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

Three-Dimensional Dynamic Response of Buried Pipelines to Incident Longitudinal and Shear Waves

Scattering of flexural waves by cavities in a plate

The elastic properties of many materials in sheet or plate form can be approximated with orthotropic symmetry. In many sheet material manufacturing industries (e.g., the paper industry), manufacturers desire knowledge of certain anisotropic elastic properties in the sheet for handling and quality issues. Ultrasonic wave propagation in plate materials forms a method to determine the anisotropic elastic properties in a nondestructive manner. This work explores exact and approximate analysis methods of ultrasonic guided wave propagation in thin layers, explicitly dealing with orthotropic symmetry and propagation off-axis with respect to the manufacturing direction. Recent advances in full-field ultrasonic imaging methods, based on dynamic holography, allow simultaneous measurement of the plate wave motion in all planar directions within a single image. Results from this laser ultrasonic imaging approach are presented that record the lowest anti-symmetric (flexural) mode wavefront in a single image without scanning. Specific numerical predictions for flexural wave propagation in two distinctly different types of paper are presented and compared with direct imaging measurements. Very good agreement is obtained for the lowest anti-symmetric plate mode using paper properties independently determined by a third party. Complete determination of the elastic modulus tensor for orthotropic layers requires measurement of other modes in addition to the lowest anti-symmetric. Theoretical predictions are presented for other guided wave modes [extensional (S), flexural (A), and shear-horizontal (SH)] in orthotropic plates with emphasis on propagation in all planar directions. It is shown that there are significant changes in the dispersion characterization of these modes at certain frequencies (including off-axis mode coupling) that can be exploited to measure additional in-plane elastic moduli of thin layers. At present, the sensitivity of the imaging measurement approach limits experimental investigation to relatively large amplitudes easily produced by flexural wave motion (>0.1 nm). Extension of the measurement range and application to other plate wave modes are in progress and shall be reported in future work.

Off-axis propagation of ultrasonic guided waves in thin orthotropic layers: theoretical analysis and dynamic holographic imaging measurement

Elastic Wave Propagation in Laminated Composite Plates

Scattering of Rayleigh-Lamb waves by a normal surface-breaking crack in a plate has been studied both theoretically and experimentally. The two-dimensionality of the far field, generated by a ball impact source, is exploited to characterize the source function using a direct integration technique. The scattering of waves generated by this impact source by the crack is subsequently solved by employing a Green's function integral expression for the scattered field coupled with a finite element representation of the near field. It is shown that theoretical results of plate response, both in frequency and time, are similar to those obtained experimentally. Additionally, implication for practical applications are discussed.

Subhendu K. Datta

Papers

Three-Dimensional Dynamic Response of Buried Pipelines to Incident Longitudinal and Shear Waves

Scattering of flexural waves by cavities in a plate

Off-axis propagation of ultrasonic guided waves in thin orthotropic layers: theoretical analysis and dynamic holographic imaging measurement

Elastic Wave Propagation in Laminated Composite Plates

Experimental and Theoretical Study of Rayleigh-Lamb Waves in a Plate Containing a Surface-Breaking Crack