Table Of Content

nciassiried curity Classification ot tins page REPORT DOCUMENTATION PAGE a Report Security Classification: Unclassified lh Restrictive Markings r a Security Classification Authontv 3 Distrinution/Avaiiabiliry ot Report b Declassification;Downgrading Schedule Approved for public release: distribution is unlinuted. Performing Organization Report Numhensi 5 Monitoring Organization Report Numbens) a Name ot Performing Organization oh Office Symbol "a Name of Monitoring Organization Javal Postgraduate School (ifapplicable) 33 Naval Postgraduate School c Address icitw state, and ZIP code) 7b Address (city, slate, and ZIP code) Monterey CA 93943-5000 Monterey CA 93943-5000 a Name of Funding/Sponsoring Organization 6b Office Symbol 9 Procurement instrument Identification Numoer (ifapplicable) .. . . ddress (ciA', state, and ZIP code) 10 Source or Funding Numbers Program Element No Project No Task No Work Unit Accession NUMERICAL MODELING OF A FREE-FLOODED PIEZOELECTRIC SONAR RING 1 Title (include security classification) TRANSDUCER 2 Personal Author(s) Tiong Beng Tav 3a Type of Report 13b Time Covered 14 Date of Report (year, month, day) 15 Page Count laster's Thesis From To March 1993 114 6 Supplementary Notation The views expressed in this thesis are those of the author and do not reflect the official policy or position f the Department of Defense or the U.S. Government. 7 Cosati Codes 18 Subject Terms (continue on reverse ifnecessary and identify by block number) ield Group Subgroup Numerical Modeling, Pizoelectric. Ring Transducer, Free-Flooded. 9 Abstract (continue on reverse ifnecessary and identify by block number) A two-dimensional finite element model of a low frequency, free-flooded piezoelectric thin ring sonar transducer was eveloped for use with the ATTLA code. Effective material properties for the ring were determined from in-air modal analyses using ATILA. These were adjustec 3 obtain the closest agreement between the calculated ring resonance frequency and coupling coefficient and measured data applied by the manufacturer. In addition, equations for the electrical admittance for this transducer in air were developed based i n analytical approach published by Hong-zhang Wang (J. Acoust. Soc. Am. 79, 164-176 (1986)). A MATLAB program was 'ritten to implement these equations and to calculate various electromechanical network parameters. The calculated values agreed dth measured values to within 5 percent. An in-water harmonic analysis, in which the transmitting voltage response and the directivity pattern are computed, was erformed using the ATILA code. In general, results obtained using the finite element model and manufacturer's measured value gree within 10 percent. The effects of changes in material properties on acoustic performance of the transducer were investigate* le results are discussed. Distribution/AvailabilityofAbstract 21 Abstract Security Classification c unclassified/unlimited _ same as report DTIC users Unclassified 2a Name ofResponsible Individual 22b Telephone (include Area Code) 22c Office Symbol teven R. Baker 408-656 2729 Code PH/Ba D FORM 1473,84 MAR 83 APRedition may be used until exhausted security classification ofthis p All other editions are obsolete Unclassil T?^Rkh? Approved for public release; distribution is unlimited. Numerical Modeling of a Free-Flooded Piezoelectric Ring Sonar Transducer by Tiong Beng Tay Major, Republic of Singapore Navy B. Eng (Hons) National University of Singapore, 1985 , Submitted in partial fulfillment of the requirements for the degrees of MASTER OF SCIENCE IN ENGINEERING ACOUSTICS and MASTER OF SCIENCE IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL March^9 93 . ABSTRACT A two-dimensional finite element model of a low frequency, free- flooded piezoelectric thin ring sonar transducer was developed for use with the ATILA code. Effective material properties for the ring were determined from in-air modal analyses using ATILA. These were adjusted to obtain the closest agreement between the calculated ring resonance frequency and coupling coefficient and measured data supplied by the manufacturer. In addition, equations for the electrical admittance for this transducer in air were developed based on an analytical approach published by Hong- zhang Wang (J. Acoust. Soc. Am. 79, 164-176 (1986)). A Matlab program was written to implement these equations and to calculate various electromechanical network parameters. The calculated values agreed with measured values to within 5 percent An in-water harmonic analysis, in which the transmitting voltage response and the directivity pattern are computed, was performed using the ATILA code. In general, results obtained using the finite element model and manufacturer's measured values agree within 10 percent. The effects of changes in material properties on acoustic performance of the transducer were investigated; the results are discussed. in / / V I C.l TABLE OF CONTENTS INTRODUCTION I. 1 TRANSDUCER DESCRIPTION II. 4 METHODS OF ANALYSIS III. 12 A. INTRODUCTION 12 B. RING AND CAVITY MODE FREQUENCIES [Ref. 3] 12 C. FINITE ELEMENT ANALYSIS. THE ATILA CODE 14 1. Harmonic Analysis of a Radiating Piezoelectric Transducer 15 2. Modal Analysis ofa Piezoelectric Transducer 19 D. STANDARD NETWORK ANALYSIS [Ref. 2] 20 1. Vibration of Unloaded Tube 22 IV. TWO-DIMENSIONAL FINITE-ELEMENT MODEL 26 A. INTRODUCTION 26 B. CHARACTERISTICS OF THE MODEL 27 1. Material Properties 27 a. Unwrapped Piezoelectric ceramic Ring 27 b. Wrapped Piezoelectric Ceramic Ring 29 IV .. c. Encapsulam Materials ana Mourning Plate 30 2. Types of Elements .... 30 3. Constraints on Mesh Design (Ref. !1 31 a. Aspect ratio 31 b. Internal angles 31 c. Element size 31 d. Interelement compatibility 31 e. Radiation boundary elements 31 f. Boundary Conditions 33 4. Final Mesh Designs 34 V. RESULTS 39 A. MATERIAL PROPERTIES OF EQUIVALENT HOMOGENEOUS RING 39 Unwrapped Equivalent Homogeneous Ring 39 1 2. Wrapped Equivalent Homogeneous Ring 43 B. IN-WATER HARMONIC ANALYSES 46 1 Mounting Plate Not Included 46 2. Mounting Plate Included 48 C. COMPARISON OF CAVITY MODE FREQUENCY [Ref. 3] 49 D. EFFECT OF ENCAPSULANT MATERIAL PROPERTIES CHANGE 50 E. THE ANALYTICAL MODEL 52 The Unloaded Case 52 1. CONCLUSIONS VI. 54 SUGGESTIONS FOR FUTURE WORK VII. 56 APPENDIX A 57 INPUT DATA FILE FOR HARMONIC FINITE ELEMENT MODEL 57 APPENDIX B 96 MATLAB PROGRAM FOR ANALYTICAL MODEL OF UNLOADED TRANSDUCER 96 APPENDIX C 98 TYPICAL VALUES FOR MATERIALS CONSTANTS 98 APPENDIX D ioo SAMPLE CALCULATIONS FOR THE EFFECTIVE ELASTIC CONSTANTS OF THE FIBERGLASS WRAPPED CERAMIC RING 100 LIST OF REFERENCES 103 BIBLIOGRAPHY 105 INITIAL DISTRIBUTION LIST 106 VI