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

Transient ultrasonic guided waves in anisotropic layered plates with finite and infinite width are presented in this article. A semianalytical finite-element method is adopted to study the guided waves in both infinite- and finite-width elastic plates. Three-noded beam elements in the thickness direction are used in infinite plate model, whereas the cross section of the finite-width plate is represented by nine-noded quadrilateral elements. Propagation in the axial direction is modeled by analytical wave functions. Elastodynamic Green’s functions are derived using modal summation in the frequency–wave number and time–space domains. Results for dispersion and transient analysis of guided waves in infinite nickel plates are presented and compared with those of finite-width plates. Group velocities are calculated and wave arrival times are computed for different plate cross sections. Numerical results show a significant influence of the plate aspect ratio on the dispersion and transient wave response. The co...

Transient ultrasonic guided waves in layered plates with rectangular cross section

The scattering of elastic waves by elastic inclusions surrounded by interface layers is a problem of interest for nondestructive evaluation of interfaces in composites. In the present paper the scattering by a single elastic inclusion is studied. The scattering problem is solved by means of the null field approach and the properties of the interface layer enters through the boundary conditions on the inclusion

Elastodynamic Scattering From Inclusions Surrounded by Thin Interface Layers

A hybrid method is presented for analyzing scattering of time-harmonic plane strain waves by cracks in an infinite laminated composite plate. The modeling is achieved by dividing the domain into two regions: an interior region that consists of the cracks and a finite region of the plate around the cracks; and an unbounded exterior region. The hybrid method combines a finite element formulation in the interior region with a wave-function expansion representation in the exterior region. The method is illustrated through solving the problem of scattering by a symmetric normal-edge crack. Numerical results for the reflection coefficients are presented for an isotropic plate, a homogeneous fiber-reinforced plate, and a laminated fiber-reinforced plate. The validity and accuracy of the results are checked by satisfaction of the reciprocity relations and the principle of energy conservation. The technique presented can be used to characterize cracks in laminated composite plates.

Plane-strain-wave scattering by cracks in laminated composite plates

Ultrasonic waves provide an efficient means of characterizing defects in structures. For this purpose it is necessary to analyze scattering by such defects. However, scattering by crack-like defects in a plate-like structure is a complicated phenomenon and the problem is made more difficult if it is a composite plate. In recent years considerable progress has been made toward understanding wave propagation in anisotropic composite plates [1–5], but not much work has been done on the scattering by cracks in a composite plate. Recently Karim and Kundu [6] and Karim et al. [7] studied scattering of elastic waves in a layered half-space and in layered fiber-reiforced composite plates by interface cracks using a boundary integral formulation. They considered antiplane motions. Although this method can be extended to plane strain motion the computional effort is considerably amplified if one considers a plate geometry. Besides, the method used by these authors is limited to planar defects. For arbitrarily shaped scatterers Sanchez-Sesma [8] reviewed various applicable methods. Most of these numerical methods require considerable computational effort to evaluate the response. Their applicability to layered and anisotropic medium is also limited.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=2721&context=qnde

Scattering of an Impact Wave by a Crack in a Composite Plate

An analysis of the propogation of thermoelastic waves in a homogeneous, anisotropic, thermally conducting plate has been presented in the context of the generalized Lord-Shulman theory of thermoelasticity. Three different methods are used in this analysis: two of them are exact and the third is a semianalytic finite element method (SAFE). In our exact analysis, two different approaches are used. The first one, which is applicable to transversely isotropic plate, is based on introducing displacement potential functions, whereas in the second approach, which is applicable to any triclinic material, we rewrite the governing equations and boundary conditions in a matrix form. Finally, in the SAFE method, the plate is discretized along its thickness using N parallel, homogeneous layers, which are perfectly bonded together. Frequency spectrum and dispersion curves are obtained using the three methods and are shown to agree well with each other. The effects of thermal relaxation time and coupling term are also i...

Subhendu K. Datta

Papers

Transient ultrasonic guided waves in layered plates with rectangular cross section

Elastodynamic Scattering From Inclusions Surrounded by Thin Interface Layers

Plane-strain-wave scattering by cracks in laminated composite plates

Scattering of an Impact Wave by a Crack in a Composite Plate

Thermoelastic waves in an anisotropic infinite plate