摘要:

A special analytical method, which combines the parabolic approximation (KZ equation) with nonlinear geometrical acoustics, is developed to model nonlinear and diffraction effects near the axis of a finite amplitude sound beam. The corresponding system of nonlinear equations describing waveform evolution is derived. For the case of an initially sinusoidal wave radiated by a Gaussian source, an analytic solution of the coupled equations is obtained for the paraxial region of the beam. The axial solution is expressed in both the time and frequency domains, and is analyzed in detail for both unfocused and focused beams in their preshock regions. Harmonic propagation curves are compared with finite difference solutions of the KZ equation, and good agreement is obtained for a variety of parameter values.

ISSN:0001-4966    

DOI:10.1121/1.418158

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

The Foldy–Wouthuysen transformation can be used to reduce the relativistic Klein–Gordon equation to the nonrelativistic Schrödinger equation. This technique is modified and applied to the problem of wave propagation through media with a range-dependent index of refraction. The forward and backward propagating components of the field are decoupled order-by-order to produce a perturbative expansion of the range-dependent parabolic equation. The result includes energy-conserving correction terms that can be associated with a rapid fluctuation of energy between forward and backward propagating solutions of the Helmholtz equation. The approach selects out physical processes which accumulate over the entire range of propagation, distinguishing them from effects which depend solely on the initial and final values of the index of refraction and its derivatives. It is also shown that the corresponding backscatter mechanism is fundamentally nonperturbative, so that the parabolic equation technique as applied to the problem of propagation through range-dependent media generates an asymptotic expansion of the exact solution. This procedure has been applied to long-distance low-frequency propagation through a sound channel with internal waves. For this application, the expansion parameters are typically very small, so the propagation distances must be very large for the effect to be detectable.

ISSN:0001-4966    

DOI:10.1121/1.418159

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

Although variations in the density,ρ, are naturally incorporated into finite-difference parabolic equation (PE) solvers, split-step PE algorithms traditionally account for density changes by adding to the refractive index terms containing derivatives ofρ. As a consequence, geoacoustic density profiles that contain step discontinuities at layer interfaces must be smoothed appropriately before these extra terms can be evaluated. In this paper, a new hybrid method is proposed for treating density inhomogeneities in the split-step PE. This approach involves splitting the differential operator into density-independent and density-dependent components. While the former terms may be evaluated with the split-step Fourier technique, the influence of density changes is handled through a finite-difference procedure. Such an algorithm can be easily implemented in recently proposed hybrid split-step/finite-difference and split-step/Lanczos PE solvers. [J. Acoust. Soc. Am.96, 396–405 (1994)].

ISSN:0001-4966    

DOI:10.1121/1.418160

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

The effects of internal waves on low-frequency (25 Hz) narrow-band source localization performance are investigated at a very long range (1000 km). Sound-speed perturbations induced by internal waves obeying the Garrett–Munk spectral model are incorporated into the normal mode solution to the wave equation using the adiabatic approximation. Sensitivity of source localization on the internal wave modal content is examined. For the entire range of signal-to-noise ratios (SNR) and degrees of internal-wave field structure, the optimal uncertain field processor (OUFP) provides both the signal processing algorithm as well as the limitations on source localization performance. For high SNR, the localization errors are local and the performance level of the OUFP is predicted by the hybrid Cramer–Rao lower bound (CRLB). In fairly structured internal-wave environments, significant performance gains are made optimally localizing the source. Under very random internal-wave environments, the environmental variability limits the performance of all signal processing algorithms.

ISSN:0001-4966    

DOI:10.1121/1.418161

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

A theoretical model, based on mode theory, is presented in order to study the behavior of the Stoneley wave when it reaches the extremity of a thick plate immersed in a liquid. The superposition of two phenomena is established: the first one being the simple forward diffraction of the Stoneley wave in the liquid and the second one being its conversion into two generalized Rayleigh waves which propagate on the same plane as the incident Stoneley wave or along the vertical end face of the solid support. The theoretical analysis is in good agreement with the experimental observations of Tinel [Ph.D. Thesis, Université Le Havre, France (1991)].

