Doctoral Defense - Yoganandh Madhuranthakam

About the Event

The Department of Electrical and Computer Engineering 

Michigan State University 

Ph.D. Dissertation Defense 

Wednesday, July 16, 2025, at 10:00 am 

Electrical and Computer Engineering Conference Room EB 2219 

Join Zoom: https://msu.zoom.us/j/3557769134?omn=93399804917

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ABSTRACT

NONLINEAR ACOUSTIC WAVE PROPAGATION IN LAYERED MEDIA AND ITS APPLICATION TO CHARACTERIZING MATERIAL NONLINEARITY

BY: YOGANANDH MADHURANTHAKAM

ADVISOR: DR. SUNIL KISHORE CHAKRAPANI

This dissertation investigates nonlinear acoustic wave propagation in inhomogeneous media for measuring the acoustic nonlinearity parameter (β), which reflects how material stiffness responds to large deformations and serves as a sensitive indicator of internal microstructural features such as dislocations, precipitates, and early-stage damage in solids and fluids. Conventional techniques, such as contact-based detection and interferometry, face limitations due to calibration sensitivity, variability, and geometric constraints. Immersion-based methods improve repeatability but introduce modeling challenges related to diffraction, attenuation, and multilayer interactions. To overcome these, a theoretical model based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was developed for n-layer media, featuring a novel diffraction correction that ensures Fresnel zone continuity that doesn't violate the physics of diffraction. This model supports an inversion algorithm that estimates β by minimizing slope differences between measured and predicted second harmonic pressures. The model was validated using fused silica and the inversion algorithm was used to predict β of rolled aluminum, showing strong agreement with literature values of β. 

To further understand nonlinear wave propagation in n-layer media, a unified model for nonlinear diffraction and attenuation in layered media is proposed. Unlike conventional layer-wise models that treat each layer as a new source, the unified model incorporates three key hypotheses: (1) the existence of a single Fresnel zone across all layers, (2) accumulated second harmonic waves propagate linearly and diffract with the source frequency, and (3) their attenuation is frequency-dependent. These hypotheses were tested by defining four cases and validated using numerical simulations. The results suggest that the unified model shows better agreement with numerical results than existing layer-wise approaches, especially for the high impedance mismatch cases. 

To simplify the present experimental procedure for measuring the calibration function of a transducer, a novel narrowband calibration method was developed. Measurement of narrowband calibration functions at specific frequencies of interest was demonstrated using immersion transducers. The sensitivity of the technique was assessed by evaluating the calibration function and the corresponding β of water for different values of source power, propagation length, and reflection coefficient. 

To further simplify the process of measuring the acoustic nonlinearity parameter β, a reference-based inversion framework was developed. This eliminates the need to calibrate the transducer by normalizing the second harmonic response using the response from a reference solid with known nonlinearity. This framework combines the previously developed theoretical model for nonlinear wave propagation with experimental measurements from immersion tests. Specifically, the ratio of second harmonic amplitudes measured for the test and reference solids is matched to the corresponding 

ratio of diffraction and attenuation losses predicted by the model. This method was used to measure β for cast aluminum, Ti-64, and SS 420, and the measured values were consistent with those reported in the literature. 

Measuring acoustic nonlinearity (B/A) and attenuation in liquids is crucial to understand their molecular structure and has been used to study contrast agents in ultrasound imaging and the compressibility and pressure-density relationship of fluids. To enable such characterization without calibration requirements or large sample volumes, the reference-based approach of solids was extended to liquids. The test involves placing a small amount of liquid in a thin-walled container that is immersed in water, forming a three-layer configuration similar to the method used for solids. This technique was used to successfully measure both B/A and α of salt water, olive oil, and fresh and degraded engine oils. 

Together, these contributions establish a robust, calibration-independent framework for nonlinear acoustic characterization in solids and liquids. By integrating modeling, inversion, calibration, and application across diverse materials, this work advances ultrasonic nondestructive evaluation and enables new approaches in nonlinear acoustics. 

Persons with disabilities have the right to request and receive reasonable accommodation. Please call the Department of Electrical and Computer Engineering at 355-5066 at least one day prior to the seminar; requests received after this date will be met when possible.