the reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Studying variations of the reflected wave's velocity and amplitude, we describe how the propagation of primary and secondary reflected waves responds sensitively to the states of the adjacent linear media. Experimental results are found to be in agreement with the theoretical analysis and numerical simulation. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a nite element model (FEM)using the commercially available software Abaqus, which takes into account many of these characteristic features. The nite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specfic application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.</p