ISSN:0001-4966    

DOI:10.1121/1.418162

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

The propagation of a Stoneley wave through an inclusion near a liquid/solid interface is investigated on the basis of mode theory [Briers et al., J. Acoust. Soc. Am.95, 1953–1966, 1967–1976 (1994)]. An expression for the phase and amplitude changes of the Stoneley wave is derived and analyzed in the case of a thin (kd≪1) and of a thick (kd≫1) inclusion of arbitrary length (kdis the multiplication of the liquid wave number with the thickness of the inclusion).

ISSN:0001-4966    

DOI:10.1121/1.418163

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

This study shows, on the basis of a mode theory, that as a Gaussian ultrasonic beam strikes the edge of a thick plate immersed in a liquid, a Stoneley wave is generated along the liquid/solid interface. As expected, the largest amplitude for the excited Stoneley wave is obtained for normal incidence at the edge but a secondary maximum appears at Rayleigh angle incidence. In this way, it is proved theoretically that the conversion phenomenon of a Stoneley wave into a generalized Rayleigh wave at the extremity of a fluid loaded thick plate is reversible, as was observed experimentally by Tinel [Ph.D. thesis, Université Le Havre, France (1991)].

ISSN:0001-4966    

DOI:10.1121/1.418164

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

A study of the use of large transducers (80 mm×40 mm, 3.2 MHz center frequency) for the measurement of ultrasonic transmission coefficients is reported. Tests have been carried out on thick and thin glass plates and on a unidirectional carbon fiber composite plate. The material properties of the plates were obtained by comparing the transmission coefficient results at particular angles with the predictions of plane-wave theory for different material properties; the properties giving the best fit were then used to predict the transmission coefficients at other angles. The results of this preliminary study show that the use of large transducers makes it possible to obtain excellent agreement between measured transmission coefficients at all angles and those predicted using plane-wave theory. The large transducers give clearer definition of the transmission maxima than is obtained with smaller, conventional transducers, and also give good agreement with the predicted transmission coefficient amplitudes. This should improve the accuracy of inversion procedures for the determination of the real parts of the elastic constants from the frequencies of the transmission maxima, and the good amplitude agreement opens up the possibility of obtaining accurate estimates of the imaginary parts of the elastic constants.

ISSN:0001-4966    

DOI:10.1121/1.418103

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

Transmission rates and dispersion relations ofSHphonons in a (111) superlattice are calculated. Unlike the case of a (100) superlattice, phonon stop bands appear inside the folded Brillouin zone in general rather than at the center and edges. A superlattice structure factor is introduced appropriately for phonon reflection or Bragg conditions in the superlattice. More importantly, the transfer matrix contains information not only about the dispersion relation, but also about the condition for frequency bands or stop bands in the dispersion relation, and the extinction rule for the Bragg reflection. The locations of the stop bands inside of the folded zone are defined as a function of frequency and incidence angle of the phonons.

ISSN:0001-4966    

DOI:10.1121/1.418165

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP

摘要:

An experimental investigation of sound propagation in a single pore of circular cross section is described. By working at low frequencies and in various pressure ranges, viscous and thermal penetration depths which range from less than, to much greater than, the pore radius are achieved. The system is an experimental model for a pore in either sound absorbing material or the “stack” region of a thermoacoustic engine. The measured acoustic response compares favorably with theoretical predictions. Deviations are attributed to the cell geometry. In certain ranges of pressure and frequency, simple scaling properties may be utilized to determine the relative viscosity and thermal diffusivity of gases. Measurements of both quantities (relative to those of argon) for helium, neon, nitrogen, krypton, and water vapor (viscosity only) are presented and compared with known values. Practical applications of the experimental technique are discussed.

ISSN:0001-4966    

DOI:10.1121/1.418166

出版商:Acoustical Society of America    

年代:1997

数据来源: AIP