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

The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates
The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates
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 short-circuiting 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.
0022-460X
3931-3948
Squicciarini, G.
c1bdd1f6-a2e8-435c-a924-3e052d3d191e
Thompson, D.J.
bca37fd3-d692-4779-b663-5916b01edae5
Corradi, R.
552534b9-b008-48e3-99b1-63ad999a6eac
Squicciarini, G.
c1bdd1f6-a2e8-435c-a924-3e052d3d191e
Thompson, D.J.
bca37fd3-d692-4779-b663-5916b01edae5
Corradi, R.
552534b9-b008-48e3-99b1-63ad999a6eac

Squicciarini, G., Thompson, D.J. and Corradi, R. (2014) The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates. Journal of Sound and Vibration, 333 (17), 3931-3948. (doi:10.1016/j.jsv.2014.04.022).

Record type: Article

Abstract

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 short-circuiting 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.

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e-pub ahead of print date: 1 May 2014
Published date: 18 August 2014
Organisations: Dynamics Group

Identifiers

Local EPrints ID: 369232
URI: https://eprints.soton.ac.uk/id/eprint/369232
ISSN: 0022-460X
PURE UUID: 37c53ce8-9292-4b1a-8a72-1054d6df515c
ORCID for G. Squicciarini: ORCID iD orcid.org/0000-0003-2437-6398
ORCID for D.J. Thompson: ORCID iD orcid.org/0000-0002-7964-5906

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Date deposited: 30 Sep 2014 11:43
Last modified: 17 Sep 2019 01:06

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