Skip to main content
SpringerLink
Log in
Book cover

Power Transducers for Sonics and Ultrasonics pp 86–108Cite as

Physics of Array Element Interaction Phenomena

  • Conference paper

Abstract

In a sonar array, the Interaction between sources affects the radiation loading on each individual source, the power6 it radiates and the radiation pattern of the array. This interaction is characterized by the mutual radiation impedance which is an essential parameter determining array behavior. Low-frequency transducers in a volumetric array with small size requirements are subject to much larger mutual interaction and scattering than in conventional arrays. Recent deep water tests by NUSC have shown significant deviations between experimental results and the classical theoretical treatment. This paper presents a review of array interaction phenomena, classical theoretical developments, experimental measurements and array performance effects. A case study of a recent low-frequency volumetric array test is discussed.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Akay A. (1990). “Radiation from a finite array of simple sources,” J. Acoust. Soc. Am. 87, 1449–1454

    ADS  Google Scholar 

  • Alperin H.A. (1956). “Mutual radiation impedance of pistons (of ka=0.40) symmetrically arranged in a stiff plane baffle,” US Navy Underwater Sound Laboratory, New London, CT, Tech Memo No. 1150–64–56 (13 June)

    Google Scholar 

  • Anderson V.C. (1977). “Efficient computation of array patterns,” J. Acoust. Soc. Am. 61, 744–755

    ADS  Google Scholar 

  • Anderson V.C. (1977). “Efficient computation of array patterns,” J. Acoust. Soc. Am. 61, 744–755

    ADS  Google Scholar 

  • Arase E.M. (1964). “Mutual radiation impedance of square and rectangular pistons in a rigid baffle,” J. Acoust. Soc. Am. 36, 1521–1525

    ADS  Google Scholar 

  • Arase E.M. (1964). “Mutual radiation impedance of square and rectangular pistons in a rigid baffle,” J. Acoust. Soc. Am. 36, 1521–1525

    ADS  Google Scholar 

  • Atwood J.F., and Sherman C.H. (1962). “Example of interaction effects in transducer arrays,” US Navy Underwater Sound Laboratory, New London, CT, Tech Memo No. 912–20–62 (March)

    Google Scholar 

  • Awatani J. (1957). “Note on acoustic radiation pressure,” J. Acoust. Soc. Am. 29, 392

    ADS  Google Scholar 

  • Bank G., and Wright J.R. (1990). “Radiation impedance calculations for a rectangular piston,” J Audio Eng Soc 38, 350–353

    Google Scholar 

  • Belyakov I.I., and Smaryshev M.D. (1972). “Radiation impedance and gain of a onedimensional array of rings on an infinite rigid cylinder,” Sov Phys - Acoust 18, 154

    Google Scholar 

  • Bergassolli A., and Brodut M. (1971). “Impedance acoustique d’un piston rectangulaire sur cran plan,” Acustica 25, 61–63

    Google Scholar 

  • Bergassolli A., and Brodut M. (1971). “Impedance acoustique d’un piston rectangulaire sur cran plan,” Acustica 25, 61–63

    Google Scholar 

  • Berman A., and Clay C.S. (1957). “Theory of time-averaged-product arrays,” J. Acoust. Soc. Am. 29, 805–812

    ADS  Google Scholar 

  • Biot M.A., and Tolstoy I. (1957). “Formulation of wave propagation in infinite media by normal coordinates with an application to diffraction,” J. Acoust. Soc. Am. 29, 381–391

    ADS  Google Scholar 

  • Bouwkamp C.J. (1946). “A contribution to the theory of acoustic radiation,” Phil Res Rep 1, 262–264

    Google Scholar 

  • Bouwkamp C.J. (1954) Rep Prog Phys 17, 35

    MathSciNet  ADS  Google Scholar 

  • Brown J.L. Jr, and Rowlands R.O. (1959). “Design of directional arrays,” J. Acoust. Soc. Am. 31, 1638–1643

    Google Scholar 

  • Burnett D.S. (1969). “Radiation impedance functions of rectangular pistons and their applications to sound transmission through finite depth apertures,” PhD Dissertation, University of California, Berkeley.

