Nonlinear Resonant Spectroscopy Research Articles

Evaluation of self-healing in concrete using linear and nonlinear resonance spectroscopy

In this study, self-healing in concrete incorporating two types of healing agents, i.e., 1) a self-healing capsule and 2) supplementary cementitious materials with crystalline admixtures, is monitored using linear and nonlinear resonance acoustic spectroscopy techniques. Beam-shaped concrete specimens are prepared using the healing agents, and after 28 days, a single vertical crack with a width ranging from 0.25 to 0.35 mm is generated at the center of the specimens. To monitor the self-healing process in concrete, the samples are vibrated via impact-based excitation methods in the flexural and longitudinal directions, whereas the linear resonance frequency and acoustic nonlinearity parameter α are measured for two months. Additionally, the acoustic nonlinearity parameter is analyzed using two different methods: 1) multiple impacts with manually controlled amplitude, and 2) single impact with artificially controlled amplitude by changing the windowing region in a signal. Test results show that the linear resonance frequency increases up to 86%–97% that of the uncracked condition after 63 days of self-healing. The linear trend of the resonance frequency is correlated significantly with the decrease in the external crack area, but the change in α is affected by the presence of partially filled cracks than by the overall crack area.

Nondestructive evaluation of solid cargo inside cylindrical containers with linear and nonlinear resonance spectroscopy

Nondestructive evaluation (NDE) of cylindrical containers is of critical importance because of their ubiquity in industrial applications. However, there is a paucity of research on the NDE of solid cargo inside sealed enclosures with external sensors. This talk covers the application of linear and nonlinear resonance spectroscopy to the NDE of cargo inside cylindrical containers. The first study focused on a Transnuclear-32 (TN-32) cask used for the dry storage of spent nuclear fuel assemblies. The modes of the TN-32 were measured onsite and Finite Element Analysis was used to investigate modal changes due to loadings of fuel assemblies. Because of the difficulties introducing damage to fuel assemblies inside a TN-32, a 1:6 scaled cask containing 32 mock-up fuel assemblies was manufactured for laboratory studies. Using the linear approach, metrics were developed that could detect cargo damage down to the single assembly level. To resolve the signatures of damaged versus missing assemblies, nonlinear ultrasound resonance spectroscopy was utilized to investigate the contact nonlinearity between a smaller scale container and loose spheres which mimicked internal debris. Based on the resulting data, a phenomenological contact-loss model was developed which could estimate the total mass of the spheres regardless of the material and radius.

Fatigue damage evaluation of carbon fiber reinforced composites using nonlinear resonance spectroscopy

The present work explores the use of nonlinear resonance spectroscopy to detect early fatigue damage in carbon fiber-epoxy composite laminates. The objective is to test composite samples at mid to high cycle fatigue (>10∧3 cycles), so that the damage evolution could be tracked. The nondestructive nature of the testing method ensures that the sample can be loaded and tested till failure, i.e. interrupted fatigue testing. The acoustic nonlinear response tracked over the fatigue life of the sample includes, the nonlinear frequency shift and modal damping ratio. Additionally, slow dynamic diagnostics was also carried out to investigate the recovery rate and recovery time. The samples that were tested were all quasi-isotropic laminates under 4-point bending load. These included a pristine sample, and two samples with impact damage to introduce variability. Tracking the nonlinear parameters over fatigue life showed a non-monotonic increase in nonlinearity. Conjectures based on acoustic response to microdamage and different stages of fatigue were used to explain the observed variation.

Multiscale model to study dislocation dynamics in nonlinear resonance spectroscopy of crystalline solids

This letter reports on a multi-scale model which captures the dislocation dynamics due to applied vibration stress and its influence on the bulk nonlinear response in a nonlinear resonance spectroscopy experiment. Due to dislocation dynamics, a sinusoidal variation in frequency shift could be observed at the low applied stress range, which was consistent with NRS experiments carried out on cold drawn steel. Using the model, NRS response to “Buck hook” phenomenon was also explored. The results showed that the frequency shift can exhibit three strain regions similar to non-classical nonlinear materials. Further discussions highlight the non-classical nonlinear nature of crystalline solids with lattice defects.

Influence of laminate sequence and fabric type on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

This paper presents the study of influence of laminate sequence and fabric type on the baseline acoustic nonlinearity of fiber-reinforced composites. Nonlinear elastic wave techniques are increasingly becoming popular in detecting damage in composite materials. It was earlier observed by the authors that the non-classical nonlinear response of fiber-reinforced composite is influenced by the fiber orientation [Chakrapani, Barnard, and Dayal, J. Acoust. Soc. Am. 137(2), 617-624 (2015)]. The current study expands this effort to investigate the effect of laminate sequence and fabric type on the non-classical nonlinear response. Two hypotheses were developed using the previous results, and the theory of interlaminar stresses to investigate the influence of laminate sequence and fabric type. Each hypothesis was tested by capturing the nonlinear response by performing nonlinear resonance spectroscopy and measuring frequency shifts, loss factors, and higher harmonics. It was observed that the laminate sequence can either increase or decrease the nonlinear response based on the stacking sequence. Similarly, tests were performed to compare unidirectional fabric and woven fabric and it was observed that woven fabric exhibited a lower nonlinear response compared to the unidirectional fabric. Conjectures based on the matrix properties and interlaminar stresses were used in an attempt to explain the observed nonlinear responses for different configurations.

