Numerical modeling of a free-flooded piezoelectric ring sonar transducer.

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by  Tay, Tiong Beng.;Baker, Steven R.;Pieper, Ronald J.;Wilson, O. B.(Oscar Bryan),

nciassiried
curity Classification ot tins page
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a Report Security Classification: Unclassified lh Restrictive Markings
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a Security Classification Authontv 3 Distrinution/Avaiiabiliry ot Report
b Declassification;Downgrading Schedule Approved for public release: distribution is unlinuted.
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Javal Postgraduate School (ifapplicable) 33 Naval Postgraduate School
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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