Analysis of near field sound radiation from a resonant unbaffled plate using simplified analytical models

Near field radiation behavior of an unbaffled square plate with free edges, which is excited by a harmonic force at its midpoint, is analytically, computationally and experimentally studied. Emphasis is on the applicability of simplified analytical models to predict the near field sound pressures and spatially-averaged surface and acoustic intensities. First, the plate is computationally discretized into equal segments that are replaced by simple, phase-correlated discrete acoustic sources. Piston radiator models (with and without mutual radiation impedance terms) as well as pulsating sphere models are employed to exhibit the contribution of mutual impedance terms. The near field pressure and spatially-averaged intensity radiated from phase-correlated discrete sources are calculated based on the premise that their individual phases are obtained from the plate (surface) vibration measurements. The importance of mutual impedance terms on the near field radiation is highlighted. Second, the two-microphone acoustic intensity and the surface intensity techniques are employed to determine the spatially-averaged intensity spectra, like analytical models. Results are examined on both narrow and 1/3 octave band bases up to 1600 Hz covering radiation from several plate vibration modes. Finally, an indirect boundary element model is used to predict spatially-averaged intensity spectra, as well as to simulate the two-microphone method given surface vibration data. All predictions are compared with analogous measurements. Discrepancies between theory and experiments (and even between two intensity measurements) are discussed along with possible sources of error.