Volume 113, Issue 5, May 2003
Index of content:
- STRUCTURAL ACOUSTICS AND VIBRATION 
113(2003); http://dx.doi.org/10.1121/1.1561493View Description Hide Description
Flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by the well-known factor A quantitative analysis of a plate of finite lateral width displays the plate-to-beam transition, and permits asymptotic analysis that shows the leading order dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff–Rayleigh theories, and isotropic plates are considered for Mindlin’s theory with and without rotational inertia. A frequency-dependent Young’s modulus for beams or strips of finite width is suggested, although the form of the correction to the modulus is not unique and depends on the theory used. The sign of the correction for the Kirchhoff theory is opposite to that for the Mindlin theory. These results indicate that the different plate and beam theories can produce quite distinct behavior. This divergence in predictions is further illustrated by comparison of the speeds for antisymmetric flexural, or torsional, modes on narrow plates. The four classical theories predict limiting wave speeds as the plate width vanishes, but the values are different in each case. The deviations can be understood in terms of torsional waves and how each theory succeeds, or fails, in approximating the effect of torsion. Dispersion equations are also derived, some for the first time, for the flexural edge wave in each of the four “engineering” theories.
113(2003); http://dx.doi.org/10.1121/1.1564021View Description Hide Description
Symmetric Lamb waves on plates exhibit anomalies for certain regions of frequency. The phase velocity appears to be double-valued [M. F. Werby and H. Überall, J. Acoust. Soc. Am. 111, 2686–2691 (2002)] with one of the branches having a negative group velocity relative to the corresponding phase velocity. The classification of the symmetric plate modes for frequencies appearing to have a double-valued phase velocity is reviewed here. The complication of a double-valued velocity is avoided by examining mode orthogonality and the complex wave-number spectra. Various authors have noted an enhancement in the backscattering of sound by elastic shells in water that occurs for frequencies where symmetric leaky Lamb waves (generalized to case of a shell) have contra-directed group and phase velocities. The ray diagram for negative group velocity contributions to the scattering by shells [G. Kaduchak, D. H. Hughes, and P. L. Marston, J. Acoust. Soc. Am. 96, 3704–3714 (1994)] is unusual since for this type of mode the energy on the shell flows in the opposite direction of the wave vector. Circumnavigation of the shell is not required for the leaky ray to be backward directed.
113(2003); http://dx.doi.org/10.1121/1.1559173View Description Hide Description
The radiation of sound from geometrically simple vibrating structures into stationary fluids is well understood. However, to date, very few investigations have considered the effects of fluid convection on structural acoustic radiation. The purpose of this investigation is to quantify the effects that fluid flow has on the sound radiated from rectangular vibrating plates. The discussion includes a description of the fundamental physics associated with a simply supported, vibrating, rectangular plate imbedded in an infinite baffle and radiating into a semi-infinite convected fluid field. This is followed by a discussion of the computational approach used to calculate the plate radiation efficiency. Finally, numerical results are presented which demonstrate the effect that convection has on the radiation efficiency. The primary effect is a significant increase in radiation efficiency in the mid-wave number region, which is attributable to an effective decrease in the critical frequency.
Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship113(2003); http://dx.doi.org/10.1121/1.1560164View Description Hide Description
Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.