There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

Wave propagation and group velocity

Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.

Ultrasonic Guided Waves in Solid Media

The paper provides a state of the art review of guided wave based structural health monitoring (SHM). First, the fundamental concepts of guided wave propagation and its implementation for SHM is explained. Following sections present the different modeling schemes adopted, developments in the area of transducers for generation, and sensing of wave, signal processing and imaging technique, statistical and machine learning schemes for feature extraction. Next, a section is presented on the recent advancements in nonlinear guided wave for SHM. This is followed by section on Rayleigh and SH waves. Next is a section on real-life implementation of guided wave for industrial problems. The paper, though briefly talks about the early development for completeness,. is primarily focussed on the recent progress made in the last decade. The paper ends by discussing and highlighting the future directions and open areas of research in guided wave based SHM.

https://iopscience.iop.org/article/10.1088/0964-1726/25/5/053001/pdf

Guided wave based structural health monitoring: A review

Monitoring the structural condition of road and airport pavement is an extremely critical task to ensure the safety and efficiency of teh transportation. The topic is relevant to both civil and military transportation infrastructure. The presence of damage in pavement, including surface cracking, depressions, swells, and wear, is inevitable due to the sever environmental and service loads that these structures must be subject to. Existing NDE techniques aimed at assessing the structural condition of pavement include Falling Weight Deflectometer, Ground Penetrating Radar, and acoustic methods based on surface waves.
This paper presents improvements to the traditional surface-wave method for the detection of surface-breaking cracks in pavement. The advances include 1) the modeling of the problem as dipsersive waves propagating in a multilayer system, 2) the inclusion of post-processing algorithms based on the Wavelet Transform to improve the sensitivity and accuracy of the inspection, and 3) the use of non-contact, air-coupled acoustic detectors to enhance the mobility of the inspection unit.
The crack detection procedure consists of first generating a dispersive wave with an impulse hammer, and then measuring the changes in velocity, amplitude and/or frequency content as the wave travels across the flaw with the aid of the Continuous Wavelet Transform. Multilayer wave propagation modeling provides a better understanding of the experimental results by predicting how the various frequencies interact with cracks of different depths.
The results of field tests will be presented for both rigid (concrete-based) and flexible (bitumen-based) pavement with surface cracks.

Mobile acoustic system for the detection of surface-breaking cracks in pavement

A novel Augmented Reality (AR) tool for structural health monitoring is illustrated in this work. It provides maintenance operators with the results of an impact detection methodology. It interacts with an eyepiece allowing the inspector to see the estimated impact position on the structure. Electric signals are collected by a network of piezosensors bonded on the structure to be monitored. Dispersive propagation compensation is performed to improve estimation robustness. Hyperbolic beamforming is exploited to locate the impact. Real-time impact data are finally fed to the AR eyepiece. The proposed approach is tested on a Cessna 150 engine cowling. Experimental results confirm the feasibility of the method and its exploitability in maintenance practice.

Augmented Reality Tools for Structural Health Monitoring Applications

Guided waves in Structural Health Monitoring per-mit to detect different types of damage inside a structure, such as cracks, as well as external impacts. A precise localisation of the damage or the impact point is necessary in order to improve the reliability and accuracy of monitoring approaches. A localisation algorithm based on the estimation of the waves Direction of Arrival (DoA) by means of a DFT-Based Continuous Wavelet Transform decomposition is presented in this work. The approach exploits a multiresolution DFT-Based CWT decomposition applied to the signals acquired by cluster of three piezoelectric (PZT) transducers in 60 degrees configuration. The multiple frequency-based filtering of the signals in the wavelet domain counteracts the complexity caused by the dispersive characteristics of the material. Subsequently the cross-correlation method and the angle estimation are applied for each computed scale. Finally, the Direction of Arrival is computed by an averaging procedure across scales. The approach is validated by means of an experimental setup. The results show the accuracy of the proposed algorithm, enabling to estimate the DoA with an average error of 1.15 degrees and a maximum error of 1.74 degrees.

Lamb waves Direction of Arrival estimation based on wavelet decomposition

We provide an analytical formulation to model the propagation of elastic waves in a homogeneous half-space supporting an array of thin plates. The technique provides the displacement field obtained from the interaction between an incident wave generated by a harmonic source and the scattered fields induced by the flexural motion of the plates. The scattered field generated by each plate is calculated using an ad-hoc set of Green's functions. The interaction between the incident field and the scattered fields is modeled through a multiple scattering formulation. Owing to the introduction of the multiple scattering formalism, the proposed technique can handle a generic set of plates arbitrarily arranged on the half-space surface. The method is validated via comparison with finite element simulations considering Rayleigh waves interacting with a single and a collection of thin plates. Our framework can be used to investigate the interaction of vertically polarized surface waves and flexural resonators in different engineering contexts, from the design of novel surface acoustic wave devices to the interpretation of urban vibrations problems.

A multiple scattering formulation for finite-size flexural metasurfaces

In this work, a novel piezoelectric sensor for guided waves detection on laminate composite and metallic structures is presented. The sensor is composed by two electrodes (E1 and E2) on the top surface of the device, plus a common electrode (EC) on the bottom surface, which is bonded to the structure to be inspected. E1 has a circular shape, whereas E2 is shaped as a segment of a logarithmic spiral (or spira mirabilis). Because of this asymmetric shaping, the wavefront of a generic acoustic event (e.g. the one generated by an impact) hits the electrodes in two points whose distance D varies with the Direction of Arrival (DoA) of the wave itself. With a dedicated processing procedure, the information about the distance D first, and then about the DoA can be retrieved from the waveforms acquired and digitized at the two electrodes E1 and E2. In particular, the procedure computes the cross-correlation of the dispersion compensated signals, and extracts the distance D by looking at the position of the maximum of the cross-correlation envelope. Here, a first experimental test is performed to validate the effectiveness of the proposed technology.

Alessandro Marzani

Papers

Mobile acoustic system for the detection of surface-breaking cracks in pavement

Augmented Reality Tools for Structural Health Monitoring Applications

Lamb waves Direction of Arrival estimation based on wavelet decomposition

A multiple scattering formulation for finite-size flexural metasurfaces

Spira Mirabilis: a shaped piezoelectric sensor for impact localization