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Scale Models of Acoustic Scattering Problems Including Barriers and Sound Absorption

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University of Kentucky UKnowledge Theses and Dissertations--Mechanical Engineering Mechanical Engineering 2018 SCALE MODELS OF ACOUSTIC SCATTERING PROBLEMS INCLUDING BARRIERS AND SOUND ABSORPTION Nan Zhang University of Kentucky, [email protected] Author ORCID Identifier: https://orcid.org/0000-0003-2707-8716 Digital Object Identifier: https://doi.org/10.13023/etd.2018.304 Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Recommended Citation Zhang, Nan, "SCALE MODELS OF ACOUSTIC SCATTERING PROBLEMS INCLUDING BARRIERS AND SOUND ABSORPTION" (2018). Theses and Dissertations--Mechanical Engineering. 119. https://uknowledge.uky.edu/me_etds/119 This Master's Thesis is brought to you for free and open access by the Mechanical Engineering at UKnowledge. It has been accepted for inclusion in Theses and Dissertations--Mechanical Engineering by an authorized administrator of UKnowledge. For more information, please contact [email protected]. STUDENT AGREEMENT: I represent that my thesis or dissertation and abstract are my original work. Proper attribution has been given to all outside sources. I understand that I am solely responsible for obtaining any needed copyright permissions. I have obtained needed written permission statement(s) from the owner(s) of each third-party copyrighted matter to be included in my work, allowing electronic distribution (if such use is not permitted by the fair use doctrine) which will be submitted to UKnowledge as Additional File. I hereby grant to The University of Kentucky and its agents the irrevocable, non-exclusive, and royalty-free license to archive and make accessible my work in whole or in part in all forms of media, now or hereafter known. I agree that the document mentioned above may be made available immediately for worldwide access unless an embargo applies. I retain all other ownership rights to the copyright of my work. I also retain the right to use in future works (such as articles or books) all or part of my work. I understand that I am free to register the copyright to my work. REVIEW, APPROVAL AND ACCEPTANCE The document mentioned above has been reviewed and accepted by the student’s advisor, on behalf of the advisory committee, and by the Director of Graduate Studies (DGS), on behalf of the program; we verify that this is the final, approved version of the student’s thesis including all changes required by the advisory committee. The undersigned agree to abide by the statements above. Nan Zhang, Student Dr. David W. Herrin, Major Professor Dr. Alexandre Martin, Director of Graduate Studies SCALE MODELS OF ACOUSTIC SCATTERING PROBLEMS INCLUDING BARRIERS AND SOUND ABSORPTION _________________________________ THESIS _________________________________ A Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering in the College of Engineering at the University of Kentucky By Nan Zhang Lexington, Kentucky Director: Dr. David W. Herrin, Professor of Mechanical Engineering Lexington, Kentucky 2018 Copyright © Nan Zhang 2018 ABSTRACT OF THESIS SCALE MODELS OF ACOUSTIC SCATTERING PROBLEMS INCLUDING BARRIERS AND SOUND ABSORPTION Scale modeling has been commonly used for architectural acoustics but use in other noise control areas is nominal. Acoustic scale modeling theory is first reviewed and then feasibility for small-scale applications, such as is common in the electronics industry, is investigated. Three application cases are used to examine the viability. In the first example, a scale model is used to determine the insertion loss of a rectangular barrier. In the second example, the transmission loss through parallel tubes drilled through a cylinder is measured and results are compared to a 2.85 times scale model with good agreement. The third example is a rectangular cuboid with a smaller cylindrical well bored into it. A point source is placed above the cuboid. The transfer function was measured between positions on the top of the cylinder and inside of the cylindrical well. Treatments were then applied sequentially including a cylindrical barrier around the well, a membrane cover over the opening, and a layer of sound absorption over the well. Results are compared between the full scale and a 5.7 times scale model and correlation between the two is satisfactory. KEYWORDS: Scale Modeling, Acoustic Scattering, Noise Reduction, Transfer Function, Finite Element Method. Nan Zhang Student’s Signature 25th July, 2018 SCALE MODELS OF ACOUSTIC SCATTERING PROBLEMS INCLUDING BARRIERS AND SOUND ABSORPTION By Nan Zhang Dr. Alexandre Martin Director of Graduate Studies Dr. David W. Herrin Director of Thesis 25th July, 2018 Date To my family ACKNOWLEDGEMENTS Firstly, I would