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Transcription

1 ADt-R NONLINEAR AND RANDOM PHENOMENA IN ELECTROMAGNETIC AND 1/1 - ACOUSTIC WAVE PROPROATION(U) STANFORD UNIV CA J1 I KELLER MAR 97 ARO IS-MA DRR K-N24 Eu"'..E UINCLASSIFIED FIG 20/11 NI.

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3 -U N C L A S S I F I E D I& VNTT UREIn AD-A SQATYvt. AON UYHOITY3. OISTRIUUTION/AVAILAUIUI'r OF REPORr P O U T O ~ P 5 E,-,01 -- D T iue 010A IFCAT CHEULEApproved IDONGPAMG for public release; distribution unlimited. t* 4. PE11111MOIINGS OAGANIZAOMTIOI REPORT NUMERS) S. MONITORING ORGANIZATION REPORT N Wt L t.-. I- ARO MA V JUN b.nam OF PERFORMING OlIGANIZATIORI 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION Stanford Univ. U. S. Army Research Office A GL. ADONESS Wily, Stee.. and ZJP Code) 7b. ADDRESS (City, State, and ZIP Code) Stanford. CA P. 0. Box Research Triangle Park, NC I&. NAME OF FUtiOISPONSONING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER U. S. Army Research Office DAAG K-0024 O ASNATO ".1at n X oe 10. SOURCE OF FUNDING NUMBERS P. 0. Box PROGRAM PROJECT TASK IWORK UNIT - Research Triangle Park, NC ELMN O1O O CESO O 11I. TITLE Onmie Secweroly C1140f.uionD Nonlinear and Random Phenomei 7 in Electromagnetic and Acoustic Wave Propagation I3a. TYPE OF REPOR 13b. TIME COVERED 14. DATE OF REPORT (Year. Mnh a)5 * -e at FM1 15 V85 TO 1/14/8A March 87 PG IS.SUPLEENAR NOATONThe view, opinions and/or findings contained in this report are those *. ~. of V h ut ecos s nfica,??adghudno rtment of the Army position, *' SI*. COSATI COOES 15. SUBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD GROUJP SUBU4ROUP Electromagnetic Wave Propagation,' Acoustic Wave Propagation: llamii Brpa"A.t'Acoustoelastic Effect; 19 ABSTRACT (Coiwlnue an reverse if necessary and identify by block number) The acoustoelastic effect is the dependence of sound speed upon stress in an elastic solid due to nonlinearity.\this effect can be u sed for nondestructive testing of *structural components of aircraft, vehicles, etc. -A theory of the effect was developed which involved analyzing acoustic wave propagation in random anisotropic solids. A related theory of the effective elastic constants of solids composed of aggregates of polycrystals was also developed. For anisotropic composite mateirials reciprocal relations satisified by their effective thermal or electrical conductivity tensors were discovered. In the case of scalar materials such relations have been very useful, so the new ones may be useful too. It has also been shown how the elastic properties of the ground could be determined from seismic scattering data. This method used Oe Born approximation, and led to 4- Vnir~prtrananLms.C' I 20 J. DISTRISUTIONIAVAILAIUTY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION DUNCLASSIFIEMINUMiTED 0 SAME AS RPT, 0 DTIC USERS Unclassified 120. NAME OF RESPON4SIBLE INDIVIDUAL 22b. TELEPHONE (Include Area Cd)2OFFICE SYMBOL 00 FORM um- 83 APR edition may be used until exhausted. SEUIYCASFCAINO1HSPG All other editions are obsolete. SEUICLASSIFIAIN FTISPG UNLASIIE

4 f~r M NONLINEAR AND RANDOM PHENOMENA IN ELECTROMAGNETIC AND ACOUSTIC WAVE PROPAGATION JOSEPH B. KELLER MARCH 14, 1987 U. S. ARMY RESEARCH OFFICE CONTRACT NUMBER - DAAG K0024 STANFORD UNIVERSITY APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNIMITED

5 1. INTRODUCTION Research on nonlinear and random phenomena in wave propagation was conducted during the period covered by this report, January 15, 1985 to January 14, This research was quite successful, leading to a variety of new results. They are outlined in section 2 and presented in detail in the publications listed in section 3. The personnel participating in the work are listed in section 4 2. MAIN RESULTS The acoustoelastic effect is the dependence of ound speed upon stress In an elastic solid due to nonlinearity. This effect can be used for nondestructive testing of structural components of aircraft, vehicles, etc. Dr. Bonilla and Professor Keller developed a theory of the effect which involved analyzing acoustic wave propagation in random anisotropic solids. Dr. Bonilla also developed a related theory of the effective elastic constants of solids composed of aggregates of polycrystals. For anisotropic composite materials, Dr. Nevard and Professor Keller discovered reciprocal relations satisfied by their effective thermal or electrical conductivity tensors. In the case of scalar materials such relations have been very useful, so the new ones may be useful too. Dr. Boyse and Professor Keller showed how the elastic properties of the ground could be determined from seismic scattering data. Their method used the Born approximation, and led to results involving Fourier transforms. - - Accessionl F or 0%,,' 't._ spe% WOL" 00*68. 4

6 8. PUB3LICATIONS A. By J. B. Keller and co-authors "Uniform solutions for scattering by a potential barrier and bound states of a potential well,* Am. J. Phys. 54, , "Discriminant, transission coefficient and stability bands of Hill's equation,* J. Math. Phys. 25, , "Genetic variability due to Geographical Looenity,' J. Math. Biol. 20, , "Inverse elastic scattering in three dimensions,' (with W. Boyne) J.A.S.A. T9, , "Reciprocal relations for effective conductivities of anisotropic media,' (with J. Nevard) J. Math. Phys. 26, , "Irreversibility and nonrecurrence,' (with L. Bonilla) J. Statistical Physics 42, , "One hundred years of diffraction theory,' IEEE Trans. Antennas Prop , bf AP-33, "Free boundary problems in mechanics,' in Seminar in Nonlinear Partial Differential Equations, S. S. Chern, editor, Springer -Verlag, New York, (1984). "Reaction kinetics on a lattice,' J. Chem. Phys. 84, , "The Probability of heads,' Am. Math. Monthly 93, , "Soliton generation and nonlinear wave propagation,' Phil. Trans. R. Soc. Lond. A315, , "Acousto-elastic effect and wave propagation in heterogeneous weakly anisotropic materials,' (with Luis L. Bonilla) J. Mech. Phys. Solids 83, , 1985.

7 a B. By other authors 'Effective elastic costants of polycrystalline aggregates,* - L. L. Bonilla, J. Mech. and Piys. Soids 33, , "On the stability of inverse scattering problems,' - J. Fawcett, Wave Motion 6, , "A r*ous derivation of the 'Miracle' of three-dlmensional inverse scattering theory,"- M. Chemey, J. Math. Phys. 25, , OModulational Stability of Ground States of Nonlinear Schrodinger Equations,'- Michael Weinstein, (submitted). 4. SCIENTIFIC PERSONNEL SUPPORTED BY THIS PROJECT Dr. Tomas P. Girnius Dr. Paul K. Newton Dr. lsaak Rubinstein

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