A Generalized Approach for the Acoustic Radiation From a Baffled or Unbaffled Plate With Arbitrary Boundary Conditions, Immersed in a Light or Heavy Fluid

Nélisse, Hugues; Beslin, Olivier; Nicolas, Jean

doi:10.1006/jsvi.1997.1359

Cited by 57 publications

(27 citation statements)

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“…Nelisse et al [34] proposed a study on the radiation of both baffled and unbaffled plates. A Rayleigh-Ritz approach was used to develop the plate displacement in the baffled case, as well as the pressure jump in the unbaffled case.…”

Section: Unbaffled Plate Modelsmentioning

confidence: 99%

“…From the existing methods, particularly in [29] and [33], the results presented were only focused on single modes. The radiation efficiency due to vibration in multiple modes was calculated in [30,33,34] but only up to relatively low frequency. However, this is not still adequate to give a thorough analysis, particularly to provide a complete investigation into the difference between the radiation from the baffled and unbaffled plate.…”

Section: Unbaffled Plate Modelsmentioning

confidence: 99%

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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%

Section: Unbaffled Plate Modelsmentioning

confidence: 99%

Sound radiation from perforated plates

Putra

Thompson

2010

Journal of Sound and Vibration

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“…Clearly, having a velocity field equal to zero everywhere, apart from the plate surface, makes the problem easier to solve, but this is not always fully representative of a real structure. For this reason, the problem of an unbaffled plate has also been investigated by some authors ( [16], [19] and [21][22][23][24]). Some semi-analytical methods have been proposed and the effect of boundary conditions on unbaffled plates has also been addressed ( [16] and [23]).…”

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confidence: 99%

The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates

Squicciarini

Thompson

Corradi

2014

Journal of Sound and Vibration

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The boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency. To investigate this effect in a systematic way, the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach. Whereas analytical expressions exist for simply supported boundary conditions, a numerical approach is required for other cases. Nine combinations of boundary conditions are considered, consisting of simply supported, clamped and free edges on different plate edges. The structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies.This assumption is checked against a finite element model and shown to give reliable results. It is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency. Other combinations of boundary condition give intermediate results according to the level of constraint introduced. The differences depend on frequency: excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 dB in the middle part of the shortcircuiting region, decreasing towards the critical frequency. At low frequency the differences can be even greater, in some cases up to 20 dB. These conclusions are shown to hold for a range of plate thicknesses and dimensions.Keywords: plate vibration, baffled plates, radiation efficiency, radiation ratio, boundary condition. IntroductionIn many engineering applications it is important to be able to estimate the noise radiated by a vibrating structure during its design stage. In most cases the structures under consideration, whether industrial machinery, vehicles or civil structures such as bridges, can be subdivided into smaller components; thin vibrating panels, strips and beams are often important components that are 3 responsible for noise radiation. To evaluate the noise produced a common procedure is to evaluate the vibration velocity levels of each component and to estimate their acoustic power levels through their dimensions and radiation efficiency. It is particularly useful to study the radiation efficiency of the elementary components in order to be able to characterise the acoustic performance of the structure they form.The radiation efficiency of an object at a given frequency or frequency band can be defined as the radiated sound power rad W , normalized by the radiating area S, the air density  , the speed of sound c and the space-averaged mean square vibration velocity The denominator in eq. (1) represents the power that would be radiated by a surface area S, vibrating as a rigid piston to produce plane waves, with a mean square velocity equal to the surface-averaged mean-square velocity of the actual object. Furthermore, if the me...

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“…The problem consists in "nding suitable expressions for w Q and w verifying the system of integral equations (8) and (9) as well as satisfying the boundary conditions at the edges of the plate. Various approximate functions have been tried in the case of non-porous plates where only one governing equation is considered, such as a linear combination of trigonometric and hyperbolic functions [7,8], polynomials (see reference [9] for example) or trigonometric functions [10]. The following approach is used in the present study: a possible solution for the solid de#ection is sought "rst.…”

Section: Choice Of the Mathematical Form Of The Solutionsmentioning

confidence: 99%