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

A hybrid numerical method combining finite elements and the boundary integral representation is used to investigate the transient scattering of ultrasonic waves by a crack in a plate. The incident wave models the guided waves generated by a steel ball impact on the plate. Two surface-breaking cracks and one subsurface crack are studied here. The results show that the location and depth of cracks have measurable effects on the surface responses in time and frequency domains. Also, the scattered fields have distinct differences in the three cases.

Scattering of Ultrasonic Wave by Cracks in a Plate

Scattering by an infinite transversely isotropic cylinder in a transversely isotropic medium

The dynamic response of a cylindrical tunnel embedded in a semiinfinite elastic medium is analyzed. The tunnel is assumed to be infinitely long, noncircular in cross section, and lying parallel to the plane‐free surface of the medium. The problem considered is one of plane strain, in which it is assumed that the waves are propagating perpendicular to the axis of the tunnel. Since this problem cannot be solved exactly except when the tunnel is circular, a numerical technique that combines the finite element method with the eigenfunction expansions is used. Numerical results are presented for the cases in which the tunnel is disturbed by plane longitudinal (P), vertically polarized shear (SV) and Rayleigh (R) waves. It is shown that the dynamic amplifications of the displacements and stresses induced in the tunnel depend crucially on the properties of the surrounding soil, the depth of embedment and the frequency of the incident simple harmonic disturbance.

Dynamic Stresses and Displacements in a Buried Tunnel

In recent years, the study of thermoelastic waves generated by focused laser beams has been undertaken by several researchers because the technique provides a means for noncontact generation of ultrasonic waves. Laser-generated ultrasonic waves have diverse applications ranging from material characterization to nondestructive testing of defects. Transient ultrasonic guided waves generated in an anisotropic infinite plate by a pulsed laser beam are investigated in this study. A semi-analytical finite element method (SAFEM) is adopted for this purpose. In this method, the plate is divided into parallel layers through its thickness and the displacement and temperature in each layer are approximated by quadratic polynomials in the thickness direction (z). They are assumed to be continuous functions of time and in-plane cartesian coordinates (x, y). Transient response is calculated using Fourier transformations in time and space variables (x, y). The analysis technique is applicable to a generally ani...

Laser-Generated Thermoelastic Waves in an Anisotropic Infinite Plate: FEM Analysis

A wave function expansion is used. Wave function are obtained using a propagator matrix approach for laminated isotropic cylinders and by a Rayleigh Ritz type approximation for laminate composite cylinders. The least square technique as well as the variational method are employed to evaluate the complex amplitudes and the energy flux associated with the reflected waves

Subhendu K. Datta

Papers

Scattering of Ultrasonic Wave by Cracks in a Plate

Scattering by an infinite transversely isotropic cylinder in a transversely isotropic medium

Dynamic Stresses and Displacements in a Buried Tunnel

Laser-Generated Thermoelastic Waves in an Anisotropic Infinite Plate: FEM Analysis

Reflection of Waves at the Free Edge of a Laminated Circular Cylinder