Acoustic radiation of an unbaffled vibrating plate with general elastic boundary conditions

Atalla, Noureddine; Nicolas, Jean; Gauthier, Carol

doi:10.1121/1.414727

Cited by 41 publications

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“…The core idea is to establish a coupling between the free vibration response of the structures and the acoustic medium more accurately. Atalla et al (1996) studied the acoustic radiation from un-baffled thin flat isotropic structures using Rayleigh-Ritz approximation for acoustic parameters and compared the results to the baffled case. A modal superposition technique has been utilised for the computation of coupled structure and acoustic modes by Tournour and Atalla (1998) including a novel integration scheme proposed for handling the singularities of Green's function.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Vibro-Acoustic Responses of Un-Baffled Multi-Layered Composite Structure under Various End Conditions and Experimental Validation

Sharma

Mahapatra

Panda

2017

Lat. Am. j. solids struct.

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This article presents the vibro-acoustic modeling and analysis of un-baffled laminated composite flat panels subjected to harmonic point load under various support conditions. The frequency values of the panel are obtained by using simulation model through the commercial finite element package (ANSYS) via batch input technique. Initially, the rate of convergence of the current simulation results is established by solving different examples under various edge supports. Further, the natural frequencies and corresponding modes are computed and compared with available published and experimentally obtained values. Then, the modal values are exported to LMS Virtual.Lab environment for the computation of acoustic responses of the vibrating laminated plate structure. Further, an indirect boundary element approach has been adopted to extract the coupled vibro-acoustic responses. Subsequently, the radiated sound power of the structure and the sound pressure level within the acoustic medium are computed using the present scheme and compared with the published numerical results and in-house experimental data, respectively. Finally, a comprehensive study has been performed to highlight the effect of different structural parameters (thickness ratio, aspect ratio, modular ratio and lay-up scheme), support conditions and the composite properties on the acoustic radiation responses of the laminated plate structure.

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Section: Introductionmentioning

confidence: 99%

Numerical Study of Vibro-Acoustic Responses of Un-Baffled Multi-Layered Composite Structure under Various End Conditions and Experimental Validation

Sharma

Mahapatra

Panda

2017

Lat. Am. j. solids struct.

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“…Atalla et al [30] gave a numerical solution for the sound radiation of an unbaffled plate with general boundary conditions. The Kirchhoff-Helmholtz equation allows the pressure to be defined anywhere within the volume enclosing the plate.…”

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%

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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“…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]).…”

mentioning

confidence: 99%

“…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]). In particular, results shown in [16] have shown that, in adopting simply supported and/or guided boundary conditions, the variability in radiation efficiency of an unbaffled plate is much lower than the corresponding baffled plate.…”

mentioning

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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Acoustic radiation of an unbaffled vibrating plate with general elastic boundary conditions

Cited by 41 publications

References 0 publications

Numerical Study of Vibro-Acoustic Responses of Un-Baffled Multi-Layered Composite Structure under Various End Conditions and Experimental Validation

Numerical Study of Vibro-Acoustic Responses of Un-Baffled Multi-Layered Composite Structure under Various End Conditions and Experimental Validation

Sound radiation from perforated plates

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

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