    Google Scholar 

  • Burnett D.S., and Soroka W.W. (1972). “Tables of rectangular piston radiation impedance functions with application to sound transmission loss through deep apertures,” J. Acoust. Soc. Am. 51, 1618–1623

    ADS  Google Scholar 

  • Butler J.L. (1968). “The mutual impedance between two small pistons with and without baffles,” Parke Mathematical Laboratories, Inc., Carlisle, MA, Technical Memorandum No. 2

    Google Scholar 

  • Butler J.L., and Sherman C.H. (1969). “Acoustic radiation from partially coherent line sources,” J. Acoust. Soc. Am. 47, 1290–1296

    Google Scholar 

  • Butler J.L. (1988). “An electro-acoustic model for flextensional ring shell projector,” Image Acoustic, inc. (31 March)

    Google Scholar 

  • Butler J.L. (1989). “Flextensional ring-shell transducer 3-D array model with driver options,” Image Acoustic, Inc. (10 March)

    Google Scholar 

  • Carson D.L. (1962). “Diagnosis and cure of erratic velocity distributions in sonar projector arrays,” J. Acoust. Soc. Am. 34, 1191–1196

    ADS  Google Scholar 

  • Carson D.L. (1962). “Diagnosis and cure of erratic velocity distributions in sonar projector arrays,” J. Acoust. Soc. Am. 34, 1191–1196

    ADS  Google Scholar 

  • Carter A.H., and Williams A.O. Jr (1951). “A new expansion for the velocity potential of a piston source,” J. Acoust. Soc. Am. 23, 179–184

    Google Scholar 

  • Chakraborty B. (1988). “Mutual interaction effects between array elements at different wavelengths in a coaxial circular array,” J. Acoust. Soc. Am. 83, 362–364

    ADS  Google Scholar 

  • Chakraborty B. (1988). “Mutual interaction effects between array elements at different wavelengths in a coaxial circular array,” J. Acoust. Soc. Am. 83, 362–364

    ADS  Google Scholar 

  • Chetaev D.N. (1951). “The impedance of a rectangular piston vibrating in an opening in a flat baffle,” Prik Mat Mekhan 15, 439–444

    MATH  Google Scholar 

  • Chin N.T. (1964). “Self radiation impedance of a finite free-flooding cylindrical radiator with Junger’s end correction. U. S. Navy Underwater Sound Laboratory, New London 1”. “The universal radiator, a new development in radiaptechnique,” Elektrotech 5, 365–372

    Google Scholar 

  • Flad F.R., Kuzneski J.A., and Packard W.B. (1964). “Experimental determination of mutual radiation impedance between coplanar circular pistons,” J. Acoust. Soc. Am. 36, 2005 (A)

    Google Scholar 

  • Foldy L.L. (1949). “Theory of passive linear electroacoustic transducers with fixed velocity distribution,” J. Acoust. Soc. Am. 21, 595

    ADS  Google Scholar 

  • Greenspon J.E., and Sherman C.H. (1964). “Mutual radiation impedance and nearfield pressure for pistons on a cylinder,” J. Acoust. Soc. Am. 36, 149–153

    ADS  Google Scholar 

  • Greenspon J.E., and Sherman C.H. (1964). “Mutual radiation impedance and nearfield pressure for pistons on a cylinder,” J. Acoust. Soc. Am. 36, 149–153

    ADS  Google Scholar 

  • Hanish S. (1985). “Historical account of mutual acoustic radiation interaction between elementary transducers of a large underwater sound projector array,” J. Acoust. Soc. Am. 78 (Suppl. 1), S73

    ADS  Google Scholar 

  • Hills R. Jr (1951). “Synthesis of line source directivity patterns,” J. Acoust. Soc. Am. 23, 143–144 (A)

    Google Scholar 

  • Ingard K.U. (1950). “Scattering and absorption by acoustic resonators,”PhD Dissertation, MIT.

