摘要:

This paper presents three different solutions to a one‐dimensional model of the propagation of finite‐amplitude traveling waves in rigid‐walled ducts. The first two solutions, in the nature of perturbation solutions, provide useful information for relatively weak waves; the distances for which the solutions are valid range from α1x≪1 to α1x<∞, depending on the strength of the waveform and the particular solution considered. The third solution is based on a set of first‐order coupled nonlinear differential equations with one independent and two dependent variables. This solution is useful for all values of α1xfor strengths up to those necessary for shock formation. Results include graphs of relative harmonic distortion, predictions of waveform profiles, and representative graphs illustrating the dispersive behavior of the phase speeds of the individual harmonics.

ISSN:0001-4966    

DOI:10.1121/1.1912331

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

We discuss the nonlinear generation of a second‐harmonic component in the first‐harmonic beam from a circular plane piston, radiating into a fluid. First‐order perturbation theory is used; higher harmonics, absorption, and depletion of each harmonic are ignored, although a partial correction for the last two effects is applied later. The ratio of piston diameter to first‐harmonic acoustic wavelength is assumed to be about 30 or greater. In particular, the axial behavior of the second harmonic, which has marked structure, is found to agree well with experimental results in water. Also, the average value of the second‐harmonic field is calculated over a circle coaxial with the source, parallel to it, and of the same size. This average differs considerably from the result of an oversimplification that treats the first‐harmonic beam as cylindrically collimated plane waves. When compared with measurements in water, the average agrees well at a source pressure of 3 atm but progressively less well at 5 and at 6 atm. It is suggested that both theory and experiment contribute to the discrepancies.

ISSN:0001-4966    

DOI:10.1121/1.1912332

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

A sound wave with angular frequency ω and finite amplitude ε, propagating in a rigid waveguide of any non‐rectangular cross section, is considered. The pressure and velocity potential of the wave, corresponding to each mode of the linear theory, are determined as power series in ε. The leading term is just the mode given by the linear theory and further terms are finite‐amplitude corrections to it. The wavenumber or propagation constantknof thenth mode is found to depend upon ε and is also determined as a power series. The fact thatkndepends upon ε, and the expression forkn(ε), is the most interesting consequence of the analysis. This shows that the propagation velocity ω/kndepends upon ε. The results are specialized to a waveguide of circular cross section. Then numerical values ofkn(ε) are given for a circular guide filled with air forn= 1, 2, 3, 4, and 5. The lowest mode (n= 0) is not considered because shocks occur in it. The method of analysis is a perturbation expansion adapted to eliminate secular terms. It has been used before to treat periodic finite‐amplitude sound waves in a closed container and periodic finite‐amplitude vibrations of strings and beams by J. B. Keller and L. Ting [Comm. Pure Appl. Math.19, 371 (1966)], and to treat nonlinear electromagnetic wave propagation [Phys. Rev.181, 1730 (1969)] and other nonlinear boundary‐value problems by the authors [J. Math. Phys.10, 342 (1969)].

ISSN:0001-4966    

DOI:10.1121/1.1912333

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

One of the interesting and important problems involving turbulent jets is that of determining the spectrum of the radiated sound. This has proved to be a difficult theoretical problem because the space‐time correlation of the velocity is central in the prediction of such sound characteristics. In this work, the following assumptions are used in the development. First, it is supposed, as is often the case in turbulence measurements, that the turbulent fluid has approximately Gaussian statistical characteristics. Then, it is supposed that the space‐time characteristics for the needed second‐order velocity correlation can be obtained by assuming that the fluid is approximately in “frozen flow.” From these assumptions, the higher‐frequency sound‐power spectrum is obtained in terms of an integral over the turbulence energy spectrum. For the familiar energy spectrumk−5/3, it is found that the sound spectrum behaves like ω−4/3. This is flatter than most measurements. A measured frequency spectrum of ω−3would be obtained from an energy spectrumk−5/2.

ISSN:0001-4966    

DOI:10.1121/1.1912334

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

The generation of transient signals by the propagation of large‐amplitude pulses has been investigated. Measurements of the transient signal along the axis of propagation of 10‐MHz pulses in carbon tetrachloride confirm the validity of the theoretical treatment of Berktay [J. Sound Vibration2, 435–461 (1965)]. Data are also presented for the angular dependence of the transient signals generated by 20‐MHz pulses in water.

ISSN:0001-4966    

DOI:10.1121/1.1912335

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

Plane simple compression waves of finite amplitude are studied as they propagate into a fluid medium of constant state. Shock formation and subsequent expansion, as well as rise and decay of shock strength, are determined from a boundary‐value problem of mixed type involving a fixed boundary (source) and a moving boundary (shock surface). At the source, an overpressure is arbitrarily prescribed as a function of time; at the shock surface, the simple wave solutions are shown to satisfy the exact shock‐transition conditions within an accuracy including second powers of shock strength, while the shock speed is determined precisely. Shock speed and rise and decay of shock strength are shown to be strongly dependent on the particular form of the overpressure generated at the source in the course of time. Approximation formulas are derived for weak shocks and are used in a detailed discussion of two examples.

ISSN:0001-4966    

DOI:10.1121/1.1912336

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

In some applications, coupling loss factors can be estimated either by using wave‐transmission methods or by using natural frequency‐shift methods. It is demonstrated that the two procedures give essentially the same results for a particular system. This is in contrast with the result given in a recent note which exhibited a fivefold discrepancy between the methods. An explanation for that discrepancy is proposed.

ISSN:0001-4966    

DOI:10.1121/1.1912337

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

Efficient and practical methods of simulating multivariate and multidimensional processes with specified cross‐spectral density are presented. When the cross‐spectral density matrix of ann‐variate process is specified, its component processes can be simulated as the sum of cosine functions with random frequencies and random phase angles. Typical examples of this type are the simulation, for the purpose of shaker test, of a multivariate process representing six components of the acceleration (due to, for example, a booster engine cutoff) measured at the base of a spacecraft and the simulation of horizontal and vertical components of earthquake acceleration. A homogeneous multidimensional process can also be simulated in terms of the sum of cosine functions with random frequencies and random phase angles. Examples of multidimensional processes considered here include the horizontal componentf0(t,x) of the wind velocity perpendicular to the axis (xaxis) of a slender structure, the vertical gust velocity fieldf0(x,y) frozen in space, and the boundary‐layer pressure fieldf0(x,y,t). Also, a convenient use of the present method of simulation in a class of nonlinear structural vibration analysis is described with a numerical example.

ISSN:0001-4966    

DOI:10.1121/1.1912338

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

The ultrasonic absorption in pure methylcyclohexane was measured in temperatures from 20°C to 60°C. The temperature dependence of μmaxdisagrees with that extrapolated from high‐temperature experiments by Piercy and Subrahmanyam [J. Chem. Phys.42, 4011 (1965)], but rather agrees with that derived by Pedinoff [J. Chem. Phys.36, 777 (1962)].

ISSN:0001-4966    

DOI:10.1121/1.1912339

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP

摘要:

Natural frequencies of simply supported elastic arcs vibrating in the plane perpendicular to the plane of initial curvature are obtained by applying a method previously used by the authors to determine upper‐ and lower‐bounds frequencies of curved beams. This method, based on the theory of adjoint operators, was originally proposed by Lehmann, Maehly, and Kato. The centerlines of the arcs are in the forms of circles, cycloids, catenaries, and parabolas. The numerical results obtained are plotted graphically.

ISSN:0001-4966    

DOI:10.1121/1.1912340

出版商:Acoustical Society of America    

年代:1971

数据来源: AIP