摘要:

The equations governing the propagation of longitudinal and of torsional waves in thin, tapered rods are of similar form. It is, therefore, possible to use the method by which longitudinally resonant amplitude transformers were previously designed [J. Acoust. Soc. Am.35, 1367–1378, (1963)] to design torsionally resonant transformers. These torsional transformers are capable of extremely high magnifications.

ISSN:0001-4966    

DOI:10.1121/1.1918900

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

The propagation of mechanical and thermal disturbances studied according to the coupled thermoelastic theory. In the formulation of the coupled theory of thermoelasticity, the heat‐conduction equation contains the time derivative of the dilatation as a source term. In the procedure introduced here, that term is replaced by one representing the time derivative of the dilatation at the wavefront only. In this way, the equations governing the mechanical and thermal effects are formally uncoupled, and thus are easier to solve; at the same time, it is shown that most of the coupling effect is retained. To check the approximation procedure, two one‐dimensional problems are considered. The solutions for these problems show excellent agreement with known exact solutions. The approximation is then applied to the three‐dimensional problem of the suddenly applied force in the infinite medium. Curves for the displacement and temperature distributions are provided for this case. The temperature distribution shows a discontinuity that moves with the wavefront of the dilatational wave.

ISSN:0001-4966    

DOI:10.1121/1.1918902

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

An analysis is made of the P‐head‐wave amplitude to be expected at liquid‐liquid and liquid‐solid interfaces. The minimum range at which the asymptotic approximation for the range dependence of the head‐wave amplitude holds is shown to be smaller for the liquid‐liquid than for the liquid‐solid case. The range dependence and absolute magnitudes of the head‐wave amplitude are determined experimentally by using ultrasonic techniques and are compared with the results obtained from analysis.

ISSN:0001-4966    

DOI:10.1121/1.1918904

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

Experiments are described that confirm that the amplitude of the head wave produced at a liquid layer is modified by reflection from the base of the layer. Knowing the shape of the incident wave (and, hence, of the head wave), it is possible to calculate the decay of the head‐wave amplitude with horizontal range. These rates of decay agree well with those determined experimentally.

ISSN:0001-4966    

DOI:10.1121/1.1918906

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

A geometrical theory is devised for the description and calculation of surface waves, such as Rayleigh waves, on boundaries or interfaces of elastic solids. It applies to curved surfaces and to inhomogeneous media. The theory, which is an extension of geometrical optics, involves complex rays that travel from the source to the surface, then along the surface, and finally from the surface to points in the solid. It also includes phases and amplitudes associated with each point on each ray. Geometrical formulas are derived for the determination of these phases and amplitudes. They involve certain excitation and radiation coefficients, which are also determined. The total displacement at a point is the sum of the displacements on all the rays through the point, each of which is constructed from the corresponding phase and amplitude. The theory applies to periodic waves of high frequency and short wavelength, as well as to the rapidly varying portions of any waveform. It is a generalization of the authors' earlier geometrical theory of scalar surface waves [J. Appl. Phys.31, 1039 (1960)].

ISSN:0001-4966    

DOI:10.1121/1.1918908

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

An approximate theory of vibrations of orthotropic, thick, cylindrical shells, in which the effect of transverse normal stress is retained, is deduced from the three‐dimensional theory of elasticity. The present theory contains, in addition to the usual membrane and bending terms, the influence of rotatory inertia and transverse‐shear deformation. As an application, the propagation of free harmonic waves in an infinite cylindrical shell is studied. Numerical results are given for relatively thin and thick shells of isotropic and nonisotropic materials.

ISSN:0001-4966    

DOI:10.1121/1.1918910

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

The response characteristics of beams and flat rectangular panels excited by specific acoustic fields are analyzed mathematically. Acoustic‐structural coupling‐coefficient (joint acceptance squared) frequency spectra indicate a marked sensitivity to changes in the spatial‐correlation distribution. Panel mode shapes progressively lose their wavelength selectivity as spatial correlation decreases.

ISSN:0001-4966    

DOI:10.1121/1.1918912

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

The exact nonlinear differential equations of motion for free symmetric vibration of a circular membrane have been derived and solved, approximately, by a perturbation procedure and the Ritz‐Galerkin technique. The resulting Duffing equation with a hardening‐spring characteristic for the fundamental mode of the membrane was solved for the ratio of the nonlinear to linear period of free vibration. Theoretical expressions for air virtual mass, damping, and the nonlinear spring stiffness were used to obtain an approximate solution to sinusoidal excitation of the membrane. The results from an experimental program for sinusoidal acoustic excitation of a nonlinear circular membrane have been presented. Construction of the membrane fixtures and a capacitance‐type transducer used for transient‐ and frequency‐response displacement measurements on several Mylar and aluminum membranes is described. Experimental data on the air virtual mass, frequency response at various ambient air pressures, dynamic mode shape, and damping are shown. The theoretically derived “backbone” curves of the Duffing‐equation frequency response appeared to be in very good agreement with the experimental data. The damping was found to be nonlinear, with some indications of being nonviscous as well.

ISSN:0001-4966    

DOI:10.1121/1.1918914

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

This paper is concerned with the vibration analysis of spherical shells, closed at one pole and open at the other, by means of the linear classical bending theory of shells. Frequency equations are derived ha terms of Legendre functions with complex indices, and for axisymmetric vibration the natural frequencies and mode shapes are deduced for opening angles ranging from a shallow to a closed spherical shell. It is found that for all opening angles the frequency spectrum consists of two coupled infinite sets of modes that can be labeled as bending (or flexural) and membrane modes. This distinction is made on the basis of the comparison of the strain energies due to bending and stretching of each mode. It is also found that the membrane modes are practically independent of thickness, whereas the bending modes vary with thickness. Previous analyses with the use of membrane theory have shown that one of two infinite sets of modes is spaced within a finite interval of the frequency spectrum. It is shown in this paper that this set of modes is a degenerate case of bending modes, and, if deduced by means of membrane theory, it is applicable only when the thickness of the shell is zero. When the bending theory is employed, then the frequency interval for this set of modes extends to infinity for every value of thickness that is greater than zero.

ISSN:0001-4966    

DOI:10.1121/1.1918916

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP

摘要:

This paper introduces the concept of a nonstationary shot noise, which may be viewed as Poisson‐distributed impulses with varying impulse strength. The response of a linear system to the excitation of a nonstationary shot noise is then determined by using the method of Fokker‐Planck. The more general result obtained here is reducible to the known solution associated with stationary excitation.

ISSN:0001-4966    

DOI:10.1121/1.1918917

出版商:Acoustical Society of America    

年代:1964

数据来源: AIP