Influence of fiber orientation on the inherent acoustic nonlinearity in carbon fiber reinforced composites.

This paper presents the study of non-classical nonlinear response of fiber-reinforced composites. Nonlinear elastic wave methods such as nonlinear resonant ultrasound spectroscopy (NRUS) and nonlinear wave modulation spectroscopy have been used earlier to detect damages in several materials. It was observed that applying these techniques to composites materials becomes difficult due to the significant inherent baseline nonlinearity. Understanding the non-classical nonlinear nature of the composites plays a vital role in implementing nonlinear acoustic techniques for material characterization as well as qualitative nondestructive testing of composites. Since fiber reinforced composites are orthotropic in nature, the baseline response variation with fiber orientation is very important. This work explores the nature of the inherent nonlinearity by performing nonlinear resonant spectroscopy (NRS) in intact unidirectional carbon/epoxy samples with different fiber orientations with respect to major axis of the sample. Factors such as frequency shifts, modal damping ratio, and higher harmonics were analyzed to explore the non-classical nonlinear nature of these materials. Conclusions were drawn based on the experimental observations.

In situ characterization of shallow elastic nonlinear parameters with Dynamic Acoustoelastic Testing

AbstractIn situ measurement of the elastic nonlinear site response is advantageous to provide optimal information for prediction of strong ground motion at a site. We report the first implementation of a technique known as Dynamic Acoustoelastic Testing (DAET) in situ with the ultimate goal of developing a new approach for site characterization. DAET has shown promising results at the laboratory scale for the study of nonlinear elasticity of Earth materials, detailing the full nonlinear elastic properties of the studied sample. We demonstrate the feasibility of DAET in situ and compare it to other methods (nonlinear resonance spectroscopy, wave amplitude dependence of propagation velocity, and wave distortion). Nonlinear elastic properties are characterized by DAET with the advantage of providing a local assessment compared to other methods, here at a depth of 4 m to 5 m. A vertical dynamic strain amplitude of 5 ×10−5produces a relative change in compressional wave modulus of 6%. We measure an effective parameter of quadratic elastic nonlinearity of order −103, the same order of magnitude measured at the laboratory scale in rocks and in packs of unconsolidated glass beads. Hysteresis is observed in the variation in soil elasticity as a function of the instantaneous dynamic strain that evolves as the dynamic strain amplitude is increased from 9 ×10−7to 5 ×10−5.

Anisotropy of dynamic acoustoelasticity in limestone, influence of conditioning, and comparison with nonlinear resonance spectroscopy

Anisotropy of wave velocity and attenuation induced by a dynamic uniaxial strain is investigated by dynamic acoustoelastic testing in limestone. Nonlinear resonance spectroscopy is performed simultaneously for comparison. A compressional resonance of the sample at 6.8 kHz is excited to produce a dynamic strain with an amplitude varied from 10(-7) to 10(-5). A sequence of ultrasound pulses tracks variations in ultrasonic velocity and attenuation. Variations measured when the ultrasound pulses propagate in the direction of the uniaxial strain are 10 times larger than when the ultrasound propagation occurs perpendicularly. Variations consist of a "fast" variation at 6.8 kHz and an offset. Acoustically induced conditioning is found to reduce wave velocity and enhance attenuation (offset). It also modifies "fast" nonlinear elastodynamics, i.e., wave amplitude dependencies of ultrasonic velocity and attenuation. At the onset of conditioning and beyond, different excitation amplitudes bring the material to non-equilibrium states. After conversion of velocity-strain dynamic relations into elastic modulus-strain dynamic relations and integration with respect to strain, the dynamic stress-strain relation is obtained. Analysis of stress-strain hysteresis shows that hysteretic nonlinear elasticity is not a significant source of the amplitude-dependent dissipation measured by nonlinear resonance spectroscopy. Mechanisms causing conditioning are likely producing amplitude-dependent dissipation as well.

Nonlinear acoustic resonances to probe a threaded interface

We evaluate the sensitivity of multimodal nonlinear resonance spectroscopy to torque changes in a threaded interface. Our system is comprised of a bolt progressively tightened in an aluminum plate. Different modes of the system are studied in the range 1–25 kHz, which correspond primarily to bending modes of the plate. Nonlinear parameters expressing the importance of resonance frequency and damping variations are extracted and compared to linear ones. The influence of each mode shape on the sensitivity of nonlinear parameters is discussed. Results suggest that a multimodal measurement is an appropriate and sensitive method for monitoring bolt tightening. Further, we show that the nonlinear components provide new information regarding the interface, which can be linked to different friction theories. This work has import to study of friction and to nondestructive evaluation of interfaces for widespread application and basic research.

Phase measurement in a collinear pump probe experiment: Application to molecular dynamics studies in liquids

We propose a novel approach of nonlinear resonant spectroscopy based on a collinear and degenerated pump probe experiment. This particular scheme leads to an oscillating time-resolved signal superimposed to the usual transient absorption signal. We have performed both amplitude and phase analysis of this oscillating signal as a function of the pump probe delay for different laser wavelengths. As an example, results on the resonantly excited dye molecule hexamethylindotricarbocyanine iodide (HITCI) in ethylene glycol at room temperature have been exploited in the framework of the phenomenological Brownian oscillator model. The corresponding numerical simulations have been carried out with a special emphasis on the phase sensitivity versus pump probe delay and detuning. The chromophore dynamical parameters obtained from phase variations of our signal are compared with other available spectroscopic studies.