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

Torsional Waves in an Infinite Elastic Solid Containing a Spheroidal Cavity

Dynamic response of pipelines buried in a back-filled rectangular trench in a semi-infinite medium has been investigated. The pipelines are modeled as long cylindrical shells of small thickness. By using the boundary integral representation and finite element method, we have studied the three-dimensional response to account for either pane P or SV wave incident at an arbitrary angle to the pipe-axis. In this paper numerical results are presented for the normal displacements, displacements along pipe-axis, and the hoop stresses in the pipe wall. It is shown that the response depends critically on the back-filled material as well as on the directions of propagation of the incident waves.

Dynamic Response of Pipelines Buried in Back-Filled Trenches

Using a scattered-plane-wave ensemble-average model developed for composite materials, we calculated the effective elastic constants of cast iron. We focused on the effect of graphite-particle aspect ratio on the Young modulus. Between model and observation, we found good agreement. Oblate-spheroidal graphite flakes lower the elastic stiffness much more than do spheres. To obtain good model-measurement agreement, one must use graphite’s lower third-order-bound (Kroner-bound) elastic constants.

Effect of Graphite Aspect Ratio on Cast-iron Elastic Constants

Dispersion of guided waves in laminated plates has been studied over the past thirty years. Recent work has included anisotropic layering and the subtle effects of fluid loading. References to these works can be found both in the review article by Chimenti and Nayfeh [1] and in the symposium proceedings edited by Mal and Ting [2]. More recently Braga and Herrmann detailed the features of the dispersion spectrum for anisotropic periodic media using the sextic formalism developed by Stroh [3, 4], implying coupling of inplane and out-of-plane particle motion. A similar discussion of the analysis of the acoustical or mechanical filtering predicted for such periodic media is presented by Rousseau [5]. However, guided waves in a laminated plate where the laminae have very different anisotropic (isotropic) properties from one another have not received adequate attention. This problem, which is the subject of this paper, has relevance in ultrasonic characterization of layered bonded plates when the interface (interphase) bond properties can be quite different than those of the adjacent laminae and can change during service life.

Subhendu K. Datta

Papers

Torsional Waves in an Infinite Elastic Solid Containing a Spheroidal Cavity

Dynamic Response of Pipelines Buried in Back-Filled Trenches

Effect of Graphite Aspect Ratio on Cast-iron Elastic Constants

Elastic Wave Propagation in Aluminum/Aramid-Epoxy Plates

On the performance of plate-bending elements for wave propagation problems