Abstract
This paper extends the definition of the one sided radiation impedance of a panel mounted in an infinite rigid baffle which was previously used by the authors so that it can be applied to all transverse velocity wave types on the panel rather than just to the possibly forced travelling plane transverse velocity waves considered previously by the authors. For the case of travelling plane waves on a rectangular panel with anechoic edge conditions, and for the case of standing waves on a rectangular panel with simply supported edge conditions, the equations resulting from one of the standard reductions from quadruple to double integrals are given. These double integral equations can be reduced to single integral equations, but the versions of these equations given in the literature did not always converge when used with adaptive integral routines and were sometimes slower than the double integral versions. This is because the terms in the integrands in the existing equations have singularities. Although these singularities cancel, they caused problems for the adaptive integral routines. This paper rewrites these equations in a form which removes the singularities and enables the integrals in these equations to be evaluated with adaptive integral routines. Approximate equations for the azimuthally averaged one sided radiation impedance of a rectangular panel mounted in an infinite baffle are given for all the cases considered in this paper and the values produced by these equations are compared with numerical calculations.
Highlights
The acoustical radiation impedance of one side of a finite rectangular panel mounted in an infinite rigid baffle is of importance for the prediction of sound insulation [1,2,3,4,5], sound absorption [1, 68], sound directivity [9] and sound scattering
The normalized real part of the acoustical radiation impedance of one side of a finite rectangular panel mounted in an infinite rigid baffle is the panel’s one sided acoustic radiation efficiency
This paper extends the previous definition of the radiation impedance used by the authors so that it covers standing waves as well as plane travelling waves
Summary
The acoustical radiation impedance of one side of a finite rectangular panel mounted in an infinite rigid baffle is of importance for the prediction of sound insulation [1,2,3,4,5], sound absorption [1, 68], sound directivity [9] and sound scattering. This is the appropriate assumption for a forced wave, because after the forced wave is reflected at the edges of the panel, it propagates with the free wave number of the panel rather than with the forced wave number and has a different radiation impedance unless the incident wave was freely propagating This definition works because the possibly forced plane wave has the same root mean square (rms) transverse velocity over time at all points of the panel. The authors suspect that a similar cancellation of the interactions between different travelling waves or supported modes occurs when azimuthal averaging or incident diffuse field averaging is used. This is because the results of such averaged results have proved useful in making acoustical predictions.
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