885095997

WEDNESDAY AFTERNOON, 1 MAY 1991

CARROLL, 1:30 TO 3:30 P.M.

Session 5PA

Physical Acoustics: Nonlinear Phenomena

Andres Larraza, Chair

Physics Department, Nami Postgraduate School, Monterey, California 93943

Contributed Papers

1:30

5PA1. The trans-spectral coherence in the solution of the Duffing^łs equation, undergoing chaos. P. G. Vaidya (Dept. of Mech. and Materials Eng., Washington State Univ., Pullman, WA 99164)

An analysis of the time senes generated by the Duffing’s oscillator, undergoing chaos, has been cairied out. The senes is inspcctcd for the existence of the trans-spectral cohercnce, which is the coherence be-tween two different spectral components. (Tlie techniquc to calculate such coherence has been demonstrated previous!y by Vaidya and Anderson.) In the case of the Duffing’s equatiou. a significant coherence is seen across the trans-spectrum. This shows the presence of order, co-existing with randomness, in this series. A compauion paper at this conference explains the origin of such order.

1:45

5PA2. ExŁstence of a hierarchy of periodic components in the solution of the Duffing*s equation, undergoing chaos. P. G. Vaidya and Amit Athalye (Dept. of Mech. and Materials Eug., Washington State Univ., Pullman, W A 99164)

Chaos is rccognized as a State manifesting the characteristics of both order and randomness. An analysis of the Duffing*s oscillator, undergoing chaos, has been carried out. The solution is written as a sum of a periodic solution, representing a limit cyclc, and a residue. When the residue is assumed to be smali, it is shown to be governed by a linear nonautonomous equation that is unstable. When the residue is allowed to be large, it is governed by an cąuation whose solution is once again bounded and chaotic. This new solution can, in tum, be represented as the sum of a periodic and a chaotic solution. This process in theory can be carricd out indcfinitely. The analysis sheds some light on the naturę of chaos generated by the Duffing’s equation, and it also explains the significant amount of the trans-spectral coherence observed in the time series generated by its solution.

describe propagation of axisymmetric convergent and divergent waves. The present problem concerns nonlinear pulse propagation in a focused field. In order to initialize the moving window convected by NPE. a linear spherical wave assumption is madc adjacent to the transducer; i.e., inside the convcrging beam, the input field is represented as a linear spherical wave, while outside the beam, the input field is considercd to be zero. Temporal waveforms arc computed on- and off-axis and are compared to the experimental data by Baker and Humphrey (Frontiers of Nonlinear Acoustics 12th ISNA, pp. 185-190 (1990)]. (Work sup-ported by George W. Woodruff endowment.]

2:15

5PA4. Harmonie generation in focused sound reflected from a curved surface. Inder Raj S. Makin (Biomed. Eng. Próg., The Univ. of Texas at Austin, Austin, TX 78712-1084) and Mark F. Hamilton (The Univ. of Texas at Austin, Austin, TX 78712-1063)

In an earlier presentation (A. Averkiou and M. F. Hamilton, J. Acoust. Soc. Am. Suppl. 1 85, S93 (1989)], as analysis of the linear propagation and reflection of a focused Gaussian beam was reported. The reflecting surface was assumed to be slightly curved and perfectly rigid. Here, second harmonie generation in the incidcnt and reflected beams is investigated, with absorption and finite surface impedance now taken into account. Closed-form Solutions for the second harmonie pres-sure and power are derived from the KZK nonlinear parabolic wave equation. Propagation curves and beam patterns are presented for var-ious target curvatures and impedances. Both before and after reflection, the transverse distribution of the second harmonie pressure is equal to the square of the transverse distribution of the fundamental pressure. Variations in the relative phase between the fundamental and second harmonie components, due to propagation through foci and reflection from the target, significantly influence the process of harmonie generation. Implications for ultrasonic imaging are discussed. (Work sup-ported by NSF, the David and Lucilc Packard Foundation, and the Texas Advanccd Research Program.]

2:00

5PA3. A venśon of NPE for nonlinear propagation of ultrasonic pubes in focused field. Gee-Pinn James Too, Jerry H. Ginsberg, and Jacqueline Naze Tjdtta (School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332)

The NPE (nonlinear progressive wave equation) and associated Computer program are a time domain representation that was developed by McDonald and Kuperman to study waveguide problems. The present work extends the earlier studies (Too and Ginsberg (1989— 1990)], which developed a modified version of NPE in terms of axisym-mełric cylindrical coordinatcs to describe propagation of finite-amplitude sound beams. In the present studies, a new version of NPE is studied in which axisymmetric spherical coordinatcs are employed to

1928 J. Acoust. Soc. Am.. Vol. 89, No. 4, Pt. 2, April 1991

2:30

5PA5. Finite-amplitude wave propagation through a two-phase system using coupled generalized Burgers* eąuations. A. Benharbit (Dept. of Math., Pcnn State Univ.—York Campus), T. S. Margulies (U.S. Nuclear Regulatory Commission, Washington, DC 20555), and W. H. Schwarz (Johns Hopkins Univ., Baltimore, MD 21218)

The propagation of finite-amplitude acoustic waves through a system of fluid particles in a fluid mairix (aerosols or emutsions) has been cxamined theoretically by using the continuum vo!ume-averaged bal-ance equations and linear constitutive equations for a two-phase system. Utilizing the technique developed by Lighthill for clean perfect gases, and by Davidson (G. A. Davidson, J. Sound Vib. 38. 475-495 (1975)],

12lst Meeting: Acoustical Sodety of America 1928