2004981Plate dynamics lab 2: a hammer on a hung plate by Rayleigh-Ritz and by Mindlin-Reissner finite elementsJeremy Magland 1function [acoustic, radiation] = plate_radiation(freqs, volume_part, params, P)
2% PLATE_RADIATION Pressure at the microphone per unit modal acceleration.
3%
4% [acoustic, radiation] = plate_radiation(freqs, volume_part, params, P)
5% gives, for each mode, the coefficient a such that the mode's contribution
6% to the pressure at the microphone is a * q_tt(t):
7%
8% a = rho_air / (2 pi r) * V * sqrt(min(1, f / f_c)),
9%
10% where V is the mode's volume participation (the integral of the mass-
11% normalized shape over the plate: a compact-source estimate for a
12% microphone on the plate's normal at distance r), and the square-root
13% factor stands for the front/back cancellation of a small unbaffled plate
14% below its coincidence frequency f_c (plate_setup). It is a smooth
15% estimate of the radiation efficiency, not a solution of the diffraction
16% problem, so the output is meaningful in timbre and decay while its
17% absolute level is only approximate.
19freqs = freqs(:)';
20volume_part = volume_part(:)';
21radiation = sqrt(min(1, max(freqs / P.critical_frequency, 1e-4)));
22acoustic = params.mic.air_density / (2 * pi * params.mic.distance) * volume_part .* radiation;
23end