The average specific forced radiation wave impedance of a finite rectangular panel

Abstract

The average specific forced radiation wave impedance of a finite rectangular panel is of importance for the prediction of both sound insulation and sound absorption. In 1982, Thomasson published numerical calculations of the average specific forced radiation wave impedance of a square of side length 2e for wave number k in half octave steps of ke from 0.25 to 64. Thomasson's calculations were for the case when the forced bending wave number k b was less than or equal to k. Thomasson also published approximate formulas for values of ke above and below the published results. This paper combines Thomasson's high and low frequency formulas and compares this combined formula with Thomasson's numerical calculations. The real part of the approximate formula is between 0.7 dB higher and À1 dB lower than the numerical calculations. The imaginary part of the approximate formula is between 2.3 dB higher and À2.6 dB lower than the numerical calculations. This paper also gives approximate formulas for the case when k b is greater than or equal to k. The differences are between 0.8 and À1.2 dB for the imaginary part and between 6.2 and À2.4 dB for the real part.

The acoustic radiation impedance of a rectangular panel

“…: (10) This agrees with equation (10) of [11] which was derived using the authors' previous definition.…”

“…There were also comparisons with five extra numerical values which were read from Thomasson's [8] graphs. The authors [10] also compared the first author's [20] approximate formulae for the real part of the impedance with Thomasson's [8] numerical calculations and discovered that they were a better approximation than the combined version of the real part of Thomasson's [8] formulae.…”

“…The expression for the side length of the equivalent square is also part of equation (7.7) of Leppington et al [13] and the second term of equation (2.39a) of Maidanek [18]. Approximate formulae when ke[1 were derived for the m¼1 case and for the m≪1 case and later [11] for the m[1 case. Formulae for the upper limit m (115) of applicability of the formula for the m≪1 case and for the lower limit m (134) of applicability of the formula for the m[1 case were derived.…”

“…If the isotropic rectangular panel S is simply supported in the infinite rigid baffle, each of its transverse velocity modes has the transverse velocity amplitude on the surface of the panel given by equation (11). Each of these modes has m and n positive integer half wavelengths in the directions of the x and y axes respectively.…”

In situ measurements of the oblique incidence sound absorption coefficient for finite sized absorbers

“…However, Thomasson 4 developed a high frequency approximation of the radiation impedance. Davy et al 22 recently established an updated simplified expression, which is an alternative approximation of Thomasson's high frequency approximation. In this paper, numerical integration of Eq.…”