    Google Scholar 

  • Ingard K.U., and Lamb G.L. (1957). “Effect of a reflecting plane on the power output of sound sources,” J. Acoust. Soc. Am. 29, 743–744

    ADS  Google Scholar 

  • Jacobsen O. (1976). “Some aspects of the self and mutual radiation impedance concept with respect to loudspeakers,” J Audio Eng Soc 24, 82–92

    Google Scholar 

  • Johnson H.M. (1962). “Effects of radiation impedance variation on sonar transducer performance in a large array,” J. Acoust. Soc. Am. 34, 716 (A)

    Google Scholar 

  • Johnson M.P. (1988). “Velocity control and the mechanical impedance of single degree of freedom electromechanical vibrators,” J. Acoust. Soc. Am. 84, 1994–2001

    ADS  Google Scholar 

  • Joseph P.M., and Saseendran Pillai P.R. (1988). “An approach towards improving the efficiency of sonar projector arrays,” IEEE ICASSP 5, 2697–2700

    Google Scholar 

  • Karim M.M.A., and Stumpf F.B. (1986). “Effect of spherical scatterers on the driving-point impedance and directivity pattern of a sonar transducer at an air-water surface,” J. Acoust. Soc. Am. 79, 865–866

    ADS  Google Scholar 

  • Karnovskii M.I. (1941). “Mutual acoustic impedances of spherical radiators and resonators,” Doklady Akad Nauk SSSR 32, 40–43

    Google Scholar 

  • Karnovskii M.I. (1948). “Collected Works of the Kiev Cinema-Engineering Institute, The calculation of mutual acoustic impedances, vol I,” Kiev Cinema- Engineering Institute, Kiev (pp 95–113 )

    Google Scholar 

  • Karnovskii M.I. (1956). “Calculation of the radiation resistance of several types of distributed radiator systems,” Sov Phys - Acoust 2, 280–293

    Google Scholar 

  • Kass D.F., and Sherman C.H. (1959). “Radiation Patterns for an Array on a Sphere,” US Naval Underwater Sound Laboratory, New London, CT, Tech Memo No. 1 150–21–59 (7 April)

    Google Scholar 

  • Kendig P.M. (1967). “Advanced Transducer Developments,” In, Albers VM (ed) Proceedings of the NATO-Sponsored Institutes, Copenhagen, Underwater Acoustics, vol 2. Plenum Press, New York

    Google Scholar 

  • Klapman S.J. (1940). “Interaction impedance of a system of circular pistons,” J. Acoust. Soc. Am. 11, 289

    ADS  Google Scholar 

  • Korochentsev V.I., Pyatov A.P., and Subbotin A.G. (1985). “Analysis of the interaction of transducers in an array,” Sov Phys - Acoust. 31, 363–365

    Google Scholar 

  • Korochentsev V.I., Pyatov A.P., and Subbotin A.G. (1985). “Analysis of the interaction of transducers in an array,” Sov Phys - Acoust. 31, 363–365

    Google Scholar 

  • Laird D.T., and Cohen H. (1952). “Directivity patterns for acoustic radiation from a source on a rigid cylinder,” J. Acoust. Soc. Am. 24, 46–49

    ADS  Google Scholar 

  • Levine H. (1983). “On the radiation impedance of a rectangular piston,” J Sound Vib 89, 447–455

    ADS  MATH  Google Scholar 

  • Levine H. (1983). “On the radiation impedance of a rectangular piston,” J Sound Vib 89, 447–455

    Google Scholar 

  • Lowenstein C.D. (1959). “Synthesis of directive arrays,” Proc Inter Congr Acoust 3, 680–682

    Google Scholar 

  • Lowenthal S., and Tournois P. (1963). “Radiation impedance of membranes and plates, their acoustic coupling with the propagating medium,” J. Acoust. Soc. Am. 35, 1423–1428

    ADS  Google Scholar 

  • Lyon R.H. (1957). “On the low-frequency radiation load of a bass-reflex speaker,” J. Acoust. Soc. Am. 29, 654

    ADS  Google Scholar 

  • Madella G.B. (1950). “Acoustic coupling of the diaphragms in Duo-Cone loudspeakers,” Alta Frequenza 19, 267–276

    Google Scholar 

  • Maidanik G., and Westervelt P.J. (1957). “Acoustical radiation pressure due to incident plane progressive waves on spherical objects,” J. Acoust. Soc. Am. 29, 936–940

    ADS  Google Scholar 

  • Mangulis V. (1962). “Infinite array of circular pistons in a rigid plane baffle,” J. Acoust. Soc. Am. 34, 1558–1563

    ADS  Google Scholar 

  • Mangulis V. (1963). “On the radiation of sound from a piston in a nonrigid baffle,” J. Acoust. Soc. Am. 35, 115–116

    ADS  Google Scholar 

  • Mangulis V. (1964). “Relation between the radiation impedance, pressure in the far field, and baffle impedance,” J. Acoust. Soc. Am. 36, 211–212

