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The book sets the stage for nonlinear ultrasonic guided waves by introducing nonlinear wave propagation in 1D and the fundamental mathematical and continuum mechanics background necessary for the nonlinear wave propagation physics. It develops the so-called internal resonance criteria and its application to different guided wave types. An important and unique aspect covered is the selection of primary wave modes and frequencies for cumulative second harmonic generation and wave mixing. Numerical simulations will demonstrate the results of effective selection choices. Experimental methods and signal processing are critical for detecting the subtle results of nonlinearity. Finally, the author provides perspective on the future development of nonlinear ultrasonic guided wave methods for nondestructive evaluation.
Key Features
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Provides an entry point for those interested in the research and development of nondestructive evaluation using nonlinear ultrasonic guided waves.
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Self-contained in terms of the background necessary for effective analysis of nonlinear ultrasonic guided waves; it emphasizes the differences between nonlinear guided waves and nonlinear bulk waves.
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Empowers readers to become doers, as sufficient details are provided, as opposed to skipping steps to be concise.
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Examples and case studies are provided to demonstrate the application of key concepts.
1. Introduction a. Motivation b. Historical perspective c. Approach d. Content 2. Preliminaries a. Continuum mechanics b. Elastodynamics 3. Wave Equation a. Surfaces b. Plates c. Pipes d. Arbitrary sections e. Linear f. Nonlinear 4. Ultrasonic Guided Waves – Linear Features a. Phase velocity dispersion curves b. Group velocity dispersion curves c. Anisotropic waveguides d. Attenuation 5. Ultrasonic Guided Waves – Nonlinear Features a. Self-interaction i. Second harmonic generation ii. Third harmonic generation b. Mutual interaction i. Co-directional ii. Counter-propagating iii. Non-collinear 6. Selection of Primary Waves a. Cumulative secondary waves b. Non-cumulative secondary waves 7. Numerical Simulations a. Methods b. Software tools c. Sample problems 8. Sensing Systems a. Instrumentation b. Generation c. Reception d. Signal processing 9. Material - Wave Distortion Connection a. Plastic deformation b. Fatigue cracking
c. Inclusions 10. Perspective a. Current capabilities b. Future possibilities