like to express my gratitude to my advisor Professor David Herrin for his continuous guidance and support during my master study at University of Kentucky. His fund of knowledge changed my thinking perspective as an advisor. His insight broadened my life horizon as a mentor. My appreciation is also sent to Professor Tingwen Wu for his help and advice on my research work. In addition, I would also like to give my thanks to Dr. John Baker for his valuable comments and recommendations on my thesis work. I have enjoyed my life and study so much at university of Kentucky. It’s been a precious experience and memory on my life road. I want to give thanks to all my fellows and friends in Vibro-Acoustic Lab, Jonathon Chen, Gong Cheng, Huangxing Chen, Keyu Chen, Weiyun Liu, Kangping Ruan, Shujian He, Conner Campbell, Yitian Zhang, Wanlu Li, Peng Wang, Jundong Li, Caoyang Li, Ruimeng Wu, Xin Hua, Jinghao Liu, Limin Zhou, Rui He, Xin Yan, Hao Zhou and Shishuo Sun, for all the fun we have had in the past several years. Last but the most important, I would like to give my sincere thankfulness to my Lord and my family. Ephesians 1:8 the grace that he lavished on us with all wisdom and understanding. My dear mother, Guiqin Xu, who sacrifices her whole life to raise me up and taught me what person I should be. My great father, Hongzhi, Zhang, who always supports me whenever I need for what I do right, sets himself as a role model to show me how important the hardworking and integrity can change my career and life. My beloved fiancée, Jie Zhang, who cooks for me on a daily basis, holds my hands walking through with me for all the ups and downs iii I have been through. My lovely sister, Ning Ning, who brings all the laughter and enthusiasm into my life, which fills my life with full of sunshine. They make me be the best person I could ever be. I would never become the person I am now without them. Thank you, my family. I love you all. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS ..................................................................................... iii LIST OF TABLES ................................................................................................ vii LIST OF FIGURES ............................................................................................. viii CHAPTER 1 INTRODUCTION ......................................................................... 1 1.1 Introduction ............................................................................................ 1 1.2 Objectives .............................................................................................. 4 1.3 Outlines .................................................................................................. 5 CHAPTER 2 BACKGROUND ........................................................................... 6 2.1 Background on Scale Modeling .............................................................. 6 2.2 Background on Acoustic Theory ............................................................ 9 2.2.1 Analytical Approach to Determine Barrier Insertion Loss ................ 9 2.2.2 One Dimensional Wave Equation ................................................. 12 2.2.3 Acoustic Source Modeling ............................................................. 13 2.2.4 Acoustic Transmission Loss .......................................................... 15 2.3 Background on Acoustic Material ......................................................... 17 2.3.1 Limp Panel Theory ........................................................................ 17 2.3.2 Modes of Circular Panel ................................................................ 20 2.3.3 Definition and Determination of Flow Resistivity ........................... 20 CHAPTER 3 SCALE MODELING RULES FOR VIBRO-ACOUSTICS ........... 24 3.1 Introduction .......................................................................................... 24 3.2 Review of Scale Modeling Rules for Acoustics .................................... 24 3.2.1 Acoustic Wave Propagation .......................................................... 24 3.2.2 Sound Transmission through a Limp Panel .................................. 26 v 3.2.3 Sound Propagation through a Sound Absorption Material ............ 27 3.3 Summary .............................................................................................. 29 CHAPTER 4 EXAMPLE ‒ BARRIER .............................................................. 30 4.1 Barrier Insertion Loss ........................................................................... 30 4.2 Summary .............................................................................................. 34 CHAPTER 5 EXAMPLE ‒ PARALLEL TUBES ..............................................
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