Numerical Computation of the Sound Radiation From a Planar Baffled Vibrating Surface

Abstract

The sound power radiated by a plane vibrating structure can be calculated by numerical integration of the Rayleigh integral or by means of finite and boundary element methods. However, these methods are usually time-consuming due to the numerical evaluation of surface integrals. This paper reviews and discusses an alternative numerical method (the lumped parameter model) to compute the sound radiation from planar structures which is based just on surface velocity information and a direct numerical evaluation of the radiation resistance matrix of the structure. As an example, the technique is applied to estimate the sound radiated from the structural axisymmetric modes of both clamped and simply-supported circular baffled plates.

The Acoustic Impedance of a Vibrating Annular Piston Located on a Flat Rigid Baffle Around a Semi-Infinite Circular Rigid Cylinder

“…The sound radiation phenomena of single flat sources and of systems of such sources located on a flat rigid baffle have been thoroughly examined. Mainly, the acoustic pressure and the acoustic impedance of the vibrating pistons, membranes and plates have been focused (Arenas, 2008 Thompson, 1971).…”

Study of the sound radiation of a rectangular plate resting on a winkler elastic foundation

“…(9) and (10) is [21] N. A. Bastián-Monarca and J. P. Arenas Study sound radiation rectangular plate resting elastic foundation (11) where , , , and are mode shapes parameters which can be determined from boundary conditions. The boundary conditions for this case are [22] over (12) over (13) Substituting Eq. (11) into Eq.…”

“…Some previous works by Ascione and Grimaldi [2], Salari et al [3], Zheng and Zhou [4], Leissa [5], Ghosh [6], Wang [7], and Bhaskara and Kameswara [8] have analyzed the vibration characteristics of plates resting on elastic foundations. Other studies presented by Arenas and Crocker [9], Rdzanek et al [10][11], Arenas [12][13] and Arenas et al [14] have reported methods for estimating the sound power radiated from vibrating plates. However, there is a relative scarcity of information in the literature for the relationship between the sound power radiated from a vibrating plate resting on an elastic foundation and the stiffness of the elastic foundation.…”

On the Sound Radiation From a Circular Hatchway

“…However, transformation to a classical polar coordinate system will produce surface elements of different area. Therefore, to discretize a circular surface of radius a, into small elements of equal area, the surface is divided first into L equally spaced concentric rings [9]. Thus, the co-ordinates of the center point of each element are r i = a(2i -1)/2L and φ i = π(2i -1)/4(2i -1), where i = 1, 2, … , L and j = 1, 2, … , 4(2i -1).…”

“…Uniform boundary conditions at the contour of the plate are expressed with Equations 7-8 [6] (9) into Equations 7-8 (see Equation 11 in Rdzanek et al [4]). The values at which a resonance of mode (m, n) takes place are given with the eigenvalue λ mn = k mn a.…”