摘要:

In this paper we present a detailed study of the theory of free, axisymmetric vibrations of thin elastic spherical shell and demonstrate by experiment that the normal modes of vibration predicted by theory do exist. The theory, which is an expansion of an ancient study by Lamb, predicts the existence of two infinite sets of normal modes, one of which is bounded in frequency and the other unbounded. The first four modes in each set are identified by experiments on a small steel shell.

ISSN:0001-4966    

DOI:10.1121/1.1908562

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

In two‐dimensional linear acoustic theory Huygens' principle fails; the failure of Huygens' principle being manifested by the existence of a tail to the acoustic pulse. A two‐dimensional problem of importance is the radiation of acoustic pulses of various shapes by an infinitely long circular cylinder. The problem is attacked directly via the use of the Laplace transform. In the inversion of the Laplace transform, relatively new function called the NielsenW0function is encountered. Exponential, sine, and rectangular pulses are studied and their shape determined at various distances from the cylinder. Finally the passage to the steady state of a semi infinite sine wave train is outlined.

ISSN:0001-4966    

DOI:10.1121/1.1908564

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

It is noted that an electromagnetic wave incident upon the boundary of an ionized medium in the presence of a transverse magnetic field will excite, in addition to the reflected and transmitted electromagnetic waves, a reflected sound wave and a transmitted modified sound wave. It is shown that the power coupled into these acoustic waves is proportional to the magnetohydrodynamic coupling parameterβ = σ B2/ωρand to the ratio of sound velocity to light velocity. Finally it is pointed out that electromagnetic transmission through a thin ionized layer may take place by means of this modified sound wave even though the layer thickness is large compared to the electromagnetic skin depth, although the efficiency of transmission will be very low for weak magnetohydrodynamic coupling.

ISSN:0001-4966    

DOI:10.1121/1.1908566

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

An examination of the scattering process in the vicinity of cutoff is made using rigid surfaces with sinusoidal corrugations which have a maximum slope near one. Measurements of the specular amplitude for several angles of incidence are presented with small increments in frequency. The ratio of the pressure amplitude at the peaks and troughs of the corrugations as a function of frequency is also observed for several angles of incidence.

ISSN:0001-4966    

DOI:10.1121/1.1908568

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

The Rayleigh solution for reflection from a corrugated surface, and some possible modifications, are examined. For small slopes these methods produce similar analytical expressions and almost identical numerical results. When the first nonradiating term is included in the computations, the magnitude of the scattered amplitudes is essentially the same, but an estimate of the phase change as a function of frequency is provided. For larger slopes, differences appear in the analytical form as well as in the numerical results. The Rayleigh expression has advantages above cutoff, while a new approach seems better before and just after cutoff.

ISSN:0001-4966    

DOI:10.1121/1.1908570

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

The differential equation for radial vibrations of a thin cylindrical shell is derived by Hamilton's principle for the case of constant internal and transient external pressures. Both pressures are assumed symmetrical about the cylinder's axis of symmetry, and the natural frequencies and mode shapes are obtained. The general solution to the transient forced‐vibration problem is presented using integral transform methods. The general solution is then carried out in detail for the specific case where the external pressure is a step function moving over the cylinder in the axial direction. It is pointed out that such a solution may be considered as a crude model of what happens to a thin‐skinned missile during launching from a silo. Several other problems are mentioned which have the same type of governing differential equations and for which the solutions presented would be useful.

ISSN:0001-4966    

DOI:10.1121/1.1908572

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

A theory of linear systems with randomly varying parameters is developed under the assumption that the parameter processes are Gaussian processes obtained by linear filtering of white noise. By this device, the restriction to white‐noise parameter processes of previous studies has been removed.By a method related somewhat to a technique used in the theory of the multiple scattering of light, a system of linear integral equations for the determination of various second‐order moments of the system output is derived. This system can be solved explicitly in some interesting cases.A theory of stability in mean and in mean square is given for random systems. It was found that mean square stability depended only on the values of the auto‐ and cross‐correlation functions of the parameter processes at the origin and not on the detailed structure of these functions.The stability theory is applied to an RLC circuit with randomly varying capacitance. The possibility of stabalizing unstable deterministic systems with random noise is discussed.

ISSN:0001-4966    

DOI:10.1121/1.1908574

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

Approximate formulas are derived for the lowest natural frequencies of hinged elastic arcs having the center lines in the form of a circle, of a cycloid, of a catenary, and of a parabola in the case of vibrations occurring either in the plane of the initial curvature or in the plane perpendicular to the plane of the initial curvature of the arcs. Numerical results for the frequencies are presented in tabular and graphical form. The paper supplements previous published papers by the present authors in which the same problems were solved for the case of elastic built‐in arcs.

ISSN:0001-4966    

DOI:10.1121/1.1908576

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

Shots were fired at a fixed location and constant shallow depth at12‐hrintervals over a period of 15 hr. Shots fired in this way produced a highly repeatable signal. The signals were received at a fixed location 63 miles away on hydrophones at 3000‐ and 9100‐ft depths. The signals exhibit about 40% correlation over a period of12 hrand about 20% correlation over a period of 1 hr.

ISSN:0001-4966    

DOI:10.1121/1.1908578

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP

摘要:

A simple derivation is given of the phase autocorrelation function of a monochromatic signal during transmission through a medium with random fluctuations of refractive index. The resulting phase coherence function is then applied to the theory of the linear array antenna to yield a formula for the degraded directivity pattern.The analysis developed here was conceived primarily with reference to acoustic signals and sonar ranging systems, although it may be applied,mutatis mutandis, to a wider variety of acoustic and even electromagnetic problems. For concreteness, however, we shall employ a vocabulary appropriate to the case of sonar signals and antennas.The problem to be considered is the following: Given a source of monochromatic radiation situated far enough from the receiving antenna to be considered a point source, what will be the response, as a function of bearing angle, of a linear array antenna to the signal if the transmission medium has small random irregularities of its refractive index?

ISSN:0001-4966    

DOI:10.1121/1.1908580

出版商:Acoustical Society of America    

年代:1961

数据来源: AIP