Variational Formulations in Acoustic Radiation and Scattering

Pierce, Allan D.

doi:10.1016/b978-0-12-477922-8.50007-8

Cited by 40 publications

(8 citation statements)

References 248 publications

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“…Applying Euler's equation, the plate displacement solution was obtained, which involved a surface integral of the Green's function. The plate displacement was then solved using a variational approach [31]. From this, the pressure jump was neglected when calculating the velocity of the plate, allowing any boundary conditions to be derived analytically at the plate edges.…”

Section: Unbaffled Plate Modelsmentioning

confidence: 99%

Sound radiation from perforated plates

Putra

Thompson

2010

Journal of Sound and Vibration

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FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS INSTITUTE OF SOUND AND VIBRATION RESEARCH Doctor of Philosophy SOUND RADIATION FROM PERFORATED PLATES by Azma PutraPerforated plates are quite often used as a means of engineering noise control to reduce the sound radiated by structures. However, there appears to be a lack of representative models to determine the sound radiation from a perforated plate. The aim of this thesis is to develop such a model that can be used to give quantitative guidance corresponding to the design and effectiveness of this noise control measure.Following an assessment of various models for the radiation efficiency of an unbaffled plate, Laulagnet's model is implemented. Results are calculated and compared with those for baffled plates. From this, simple empirical formulae are developed and give a very good agreement with the analytical result. Laulagnet's model is then modified to include the effect of perforation in terms of a continuously distributed surface impedance to represent the holes. This produces a model for the sound radiation from a perforated unbaffled plate. It is found that the radiation efficiency reduces as the perforation ratio increases or as the hole size reduces. An approximate formula for the effect of perforation is proposed which shows a good agreement with the analytical calculation up to half the critical frequency. This could be used for an engineering application to predict the noise reduction due to perforation.The calculation for guided-guided boundary conditions shows that the radiation efficiency of an unbaffled plate is not sensitive to the edge conditions. It is also shown that perforation changes the plate bending stiffness and mass and hence increases the plate vibration.The situation is also considered in which a perforated unbaffled plate is located close to a reflecting rigid surface. This is established by modifying the Green's function in the perforated unbaffled model to include an imaginary source to represent the reflected sound. The result shows that the presence of the rigid surface reduces the radiation efficiency at low frequencies.The limitation of the assumption of a continuous acoustic impedance is investigated using a model of discrete sources. The perforated plate is discretised into elementary sources representing the plate and also the holes. It is found that the uniform surface impedance is only valid if the hole distance is less than an acoustic wavelength for a vibrating rectangular piston and less than half an acoustic wavelength for a rectangular plate in bending vibration. Otherwise, the array of holes is no longer effective to reduce the sound radiation.Experimental validation is conducted using a reciprocity technique. A good agreement is achieved between the measured results and the theoretical calculation for both the unbaffled perforated plate and the perforated plate near a rigid surface.

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Section: Unbaffled Plate Modelsmentioning

confidence: 99%

Sound radiation from perforated plates

Putra

Thompson

2010

Journal of Sound and Vibration

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“…The present analysis may nevertheless be regarded as an extension of Medwin et al's (1973) study. The condition M A < 4.53 for a subsonic underwater wave field corresponds to the incident ray angle θ i > sin −1 (a A /a W ) ≈ 12.75 • associated with the 'total reflection' phenomenon in ray acoustics theory (see for example , Tolstoy 1987;Pierce 1991). The prohibition of acoustic energy transmission under this condition would have ruled out the existence of a (subsonic) underwater wave field.…”

Section: Anticipated Featuresmentioning

confidence: 99%

Sonic-boom noise penetration under a wavy ocean: theory

Cheng

Lee

2004

J. Fluid Mech.

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Sonic-boom noise penetrating under a deep ocean is affected by its time-dependent interaction with the surface waves, which can significantly influence the perceived sound pressure level and tonal content of the disturbances at depth far greater than expected from the flat-ocean (Sawyers) model. The present theory assumes a small surface slope and a high water-to-air density ratio; the ocean surface in the analysis is modelled by a sinusoidal surface-wave train. The analysis shows that a distinct acoustic wave mode in the form of a packet of wavelets emerges in the sound field far below the surface and attenuates with increasing distance in a manner similar to the cylindrical spreading of monochromatic waves. The latter feature renders the surface waviness influence an effect of first-order importance, overwhelming the primary noise field at large depth. Detailed properties of the deep-water wave fields are examined and illustrated for the case of an incident N-wave, for which an explicit, analytic solution is obtained. The result reveals a similarity structure of the wave field with two distinct time scales and the invariance characteristics of the cylindrically spreading waves, in accord with the group-velocity concept of dispersive waves. An example is given of the interaction, illustrating the underwater waveform, sound-pressure and frequency levels.

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“…We adopt the conventional tensor notation used in mechanics, by, for example, Green and Zerna 21 and Pierce. 22 Sub-and superscript indices denote the covariant and contravariant tensor forms, respectively. The greek indices assume the values 1 or 2, and the suffix, ␣ or the symbol " ␣ means differentiation with respect to ␣ .…”

Section: A Description Of the Shell Geometrymentioning

confidence: 99%

Ray tracing over smooth elastic shells of arbitrary shape

Yang

Norris

Couchman

1996

The Journal of the Acoustical Society of America

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An efficient numerical scheme based on ray theory is developed for the analysis of elastic waves traveling over a fluid-loaded smooth elastic shell of arbitrary shape. The shell's surface is first discretized into a number of small patches. The local geometry of each patch is then approximated in a parametric form using bi-cubic spline functions. A local curvilinear coordinate frame is defined on each patch. The ray trajectories and ray-tube areas are obtained by solving a set of ordinary differential equations, the ray and transport equations, within each patch. Several numerical tests of the accuracy and efficiency of the scheme were carried out on spherical and ellipsoidal elastic shells. The numerical results for the spherical shell agree well with analytical solutions. The ray trajectories and the ray-tube areas over an ellipsoidal shell with three distinct semiaxes clearly illustrate the inhomogeneous and anisotropic effects due to the variable curvature on the shell's surface. It is also observed numerically that the magnitude of the ray-tube area along a ray is directly correlated with the stability of its trajectory.

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Variational Formulations in Acoustic Radiation and Scattering

Cited by 40 publications

References 248 publications

Sound radiation from perforated plates

Sound radiation from perforated plates

Sonic-boom noise penetration under a wavy ocean: theory

Ray tracing over smooth elastic shells of arbitrary shape

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