摘要:

An approximate solution to the equations of elasticity is obtained for the problems of steady‐state longitudinal, flexural, and torsional wave propagation in isotropic bars of infinite length and rectangular cross section. Results were obtained for sections with various ratios of width to depth. These results indicate that, in a phase‐velocity versus wavenumber plot, the higher branches exhibit a certain minimum feature; i.e., these branches approach their limiting value at bγ = ∞ from below. This feature has not been reported in the case of bars with a circular cross section.

ISSN:0001-4966    

DOI:10.1121/1.1910255

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

The axisymmetric plane‐strain vibrations of a thick‐layered orthotropic cylindrical shell are analyzed, using a generalized Fourier‐series technique that allows the determination of the frequencies and vibration modes of the composite shell in terms of those of the individual layers. These vibration modes are used to study the forced vibrations of such a shell subjected to an internal harmonic pressure. Numerical results are presented for a two‐layered orthotropic cylindrical shell.

ISSN:0001-4966    

DOI:10.1121/1.1910256

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

The phenomena of amplitude jumps and nonplanar oscillations, which are characteristic features of non‐linear resonance in stretched strings, have been studied in detail, taking the effect of damping into account. Expressions for the resonance frequency and amplitude, and the frequencies and amplitudes at which the jumps occur, have been obtained; and it has been shown that the resonance frequency is not a constant of the system but increases with the driving force. Finally, it is established that, in the presence of damping, (1) nonplanar oscillations exist only if the driving force φ exceeds a certain critical value, φu; (2) over a small interval of the driving force φj′;>φ>φwthe nature of the downward jump is qualitatively different from the (normal) downward jump occurring for values of φ greater than φj′; (3) if φ, lies in the interval φw>φ>φj, jump phenomenon is exhibited even though the oscillations are planar at all frequencies; and (4), if φφw, upward jump in amplitude is always accompanied by a transition to nonplanar motion unless the damping is very heavy.

ISSN:0001-4966    

DOI:10.1121/1.1910257

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

The beam equation for a uniform‐cross‐section, damped, elastically supported clamped‐clamped beam is solved for very general conditions of arbitrary initial, boundary, and distributed‐load conditions. The solution is based on the properties of a Hermitian operator and its orthogonal basis vectors, with which an arbitrary vector can be expanded.

ISSN:0001-4966    

DOI:10.1121/1.1910258

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

The partial differential equations governing the motion of plates, when transverse shear and rotary inertia are considered, are solved for plates bounded by elliptical and hyperbolic cylinders. By assuming product solutions for the partial differential equations (in elliptical coordinates) Mathieu's equations and Mathieu's modified equations are obtained. The resulting solutions satisfy all of eight different boundary conditions entering into the theory. The elimination of the arbitrary constants in each boundary problem leads to the frequency equation for the normal modes of vibration.

ISSN:0001-4966    

DOI:10.1121/1.1910259

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

When a closed spherical shell is suddenly enveloped by a uniform impulse, the response is a purely radial motion of each shell element. If the impulse is slightly nonuniform, this membrane “breathing mode” may be dynamically unstable due to the interaction of the membrane stress with flexural curvature. The linear solution for axisymmetric motion divides into two sets of modes. One set, the membrane modes, is essentially extensional; the second set, the composite modes, is neither purely extensional nor purely inextensional. The linear response to an arbitrary radial velocity distribution indicates that breathing mode stability may be considered with respect to perturbations exciting only composite modes. Using this result the nonlinear study shows that a cyclic energy exchange may occur between the breathing mode and rather high‐order composite modes. The ensuing deflections and stresses may be considerably in excess of those determined by consideration of the breathing mode only.

ISSN:0001-4966    

DOI:10.1121/1.1910260

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

This paper treats large‐amplitude radial oscillations of a perfectly elastic infinite cylinder made of an isotropic incompressible material. The oscillation follow a sudden setting of the cylinder into a uniform spinning motion about its longitudinal axis. By using Knowles's approach, the oscillations are analyzed for materials with essentially arbitrary constitutive equations. General conditions are found for the motions of the cylinder to be periodic. The results are specialized to three classes of rubberlike materials: Mooney‐Rivlin, Neo‐Hookean, and Ishiharaet al.‐Zahorski. Graphs are given (for some experimentally corroborated values of the elastic constants) for the frequency of oscillations and the maximum displacement of the inner radius of the tube versus the angular speed of the spin.

ISSN:0001-4966    

DOI:10.1121/1.1910261

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

Results of measurements are presented for the interaction radiation resistance and reactance for a linear array of two small magnetostrictive‐stack transducers at an air‐water surface.

ISSN:0001-4966    

DOI:10.1121/1.1910263

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

Directional reflectors for use with commercial omnidirectional underwater acoustic transducers are described herein. The reflectors are easy to construct, inexpensive, and exhibit none of the ringing characteristics found so frequently with metallic reflectors.

ISSN:0001-4966    

DOI:10.1121/1.1910264

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP

摘要:

The comments of Fand are discussed, and an outline of some recent investigations is given. It is found that the comments are incorrectly founded and that the leading point involves an issue in semantics rather than physical facts. It is not necessary to alter the conclusions of the original paper.

ISSN:0001-4966    

DOI:10.1121/1.1910266

出版商:Acoustical Society of America    

年代:1966

数据来源: AIP