    ADS  Google Scholar 

  • Mangulis V. (1964). “Kramers-Kronig or dispersion relations in acoustics,” J. Acoust. Soc. Am. 36, 211–212

    ADS  Google Scholar 

  • Mangulis V. (1964). “Kramers-Kronig or dispersion relations in acoustics,” J. Acoust. Soc. Am. 36, 211–212

    Google Scholar 

  • Martin G.E., Hickman J.S., and Byrnes F.X. (1959). “Radiation impedances and power output limitations of array elements,” Proc Inter Congr Acoust 3, 678–679

    Google Scholar 

  • Martin G.E. (1985). “Analysis of large arrays: brief theory and some techniques used In 1954– 1985” J. Acoust. Soc. Am. 78(Suppl. 1), S73

    Google Scholar 

  • Mawardi O.K. (1951). “On the generalization of the concept of impedance in acoustics” J. Acoust. Soc. Am. 23, 571–576

    MathSciNet  ADS  Google Scholar 

  • McKinney C.M., and Owen W.R. (1957). “Wedge-shaped acoustic horns for underwater sound applications,” J. Acoust. Soc. Am. 29, 940–947

    ADS  Google Scholar 

  • McMahon G.W. (1984). “Interactions in ring-shell projector arrays,” Defence Research Establishment Atlantic, Dartmouth, Nova Scotia, Tech Memo 84/J

    Google Scholar 

  • Mechel F.P. (1988). “Notes on the radiation impedance, especially of piston-like radiators,” J Sound Vib 123, 537–572

    ADS  Google Scholar 

  • Miles J.W. (1946). “The analysis of plane discontinuities in cylindrical tubes: Part I,” J. Acoust. Soc. Am. 17, 259–271

    MathSciNet  ADS  MATH  Google Scholar 

  • Miles J.W. (1946). “The analysis of plane discontinuities in cylindrical tubes: Part II,” J. Acoust. Soc. Am. 17, 272–284

    MathSciNet  ADS  Google Scholar 

  • Molloy C.T. (1948). “Calculation of the directivity index for various types of radiators,” J. Acoust. Soc. Am. 20, 387–405

    ADS  Google Scholar 

  • Nomura Y., and Aida Y. (1951). “On the radiation impedance of a rectangular plate with an infinitely large fixed baffle,” Sei Rep Res Inst Tohoku Univ Ser. B, 1 /2, 337–347

    Google Scholar 

  • Pachner J. (1951). “On the acoustical radiation of an emitter vibrating in an infinite wall,” J. Acoust. Soc. Am. 23, 185–198

    MathSciNet  ADS  Google Scholar 

  • Pachner J. (1951). “On the acoustical radiation of an emitter vibrating freely or in a wall of finite dimensions,” J. Acoust. Soc. Am. 23, 198–208

    MathSciNet  ADS  Google Scholar 

  • Pordes F., and Sherman C.H. (1959). “Measurement of variation of radiation resistance with separation of pairs of underwater transducers,” Proc Inter Congr Acoust 3, 675–677 ( Elsevier, Amsterdam )

    Google Scholar 

  • Pordes F., and Sherman C.H. (1959). “Measurement of variation of radiation resistance with separation of pairs of underwater transducers,” Proc Inter Congr Acoust 3, 675–677 ( Elsevier, Amsterdam )

    Google Scholar 

  • Porter D.T. (1964). “Self and mutual radiation impedance and beam patterns for flexural disks in a rigid plane,” J. Acoust. Soc. Am. 36, 1154–1161

    ADS  Google Scholar 

  • Porter D.T. (1964). “Self and mutual radiation impedance and beam patterns for flexural disks in a rigid plane,” J. Acoust. Soc. Am. 36, 1154–1161

    Google Scholar 

  • Porter D.T. (1965). “Effect of Thevenln equivalent Internal impedance on velocity control and acoustic power for planar broadside arrays for different driving level limitations,” U. S. Navy Underwater Sound Laboratory, New London, CT, Rept. 428 (AD615773)

    Google Scholar 

  • Porter D.T. (1965). “Broadband velocity control,” US Navy Underwater Sound Laboratory, New London, CT, Technical Memorandum No. 960–47–65

