Third harmonic shear horizontal and Rayleigh Lamb waves in weakly nonlinear plates
TL;DR: In this paper, the third order harmonic generation due to the cubic interaction of two collimated elastic waves in a homogeneous, isotropic, weakly nonlinear plate is investigated by using a fourth order expansion of strain energy density to formulate the nonlinear boundary problems.
Abstract: The third order harmonic generation (third harmonics as well as cubic sum and difference harmonics) due to the cubic interaction of two collimated elastic waves in a homogeneous, isotropic, weakly nonlinear plate is investigated by using a fourth order expansion of strain energy density to formulate the nonlinear boundary problems. Waves with both shear horizontal (SH) and Rayleigh Lamb (RL) nature are considered as primary or tertiary wave fields. The non-zero power flux condition is evaluated using characteristic parity matrices of the cubic nonlinear forcing terms and third order harmonic mode shapes. Results indicate that waves with either SH or RL nature receive power flux from a specific pattern of primary mode interaction. Further analytical evaluation of the synchronism condition enables identification of primary SH and RL modes that are able to generate cumulative third harmonics. The primary SH modes are shown to be holo-internal-resonant with third harmonic SH fields. This simply means that all points on the primary dispersion curves are internally resonant with third harmonics, which is not the case for second harmonics. Such flexibility will be advantageous for laboratory and field measurements.
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TL;DR: In this paper, the authors review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility, including the application of higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation.
Abstract: Interest in using the higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation continues to grow tremendously as the understanding of nonlinear guided wave propagation has enabled further analysis. The combination of the attractive properties of guided waves with the attractive properties of higher harmonic generation provides a very unique potential for characterization of incipient damage, particularly in plate and shell structures. Guided waves can propagate relatively long distances, provide access to hidden structural components, have various displacement polarizations, and provide many opportunities for mode conversions due to their multimode character. Moreover, higher harmonic generation is sensitive to changing aspects of the microstructures such as to the dislocation density, precipitates, inclusions, and voids. We review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility.
107 citations
TL;DR: In this paper, a review of the state-of-the-art SH wave transducers for structural health monitoring (SHM) and nondestructive testing (NDT) is presented.
67 citations
TL;DR: The use of nonlinear ultrasonics to characterize microstructural evolution is investigated with the aim of enabling earlier remaining useful life prediction and thereby greatly improving condition based maintenance as discussed by the authors.
Abstract: The use of nonlinear ultrasonics to characterize microstructural evolution is investigated with the aim of enabling earlier remaining useful life prediction and thereby greatly improving condition based maintenance. Higher harmonic generation is sensitive to microstructural features, whose evolution is indicative of ongoing damage processes. Localized plastic deformation is controlled in an aluminum sample by varying the notch length, which dictates the extent of the plastic zone. The essentials of higher harmonic generation analysis for ultrasonic guided waves are highlighted to provide a means to select a primary mode that generates a strong higher harmonic. Experimental methods to use magnetostrictive transducers for third harmonic generation measurements are described. Experimental results on aluminum plates indicate that plastic deformation increases the third harmonic by up to a factor of five and that the harmonic amplitude ratio $$A_{3}$$
/
$$A_{1}^{3}$$
is sensitive to the plastic strain magnitude. These initial results show that when the plastic strain is localized, the $$A_{3}$$
/
$$A_{1}^{3 }$$
ratio appears to be proportional to the plastic zone-to-propagation distance ratio.
54 citations
TL;DR: In this paper, the symmetric Lamb mode (S0) at low frequency region is explored, and the S0 mode is little dispersive and easy to generate, however, the secondary mode still exists, and increases linearly for significant distance.
Abstract: Nonlinear ultrasonic Lamb waves are popular to characterize the nonlinearity of materials. However, the widely used nonlinear Lamb mode suffers from two associated complications: inherent dispersive and multimode natures. To overcome these, the symmetric Lamb mode (S0) at low frequency region is explored. At the low frequency region, the S0 mode is little dispersive and easy to generate. However, the secondary mode still exists, and increases linearly for significant distance. Numerical simulations and experiments are used to validate the nonlinear features and therefore demonstrate an easy alternative for nonlinear Lamb wave applications.
54 citations
TL;DR: This Tutorial focuses on the physical principles of nonlinear ultrasonic guided waves leading to the so-called internal resonance conditions that provide a means for selecting primary waves that generate cumulative secondary waves that transform how the service lives of structural systems are managed.
Abstract: Research into the use of nonlinear ultrasonic guided waves for nondestructive evaluation is expanding at a high rate because of the great potential benefit that they possess for early detection of material degradation. However, development of inspection and testing strategies is complicated because (i) the underlying physical principles are complex, (ii) there is a broad spectrum of possible solutions but only a limited number that have been shown to be effective, and (iii) the nonlinearity is weak and thus its measurement is challenging. This Tutorial aims to provide a foundation for researchers and technology-transitioners alike, to advance the application of nonlinear ultrasonic guided waves and ultimately transform how the service lives of structural systems are managed. The Tutorial focuses on the physical principles of nonlinear ultrasonic guided waves leading to the so-called internal resonance conditions that provide a means for selecting primary waves that generate cumulative secondary waves. To detect material degradation, we are primarily interested in nonlinearity stemming from the material itself, which is represented as hyperelastic. For the special case of plates, internal resonance points have been identified and case studies are presented to illustrate some of the applications. The Tutorial has one new result not published in a research paper; finite element simulation of energy transfer from shear-horizontal primary waves to symmetric Lamb waves at the second harmonic.
47 citations
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Book•
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01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
Book•
01 Jan 1973
TL;DR: In this article, the authors apply the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators).
Abstract: This work, part of a two-volume set, applies the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators). The text also covers topics such as perturbation and variational methods.
5,211 citations
Book•
01 Sep 2004
TL;DR: In this article, the theory of elasticity was introduced and basic formulas and concepts in complex variables in the theory and application of wave propagation were discussed. But the authors did not consider the effects of wave scattering on the wave propagation experiments.
Abstract: Preface 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Wave scattering 7. Surface and subsurface waves 8. Waves in plates 9. Interface waves 10. Layer on a half space 11. Waves in rods 12. Waves in hollow cylinders 13. Guided waves in multiple layers 14. Source influence 15. Horizontal shear 16. Waves in an anisotropic layer 17. Elastic constant determination 18. Waves in viscoelastic media 19. Stress influence 20. Boundary element methods Bibliography Appendices A. Ultrasonic nondestructive testing principles, analysis and display technology B. Basic formulas and concepts in the theory of elasticity C. Basic formulas in complex variables D. Schlieren imaging and dynamic photoelasticity E. Key wave propagation experiments Index.
2,570 citations
757 citations