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

Early work on dispersion of Rayleigh and Love waves was by Love [1], who gave the first comprehensive treatment of the case of an elastic solid half-space covered by a single solid layer.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=2393&context=qnde

Rayleigh and Love Waves in Cladded Anistropic Medium

Guided waves and the transient response of multilayered superconducting tapes have been studied in this article. These tapes are usually composed of layers of a superconducting material (like YBa2Cu3O7−δ, or YBCO, for simplicity) alternating between layers of a metallic material (like nickel or silver). The tapes are thin, the thickness being in the range of 100–200 μm. The superconducting layer is orthotropic with a thickness of 5–10 μm. In applications, the tapes are long and have a finite width. In this article, we focus our attention on the dispersion of two-dimensional guided waves and the transient response of homogeneous and three-layered tapes assuming that the thickness of the superconducting layer is much smaller than the metal layer. Three tape geometries are considered: a homogeneous nickel layer, a three-layered YBCO/nickel/YBCO and a three-layered nickel/YBCO/nickel. It is found that although the total thickness of the YBCO layer is very small, the dispersion and transient response in the la...

https://blogs.uakron.edu/ernianpan/files/2014/09/036_1999JAPPanDatta.pdf

Ultrasonic waves in multilayered superconducting plates

Elastic wave propagation in laminated composite plates

This study contains three components: measurement, modeling, and inverse modeling to get the fiber elastic constants. The studied composite consisted of 70 vol % continuous uniaxial graphite fibers in a magnesium matrix. By ultrasonic‐velocity methods, we measured the composite’s complete orthotropic‐symmetry (nine‐independent‐component) elastic‐constant tensor: Cij in Voigt contracted notation. Approximately, the composite shows transverse‐isotropic symmetry. For a model, we used a wave‐scattering method in the long‐wavelength limit. The model requires two inputs: the two isotropic matrix elastic constants and the five anisotropic fiber elastic constants. We measured the first and guessed the second based on graphite‐fiber elastic constants reported by others. This guess gave good measurement‐model agreement only for C11, C22, and C33. Especially, the shear moduli Cii (i=4,5,6) agreed poorly (a 20% difference). Using inverse modeling—calculating fiber properties from measured matrix properties and measur...

Subhendu K. Datta

Papers

Rayleigh and Love Waves in Cladded Anistropic Medium

Ultrasonic waves in multilayered superconducting plates

Elastic wave propagation in laminated composite plates

Elastic constants of a graphite‐magnesium composite

Scattering of flexural waves by a crack in a plate