MODELING OF PIEZO-INDUCED ULTRASONIC WAVE PROPAGATION FOR STRUCTURAL HEALTH MONITORING A DISSERTATION SUBMITTED TO THE DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Kuldeep P. Lonkar August 2013 © 2013 by Kuldeep Prakash Lonkar. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/sm236hy1179 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Fu-Kuo Chang, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Richard Christensen I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Kincho Law Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract The process of implementing a damage detection and characterization strategy for engineering structures is referred to as structural health monitoring (SHM). Recently, damage detection using piezoelectric actuators and sensors has gained extensive at- traction. Piezoelectric actuators are used to induce elastic stress waves that can propagate for long distances in thin-walled structures with very little amplitude loss enabling inspection of large areas of a structure. These waves interact with damage and provide information on location, size, and type of damage; this information is extracted from sensor signals by diagnostic algorithms. However, these signals are sensitive to the operating conditions. Change in ambient temperature or loading con- ditions may affect the wave propagation and the sensor response leading to inaccurate diagnostics. Hence, fundamental understanding of the physics of wave propagation, their interaction with the structure, and the influence of varying operating conditions is crucial for developing appropriate diagnostic algorithms. Therefore, the prime objectives of this investigation are: (i) develop an efficient and accurate numerical model to simulate the sensor signals and the piezo-induced acoustoelastic wave propagation in prestressed homogeneous and layered media, (ii) study the effect of load on wave propagation (acoustoelastic effect) and varying am- bient temperature on the sensor signals. A numerical model called Piezo-Enabled Spectral Element Analysis (PESEA), based on spectral element method is developed. PESEA can accurately and efficiently simulate ultrasonic wave propagation in complex structures with built-in piezoelectric sensor network. Experiments and simulations are performed on metallic and compos- ite structures to verify and validate the accuracy of PESEA. Fatigue cracks in metallic iv structures and debond/delamination is laminated composite structures are modeled by separating the nodes to create volume split. Simulations are carried out to show the wave-damage interaction and the scatter in the sensor signals due to damage. These simulation results show that PESEA can be used as a powerful tool to gain physical insights into the effect of different types of damage on wave propagation and sensor response. The influence of loading on ultrasonic waves actuated and sensed by piezoelectric sensors in aluminum plate is studied. A numerical and experimental study of axially stressed aluminum plates with surface-mounted piezoelectric sensors is carried out to investigate the dependence of wave velocity on applied load. Simi- larly, simulations and experiments are presented to understand how the piezoelectric sensor signal amplitude changes with adhesives of different thickness and material when the structure is exposed to elevated temperature. In SHM, piezo-induced ultrasonic waves are used for damage detection and lo- calization. The accuracy of damage localization depends strongly depends on the a priori knowledge of the wave velocity. The estimation of the wave velocity for com- plex structures is challenging since analytical solutions only exist for simple struc- tures. Hence, PESEA simulations are used to estimate the wave velocity profile for a given structures, which is then used for the offline training of the damage diagnos- tic imaging algorithm. PESEA simulations are carried out to validate the proposed model-assisted damage diagnostics. Accuracy of damage detection and localization also depends on the number of piezoelectric sensors and their placement. In this dissertation, a methodology is presented to utilize PESEA simulations to optimize the sensor network by maximizing the probability of damage detection. PESEA is used to understand the effect of crack and uncertainty in material properties on the sensor signal. This information is then used in a genetic algorithm based optimization code. This code maximizes the probability of detection and gives an optimized sen- sor network. The proposed methodology is used to optimize the piezoelectric sensor network for a stiffened aluminum panel. This demonstrates that PESEA can be used to optimize sensor placement for a given structure and improve the accuracy of the diagnostic algorithms. v Acknowledgments First of all, I would like to express my gratitude to Professor Fu-Kuo Chang for his guidance and support during the course of my PhD. I consider myself very fortunate that I got a chance to work with him. I would like to thank Professor Richard Christensen and Professor Kincho Law for their invaluable suggestions and careful review of this work. I also wish to thank Professor Debbie Senesky for serving on my oral examination committee and Professor Peter Pinsky for chairing the examination committee. I am also grateful to Jayanthi Subramaniam, Haruko Makitani, Barbara Briscoe, Ralph Levine, Robin Murphy, Liza Julian, and Patrick Ferguson for their administrative support. In addition, I gratefully acknowledge the financial support from the National Aero- nautics and Space Administration (NASA), the Air Force Office of Scientific Research (AFOSR), and Alcoa Inc. Finally, I would like to thank my friends and family. I thank all the current and past members of the Structures and Composites Laboratory (SACL). Specifically, I wish to thank Surajit Roy, Cecilia Larrosa, Zhiqiang (Steve) Guo, Nathan Salowitz, and Yu-Hung Li for their support, valuable discussions, and friendship. I am highly in- debted to my friends especially Mayank Agarwal, Shrey Kumar Shahi, Supreet Singh Bahga, Bhupesh Chandra, Uzma Hussain Barlaskar, Rohit Gupta, Manu Bansal, and Nitin Dua for their help, support, and making my stay at Stanford memorable. I will always be grateful to my wife, Amrita, for her unconditional love and care that helped me focus on my research. I wish to thank my sister, Dhanashree, for her encouragement. Finally, I dedicate this thesis to my parents who have always supported me in all my decisions. vi Contents Abstract iv Acknowledgments vi 1 Introduction1 1.1 Structural Health Monitoring......................1 1.2 Piezoelectric Materials..........................2 1.3 Wave Propagation in Thin-Walled Structures..............3 1.4 Challenges in SHM based on Piezo-Induced Waves...........5 1.4.1 Modeling of Piezo-Induced Ultrasonic Waves..........5 1.4.2 Effect of Operating Conditions..................6 1.4.3 Diagnostic Algorithms and Optimal Sensor Placement.....8 2 Problem Statement 11 3 Method of Approach 13 3.1 Modeling of Piezo-Induced Ultrasonic Wave Propagation....... 13 3.2 Effect of Operating Conditions...................... 15 3.2.1 Effect of Load........................... 15 3.2.2 Effect of Temperature...................... 15 3.3 Model-assisted Damage Diagnostics................... 16 3.4 Model-assisted Sensor Network Optimization.............. 16 vii 4 Governing Equations for Wave Propagation 17 4.1 Introduction................................ 17 4.2 Equations of Motion........................... 17 4.3 Coupled Governing Equations...................... 22 4.3.1 Stress-Free Initial State...................... 24 4.4 Conclusions................................ 25 5 Spectral Element Method 26 5.1 Introduction................................ 26 5.2 Weak Formulation............................ 27 5.3 Solid Spectral Element.......................... 27 5.3.1 Matrix Representation of Weak Form.............. 28 5.3.2 Global System of Equations................... 32 5.3.3 Rayleigh Damping........................ 33 5.3.4 Global System of Equations for Stress-Free Initial State.... 34 5.4 Numerical Integration in Spatial Domain................ 35 5.4.1 Nodal Quadrature........................ 36 5.5 Time Integration............................. 37 5.5.1 Central Difference Method.................... 37 5.6 Layered Solid Spectral Element..................... 39 5.6.1 Numerical Integration of Stiffness Matrix............ 40 5.7 Piezo-Enabled Spectral Element Analysis................ 42 5.7.1 Implementation