    Google Scholar 

  • Porter D.T. (1966). “Examples of the effects of array size, spacing, efficiency and driving force uniformity upon array behavior,” US Navy Underwater Sound Laboratory, New London, CT, Tech memo No. 960–64–66 (June)

    Google Scholar 

  • Nomura Y., and Aida Y. (1951). “On the radiation impedance of a rectangular plate with an infinitely large fixed baffle,” Sei Rep Res Inst Tohoku Univ Ser. B, 1 /2, 337–347

    Google Scholar 

  • Porter D.T. (1966). “Examples of the effects of array size, spacing, efficiency and driving force uniformity upon array behavior,” US Navy Underwater Sound Laboratory, New London, CT, Tech memo No. 960–64–66 (June)

    Google Scholar 

  • Porter D.T. (1972). “December 1971 Status of the NUSC train of computer programs for transmitting sonar array prediction,” Naval Underwater Systems Center, New London, CT, Technical Memo TD12–10–72 (11 January)

    Google Scholar 

  • Pritchard R.L. (1951). “Discussion of papers by Pachner and by Stenzel on radiation from a circular emitter,” J. Acoust. Soc. Am. 23, 591

    MathSciNet  ADS  Google Scholar 

  • Porter D.T. (1972). “December 1971 Status of the NUSC train of computer programs for transmitting sonar array prediction,” Naval Underwater Systems Center, New London, CT, Technical Memo TD12–10–72 (11 January)

    Google Scholar 

  • Porter D.T. (1974). “January 1974 status of the NUSC train of computer programs for transmitting array prediction,” Naval Underwater Systems Center, New London, CT, Technical Memo TD12–91–74 (12 April)

    Google Scholar 

  • Porter D.T. (1985). “Effects of nonrigid mounting surfaces on array behavior,” J. Acoust. Soc. Am. 78 (Suppl. 1), S73

    ADS  Google Scholar 

  • Porter D.T. (1985). “Effects of nonrigid mounting surfaces on array behavior,” J. Acoust. Soc. Am. 78 (Suppl. 1), S73

    ADS  Google Scholar 

  • Porter D.T. (1985). “Effects of nonrigid mounting surfaces on array behavior,” J. Acoust. Soc. Am. 78 (Suppl. 1), S73

    Google Scholar 

  • Pritchard R.L. (1951). “Discussion of papers by Pachner and by Stenzel on radiation from a circular emitter,” J. Acoust. Soc. Am. 23, 591

    MathSciNet  ADS  Google Scholar 

  • Pritchard R.L. (1951). “Discussion of papers by Pachner and by Stenzel on radiation from a circular emitter,” J. Acoust. Soc. Am. 23, 591

    Google Scholar 

  • Pritchard R.L. (1953). “Optimum directivity patterns for linear point arrays,” J. Acoust. Soc. Am. 25, 879–891

    ADS  Google Scholar 

  • Pritchard R.L. (1954). “Maximum directivity index of a linear point array,” J. Acoust. Soc. Am. 26, 1034–1039

    ADS  Google Scholar 

  • Pritchard R.L. (1960). “Mutual acoustic impedance between radiators in an infinite rigid plane,” J. Acoust. Soc. Am. 32, 730–737

    MathSciNet  ADS  Google Scholar 

  • Pritchard R.L. (1951). “Mutual acoustic impedance between two circular disks,” J. Acoust. Soc. Am. 23, 143 (A)

    MathSciNet  Google Scholar 

  • Pyett J.S. (1954). “Acoustic admittance and impedance as vector quantities,” J. Acoust. Soc. Am. 26, 870

    ADS  Google Scholar 

  • Queen W.C. (1969). “The directivity of sonar receiving arrays,” J. Acoust. Soc. Am. 47, 711–720

    ADS  Google Scholar 

  • Reese J.M., and Thompson W. Jr (1981). “Acoustic coupling between two finite-sized spheres; n=2 mode,” J. Acoust. Soc. Am. 69, 1587–1590

    Google Scholar 

  • Rhian E. (1954). “An exact method for determining the directivity index of a general threedimensional array,” J. Acoust. Soc. Am. 26, 704–706

    ADS  Google Scholar 

  • Richards R.T. (1970). “A general array simulation program for predicting directivity patterns of acoustic arrays,” General Dynamics/Electronics Division, Rochester, NY, Report No. AC- 115–70

