Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook

Publisher Summary This chapter focuses on variational and related methods for the overall properties of composites. A wide range of phenomena that are observable macroscopically are governed by partial differential equations that are linear and self-adjoint. This chapter is concerned with such phenomena for materials, such as fiber-reinforced composites or polycrystals, whose properties vary in a complicated fashion from point to point over a small, “microscopic” length scale, while they appear “on average” (that is, relative to the larger, macroscopic scale) to be uniform. This chapter treats the elastic behavior of composites, and emphasizes that a number of other properties (conductivity, viscosity of a suspension, etc.) are described by the same equations. Extensions to viscoelastic and thermoelastic behavior are presented, for both of which the variational characterization given is believed to be new. Problems, such as the resistance to flow of viscous fluid through a fixed bed of particles are mentioned, and a model problem that involves diffusion is presented in some detail. This displays the same difficulty in relation to divergence of an integral and is one problem of this type that has so far been approached variationally. Methods related to the Hashin–Shtrikman variational principle are also described in the chapter.

Variational and Related Methods for the Overall Properties of Composites

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

Ultrasonic guided wave inspection is expanding rapidly to many different areas of manufacturing and in-service inspection. The purpose of this paper is to provide a vision of ultrasonic guided wave inspection potential aswe move forward into the new millennium. An increased understanding of the basic physics and wave mechanics associated with guided wave inspection has led to an increase in practical nondestructive evaluation and inspection problems. Some fundamental concepts and a number of different applications that are currently being considered will be presented in the paper along with a brief description of the sensor and software technology that will make ultrasonic guided wave inspection commonplace in the next century.

A Baseline and Vision of Ultrasonic Guided Wave Inspection Potential

On transient ultrasonic waves in a homogeneous plate with thin superconducting coating layers

Ultrasonic measurements of wave-propagation characteristics in composite and heterogeneous materials provide an excellent means to study their mechanical properties. In recent years we have studied, both theoretically and experimentally, characteristics of elastic-wave propagation in particlereinforced composites and heterogeneous materials as well as in homogeneous and laminated fiber-reinforced composites. Comparison of theoretical predictions with obervations of wave velocities has shown good agreement and has provided a way to evaluate microstructural dependence of mechanical properties of these materials. Modeling predictions coupled with observations can also be used to obtain mechanical properties of the reinforcing phase, which are sometimes not easily obtained. In this paper we present results of some of these recent studies.

Ultrasonic Velocity Studies of Composite and Heterogeneous Materials

Elastic wave scattering by surface defects like cracks, corrosion induced pits, topographic irregularitieSv etc., is of interest for ultrasonic nondestructive evaluation and in seismology. Scattering by surface-breaking cracks has been studied by many authors in recent years. References to papers on scattering by surface-breaking cracks can be found in [1,2]. The corresponding problem of cavities at the surface and topographic irregularities has been studied in seismology (see, for example, [3,4]). Almost all the studies have dealt with two-dimensional problems (for references to some 3-D scattering see [5]).

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1884&context=qnde

Three Dimensional Scattering of Elastic Waves by Surface Corrosion Pits

Elastic Constants of Porous Ceramics

Propagation of guided waves in a laminated plate is of interest for ultrasonic nondestructive evaluation of defects and for material characterization. There is a need for a thorough understanding of the wave propagation characteristics in such a plate in order to use ultrasonic means to determine the material properties, assess damage, and characterize defects. The problem is also of interest for study of acoustic emission.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=2907&context=qnde

Subhendu K. Datta

Papers

On transient ultrasonic waves in a homogeneous plate with thin superconducting coating layers

Ultrasonic Velocity Studies of Composite and Heterogeneous Materials

Three Dimensional Scattering of Elastic Waves by Surface Corrosion Pits

Elastic Constants of Porous Ceramics

Transient response of a laminated composite plate