摘要:

The axisymmetric vibrational characteristics of an elastic circular rod of finite length with stress‐free boundaries are analytically determined, and compared to approximate solutions. The solution approach consists of choosing a series of functions which term by term satisfy the governing equations and the boundary conditions on the shear stress. The boundary conditions on the axial and radial stress are satisfied by an orthogonalization procedure. This method yields an infinite eigenvalue matrix, the coefficients of which are transcendental functions of the frequency. It is found that the procedure converges and that sufficient accuracy is achieved, with truncation to a 20×20 eigenvalue matrix. Comparison is made of these results with the Pochhammer‐Chree solutions which do not permit satisfaction of the boundary conditions on the ends of the rod. This comparison shows many similarities, but also some dissimilarities. Comparisons are also made with the lowest mode of the free‐plate solution and the plane stress solution for very short rods, and with the one‐dimensional rod solution for long rods.

ISSN:0001-4966    

DOI:10.1121/1.1912835

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

Using the example of the plane motion of a membrane, an analytical method is developed for finding the approximate solution of the second‐order wave equation whose right‐hand side describes a pressure wave moving with decreasing velocity. It is assumed that the variation of the velocity includes the characteristic speed of wave propagation in the membrane. The method is elaborated for obtaining a solution which is valid in the early‐time region. It exploits the Laplace integral transform technique with appropriate approximate methods of inversion. The latter are improved here in comparison with those which have been previously developed in the analyses of similar problems, and can be easily generalized to approximate analyses of the early‐time stage of elastic waves which are caused in thin shells by a pressure wave.

ISSN:0001-4966    

DOI:10.1121/1.1912836

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

The theoretical prediction that significant regions of attenuation exist in the transmissibility curves of cantilever beams driven by dual forces of like magnitude and phase has been substantiated by the results of reciprocal experiments made on small aluminum beams and a laminated steel/viscoelastic beam. The attenuation provided by the laminated beam, which had high damping, was remarkably extensive and exceeded 15 dB at all frequencies above 100 Hz and 20 dB at all frequencies above 1.2 kHz. Agreement between theoretical prediction and reciprocal experiment has also been noted in two other cases:first, where the large region of attenuation predicted for a uniform cantilever beam was doubled in width and deepened by a factor of more than 10 when the beam was loaded by a suitably positioned lumped mass of similar magnitude to the beam mass (in fact, the resultant region of attenuation was bounded by frequencies that differed in value by a factor of 21 and was greater than 40 dB at its lowest point); andsecond, where a uniform cantilever beam was driven by forces that were not derived from an isolated source but, rather, were transmitted by two resilient mountings that supported a vibrating mass, which was used to represent a machine. Because the natural frequency of this simple mounting system fell well below the fundamental resonant frequency of the cantilever beam, the mounting system and the beam vibrated more or less independently. In consequence, the attenuation afforded by the simple mounting—essentially 12 dB/octave—superimposed on the region of attenuation noted previously in the beam transmissibility to provide an extremely large and continuous region of attenuation in the transmissibility across the combined simple mounting/beam system at all but low frequencies.

ISSN:0001-4966    

DOI:10.1121/1.1912837

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

A high‐speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder. Dispersion curves corresponding to real, imaginary, and complex propagation constants for the symmetric and the first four antisymmetric modes of propagation are given. The radial distributions of axial and radial displacements and of shear and normal stresses are given for the symmetric mode. By using a finite number of modes of propagation, an approximate solution is found for the problem of theL(0,1) mode impinging on a traction‐free interface. The reflection coefficient is determined in this way and the accompanying generation of higher order modes at the interface is shown to cause a high‐amplitude end resonance. Experimental results obtained by using the resonance method in conjunction with a long rod are presented to substantiate the calculated reflection coefficient and the frequency of end resonance. Phase velocities, based on measurements of the wavelength of standing waves and resonance frequencies, were obtained for the symmetric and first two antisymmetric modes. These measurements extend into the frequency range of more than one propagating mode. The rms deviation between theoretical and experimental results is in general less than 0.2% with the exception of the dispersion curve for theL(0,2) mode which deviates by 0.7%.