    Google Scholar 

  • Richards R.T. (1970). “A general array simulation program for predicting directivity patterns of acoustic arrays,” General Dynamics/Electronics Division, Rochester, NY, Report No. AC- 115–70

    Google Scholar 

  • Robey D.H. (1955). “On the radiation impedance of the liquid-filled squirting cylinder,” J. Acoust. Soc. Am. 27, 711–714

    MathSciNet  ADS  Google Scholar 

  • Rodgers P.H., and Van Buren A.L. (1978). “New approach to a constant beamwidth transducer,” J. Acoust. Soc. Am. 64, 38–43

    ADS  Google Scholar 

  • Rudgers A.J. (1986). “Application of a Neumann-series method to two problems in acoustic radiation theory that are formulated in terms of Green’s functions,” J. Acoust. Soc. Am. 79, 1211–1222

    MathSciNet  ADS  Google Scholar 

  • Rudgers A.J. (1987). “Radiation impedances of interacting acoustic sources expressed in terms of the individual source Green’s functions,” J. Acoust. Soc. Am. 82, 709–710

    ADS  Google Scholar 

  • Rusby J.S.M. (1960). “Measurements of the total acoustic radiation impedance of rigid pistons in an array,” Nature 186, 144–146

    ADS  Google Scholar 

  • Sawade S. (1951). “Note on radiator-array technique,” Elektrotech Z 72, 720

    Google Scholar 

  • Schenck H.A. (1968). “Improved integral formulation for acoustic radiation problems,” J. Acoust. Soc. Am. 44, 41–58

    ADS  Google Scholar 

  • Schoch A. (1941). Akust Z 6, 318

    MathSciNet  MATH  Google Scholar 

  • Sherman C.H. (1958). “Mutual radiation impedance between pistons on spheres and cylinders,” US Navy Underwater Sound Laboratory, New London, CT,Research Report No. 405

    Google Scholar 

  • Sherman C.H. (1958). “Interaction radiation impedance between rectangular pistons on an infinite cylinder,” US Naval Underwater Sound Laboratory, New London, CT, Tech Memo No. 150–29–58 (13 June)

    Google Scholar 

  • Sherman C.H. (1958). “Acoustic Radiation from spherical arrays,” US Naval Underwater Sound Laboratory, New London, CT, Tech Memo No. 1150–5–58 (20 Jan)

    Google Scholar 

  • Sherman C.H. (1959). “Mutual radiation impedance of sources on a sphere,” J. Acoust. Soc. Am. 31, 947–952

    ADS  Google Scholar 

  • Sherman C.H. (1961). “Mutual radiation impedance of fixed velocity distribution transducers,” U. S. Navy Underwater Sound Laboratory, New London, CT, Tech. Memo. 912–1–74–61

    Google Scholar 

  • Sherman C.H. (1962). “Example of interaction effects in transducer arrays: part III,” U. S. Navy Underwater Sound Laboratory, New London, CT, Tech. Memo. 912–82–62

    Google Scholar 

  • Sherman C.H. (1963). “Effect of the nearfleld on the cavitation limit of transducers,” J. Acoust. Soc. Am. 35, 1409–1412

    MathSciNet  ADS  Google Scholar 

  • Sherman C.H. (1965). “Theoretical model for mutual radiation resistance of small transducers at an air-water surface,” J. Acoust. Soc. Am. 37, 532–533

    ADS  Google Scholar 

  • Richards R.T. (1970). “A general array simulation program for predicting directivity patterns of acoustic arrays,” General Dynamics/Electronics Division, Rochester, NY, Report No. AC- 115–70

    Google Scholar 

  • Sherman C.H., and Kass D.F. (1958). “Radiation impedances for an array on a sphere,” US Naval Underwater Sound Laboratory, New London, CT, Tech Memo No. 1150–70–58 (25 Nov)

    Google Scholar 

  • Richards R.T. (1970). “A general array simulation program for predicting directivity patterns of acoustic arrays,” General Dynamics/Electronics Division, Rochester, NY, Report No. AC- 115–70

    Google Scholar 

  • Shindo T., Yoshioka T., and Fukuyama K. (1990). “Calculation of sound radiation from an unbaffled, rectangular-cross-section horn loudspeaker using combined analytical and boundary-element methods,” J Audio Eng Soc 38, 340–349

    Google Scholar 

  • Skorheim R.D. (1957). “The radiation impedance of a colinear array of finite cylindrical radiators,” MS Dissertation, US Naval Postgraduate School.

