Approximate equations for the radiation impedance of a rectangular panel

The authors have previously published approximate formulae for the average one sided specific radiation wave impedance of a finite rectangular panel mounted in a rigid infinite baffle. The panel's transverse vibration was due to a (possibly forced) two dimensional bending plane wave propagating in the panel without reflection at the edges of the panel. The average was over all the surface area of the panel and over all possible azimuthal angles of propagation direction. The radiation from waves propagating in different directions was assumed to be uncorrelated. These approximate formulae were derived from the 1982 research of Thomasson whose approximate formulae only covered the high and low frequency regions and not the mid frequency region. This paper presents more accurate versions of some of the approximate formulae. When the bending wave number is larger than the wave number of sound, the real part of the impedance is smaller than that for the case studied by Maidanik and Leppington. This is because correlated reflections are not included the case analyzed in this paper. When the bending wave number is smaller than or equals the wave number of sound, the real part of the impedance is the same for both cases.