ISSN:0001-4966    

DOI:10.1121/1.1912838

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

A fundamental operational solution of the lossless Burgers' equation is used to derive the spectrum of a two‐frequency CW source of finite amplitude as a function of range. The resulting expression is then generalized to the case of a multipleN‐frequency CW source of finite amplitude. The region of validity of these solutions is determined by specifying the critical ranges at which the wavefronts become discontinuous. Finally, a modification of these omnidirectional solutions which makes them applicable to directive sources is briefly discussed.

ISSN:0001-4966    

DOI:10.1121/1.1912839

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

The acoustic decoupling behavior of onionskin paper is examined, with emphasis on sonar transducer applications. Nonlinear changes in the sound velocity of onionskin paper with pressure are used to predict the degradation of both frequency and directional response. These results are obtained by computer analysis of a longitudinal‐vibrator equivalent circuit. The results are in reasonable agreement with the measured characteristics of a specific transducer configuration.

ISSN:0001-4966    

DOI:10.1121/1.1912840

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

A line source and a line receiver are used to measure values of group and phase velocity for circumferential waves around a thin‐walled air‐filled aluminum cylinder when the cylinder is immersed in water. These are believed to be the first experimental measurements of phase velocity of circumferential waves around a thin‐walled cylinder. Also, experimental values of attenuation are measured for pulses. These experiments are carried out for frequencies from 50 to 200 kHz, corresponding to a value ofkafrom 15 to 60. A theoretical analysis based on the equivalent mechanical impedance of a thin‐walled elastic shell is developed and numerical values are computed for comparison with the experimental data. The phase velocity measurements agree with computed values in their dependence on frequency, but the values are systematically too large by 2%. However, the experimental values measured for pulses do not show good agreement with theory.

ISSN:0001-4966    

DOI:10.1121/1.1912841

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

The techniques of linear programming have been applied to the synthesis of optimum directional patterns from arrays of point elements. The simplex method has been used to generate optimum element excitations for a given array when the desired directional characteristics are specified. Various criteria are included in the definition of optimality. Numerical examples are given for arrays of up to 70 elements. The size and geometry of arrays that can be treated by this approach are limited only by computation time and computer storage requirements.

ISSN:0001-4966    

DOI:10.1121/1.1912842

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

By considering the stochastic nature of microfluctuations in the real ocean, the conventional ray‐theory intensity relation is extended to permit consideration of partial coherence in multipath problems. The partial coherence factor is shown to be a function of the curvilinear range, the frequency, and the oceanographic conditions. In addition, a practical estimate for the standard deviation σIof the intensity about its expected value is found; σIis shown to depend on the partial coherence factor and to saturate as this factor approaches zero.

ISSN:0001-4966    

DOI:10.1121/1.1912843

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP

摘要:

This theoretical article investigates the acoustic field in the image‐interference and shadow‐zone regions for a model in which the sound velocity decreases with increasing depth from the surface. Near the surface the shadow‐zone boundary is the surface‐grazing ray, while in deeper regions this boundary is a caustic. The field near the caustic is investigated by modified ray theory based on Airy functions. A comparison of mode theory results with those of ray theory indicates that there is a −π/2 jump in the ray theory phase when the ray touches a caustic. There is, however, no such jump when the ray becomes horizontal. The normal‐mode series is absolutely convergent for ranges greater than 1.732 times the sum of the source and receiver depths. When the shadow zone is bounded by a well‐developed caustic, the series converges so slowly as to be impractical except at ranges well into the shadow‐zone region.

ISSN:0001-4966    

DOI:10.1121/1.1912844

出版商:Acoustical Society of America    

年代:1972

数据来源: AIP