    Google Scholar 

  • Skudrzyk E.J. (1954). “Die Grundlagen der Akustik,” Springer-Verlag, Vienna

    Google Scholar 

  • Skudrzyk E.J. (1971). “The foundation of acoustics,” Springer-Verlag, Vienna, New York

    Google Scholar 

  • Smaryshev M.D. (1973). “Directivity of underwater acoustic arrays,” Sudostroenie, Leningrad (in Russian)

    Google Scholar 

  • Smaryshev M.D. (1979). “Directivity of underwater acoustic arrays,” 2nd ed. Sudostroenie, Leningrad (in Russian)

    Google Scholar 

  • Steinberg B.D. (1976). “Principles of aperture and array system design,” John Wiley, New York

    Google Scholar 

  • Stenzel H. (1930). Ann Physik (5)7, 952, 965–968

    Google Scholar 

  • Stenzel H. (1942). Ann Physik (5)41,245–260

    Google Scholar 

  • Stenzel H. (1949). Ann Physik (6)4,303–324

    Google Scholar 

  • Stumpf F.B. (1964). “Interaction radiation resistance for a line array of two and three magnetostrictive-stack transducers at an air-water surface,” J. Acoust. Soc. Am. 36, 174–176

    ADS  Google Scholar 

  • Richards R.T. (1970). “A general array simulation program for predicting directivity patterns of acoustic arrays,” General Dynamics/Electronics Division, Rochester, NY, Report No. AC- 115–70

    Google Scholar 

  • Stumpf F.B., and Crum L.A. (1966). “Interaction radiation resistance and reactance measurements for two small transducers at an air- water surface,” J. Acoust. Soc. Am. 40, 1554–1555

    ADS  Google Scholar 

  • Stumpf F.B., and Junit A.M. (1980). “Effect of a spherical scatterer on the radiation reactance of a transducer at an air-water surface,” J. Acoust. Soc. Am. 67, 715–716

    ADS  Google Scholar 

  • Stumpf F.B., and Lam Y.Y. (1970). “Radiation resistance of a small transducer at a water surface near plane boundaries,” J. Acoust. Soc. Am. 47, 332–338

    ADS  Google Scholar 

  • Stumpf F.B., and Lukman F.J. (1960). “Radiation resistance of magnetostrictive-stack transducer in presence of second transducer at air-water surface,” J. Acoust. Soc. Am. 32, 1420–1422

    ADS  Google Scholar 

  • Stumpf F.B., Richards R.T., and Crum L.A. (1968). “Acoustic interaction for arrays of small magnetostrictive-stack sonar transducers at an air-water surface,” Ohio University Research Institute, Athens, Ohio, Final Technical Report (Contract Nonr4419 (01))

    Google Scholar 

  • Richards R.T. (1970). “A general array simulation program for predicting directivity patterns of acoustic arrays,” General Dynamics/Electronics Division, Rochester, NY, Report No. AC- 115–70

    Google Scholar 

  • Richards R.T. (1970). “A general array simulation program for predicting directivity patterns of acoustic arrays,” General Dynamics/Electronics Division, Rochester, NY, Report No. AC- 115–70

    Google Scholar 

  • Swenson G.W. Jr, and Johnson W.E. (1952). “Radiation impedance of a rigid square piston in an infinite baffle,” J. Acoust. Soc. Am. 24, 84

    Google Scholar 

  • Swenson G.W. Jr, and Johnson W.E. (1952). “Radiation impedance of a rigid square piston in an infinite baffle,” J. Acoust. Soc. Am. 24, 84

    Google Scholar 

  • Thompson W. Jr (1971). “The computation of self- and mutual- radiation impedances for annular and elliptic pistons using Bouwkamp’s integral,” J Sound Vib 17, 221–233

    ADS  Google Scholar 

  • Thompson W. Jr (1976). “Radiation from a spherical acoustic source near a scattering sphere,” J. Acoust. Soc. Am. 60, 781–787

    Google Scholar 

  • Thompson W. Jr (1977). ‘Acoustic coupling between two finite-sized spherical sources,’ J. Acoust. Soc. Am. 62, 8–11

