Coupling and attenuation of waves in plates by randomly distributed attached impedances

Self Cite

The propagation of diffuse energy on an unwetted flat plate with attached heterogeneities is examined using a statistical, multiple scattering approach. The statistically homogeneous heterogeneities lightly couple the membrane and flexural waves. The problem is formulated in terms of the Bethe-Salpeter equation, which governs the field covariance. It is reduced to a radiative transfer equation in the limit that the attenuations per wave number are small, i.e., when the heterogeneities are weak. This radiative transfer equation governs the diffuse energy propagation as a function of space, time, and propagation direction. Solutions of the radiative transfer equation are presented for the simple case of attached heterogeneities in the form of delta-correlated springs excited by an extensional point source. The results show the evolution of the extensional, shear, and flexural energy densities across the plate as a function of time. A similar approach is expected to apply to the more complicated case of submerged complex structures.

Section: Introductionmentioning

confidence: 87%

Section: ͑7͒mentioning

confidence: 99%

Section: ͑7͒mentioning

confidence: 99%

“…It is assumed here to be a local operator. 10 The fluctuations of the added impedance are assumed small such that the average added impedance, Z 0 ϭ͗Z͘, and covariance, ͗͑Z͑x͒ϪZ …”

Section: Stochastic Plate Equationmentioning

confidence: 99%

Section: Stochastic Plate Equationmentioning

confidence: 99%

See 3 more Smart Citations

Diffuse energy propagation on heterogeneous plates: Structural acoustics radiative transfer theory

Turner

Weaver

1996

Self Cite

The effect of internal oscillators on the acoustic response of a submerged shell

Photiadis

Bucaro

Houston

1997

The effect of a large number ͑Ϸ1000͒ of internal mechanical oscillators on the acoustic backscattering cross section of a submerged ribbed shell has been experimentally investigated. A comparison of the backscattering cross section of the shell with oscillators to that of a simple ribbed shell with no oscillators shows a number of significant effects arising from the internal structure and overall a significantly increased average scattering strength. These results are presented and several physical mechanisms which can account for the salient aspects of the observations are discussed. ͓S0001-4966͑97͒03601-1͔

Acoustics of a fluid-loaded plate with attached oscillators. Part I. Feynman rules

Photiadis

1997

The “fuzzy structure” paradigm developed by Soize and others provides a framework within which the acoustic properties of systems with complex internal structure can be explored. In this two part paper, the acoustic properties of one of the simplest such systems, a fluid-loaded plate with attached internal oscillators, are explored. In Part I, the theoretical tools needed in this investigation, the representation of the Neumann series in terms of Feynman diagrams, is presented. In most ways, the formal aspects of this development are identical to similar results from other disciplines, but the presence of damping in the system, either internal or due to radiation into the fluid, requires one to make some modifications to existing theories. The rules for evaluating averaged quantities such as G⋯GG*⋯G* involving higher-order products of the Green’s function are given. These quantities are necessary to determine a number of relevant properties of the system including the scattering cross section and the size of typical fluctuations. The Feynman rules, detailed mathematical expressions which enable averaged quantities to be evaluated for particular systems, are explicitly given for the case in which the internals are simple oscillators distributed uniformly and independently in both space and frequency. In Part II of this paper, the theoretical approach will be applied to predict a number of acoustic properties of the system.