    Google Scholar 

  • Thompson W. Jr, and Reese J.M. (1983). “Acoustic coupling between a pulsating and an oscillating sphere,” J. Acoust. Soc. Am. 74, 1048–1050

    Google Scholar 

  • Thorn J.V., and Booth N.O., Lockwood JC (1980). “Random and Partially random acoustic arrays,” J. Acoust. Soc. Am. 67, 1277–1286

    Google Scholar 

  • Toulis W.J. (1957). “Radiation load on arrays of small pistons,” J. Acoust. Soc. Am. 29, 346–348

    ADS  Google Scholar 

  • Toulis W.J. (1963). “Mutual coupling with dipoles in arrays,” J. Acoust. Soc. Am. 35, 1062–1063

    ADS  Google Scholar 

  • Swenson G.W. Jr, and Johnson W.E. (1952). “Radiation impedance of a rigid square piston in an infinite baffle,” J. Acoust. Soc. Am. 24, 84

    Google Scholar 

  • Swenson G.W. Jr, and Johnson W.E. (1952). “Radiation impedance of a rigid square piston in an infinite baffle,” J. Acoust. Soc. Am. 24, 84

    Google Scholar 

  • Waterhouse R.V. (1961). “The effect of rigid and pressure release boundaries on various multipole sources,” Cambridge Acoustical Associates, Cambridge, MA, Inc. Rep. U-117–48

    Google Scholar 

  • Waterhouse R.V. (1958). “Output of a sound source in a reverberation chamber and other reflecting environments,” J. Acoust. Soc. Am. 30, 4–13

    ADS  Google Scholar 

  • Waterhouse R.V. (1963). “Radiation impedance of a source near reflectors,” J. Acoust. Soc. Am. 35, 1144–1151

    ADS  Google Scholar 

  • Waterhouse R.V. (1965). “Mutual impedance of acoustic sources,” Proc Inter Congr Acoust 5th, Paper J-21

    Google Scholar 

  • Westervelt P.J. (1951). “Acoustic impedance in terms of energy functions,” J. Acoust. Soc. Am. 23, 347–348

    MathSciNet  ADS  Google Scholar 

  • Westervelt P.J. (1951). “The interaction of a finite amplitude acoustic wave with small obstacles and orifices,” PhD Dissertation, MIT. Physics Department, (January) Williams W., Parke N.G., Moran D.A., and Sherman C.H. (1964). “Acoustic radiation from a finite cylinder,” J. Acoust. Soc. Am. 36, 2316–2322

    MathSciNet  Google Scholar 

  • Willms W. (1954). “Bemerkungen zur Definition des vektoriellen Schall-leitwertes, des akustischen Widerstandes und der akustischen Elemente,” Acustica 4, 133–136

    Google Scholar 

  • Willms W. (1954). “Zum Begriff der Schallimpedanz,” Acustica 4, 427–432 Wolff I., and Malter L. (1929). Phys Rev 33, 1061

    ADS  Google Scholar 

  • Willms W. (1954). “Bemerkungen zur Definition des vektoriellen Schall-leitwertes, des akustischen Widerstandes und der akustischen Elemente,” Acustica 4, 133–136

    Google Scholar 

  • Woollett R.S. (1963). “Trends and problems in sonar transducer design/ IEEE Trans Ultrason Eng UE”10,116–124

    Google Scholar 

  • Yatsenko V.K. (1977). “Method for measuring the mutual impedance of two piezoelectric transducers,” Izd. Rost. Univ., Rostov-on-Don, No. 4

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. New London Laboratory, Naval Underwater Systems Center, New London, Connecticut, 06320, USA

    R. T. Richards, J. B. Blottman III & B. McTaggart

Authors
  1. R. T. Richards
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. B. Blottman III
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. McTaggart
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Acoustics Laboratory, ISEN, 41 bd. Vauban, F-59046, Lille Cedex, France

    Bernard F. Hamonic  & Jean-Nöel Decarpigny  & 

  2. US Naval Postgraduate School, 93943, Monterey, CA, USA

    Oscar B. Wilson

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Richards, R.T., Blottman, J.B., McTaggart, B. (1991). Physics of Array Element Interaction Phenomena. In: Hamonic, B.F., Decarpigny, JN., Wilson, O.B. (eds) Power Transducers for Sonics and Ultrasonics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76271-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-76271-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76273-4

  • Online ISBN: 978-3-642-76271-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation