Normal modes are widely used for the vibration analyses of structures. In contrast, acoustic computation is best performed in terms of the independent radiation modes of the structure. The independent radiation modes are obtained by diagonalization of the power transfer matrix (s-modes) or the radiation resistance matrix (s-modes). The diagonalization approach illuminates the physical insight associated with the vibro-acoustic radiation process. In the first part of this work, the independent radiation modes of baffled plate structures are computed. Further, the efficacy of using
the independent radiation modes is demonstrated for the computation of sound power from baffled plate structures of various geometries. It is found that in comparison to the a-modes, the s-modes are advantageous in the following respect (1) they incorporate the structural boundary conditions (2) the number of s-modes required is generally less than that of a-modes. The determination of these s-modes is computationally expensive, especially while dealing with complicated plate geometries. Therefore, in this work, a model reduction technique using component mode synthesis is used to obtain the s-modes for plate-like structures with different geometries.
In the next part of the work, sound power radiated from a simply supported
unbaffled rectangular plate is presented using a semi-analytical method. While the vibro-acoustic analysis of baffled plate is easily accomplished using Rayleigh Integral, no such simple formulation exists for the unbaffled plate. Usually, computationally intensive Finite Element or Boundary Element Method is used for the such vibroacoustics problem. The present work formulates a set of scaling factors to scale the results between the baffled and unbaffled configurations. The sound power radiated
from a baffled plate is calculated using an s-mode based analytical approach, whereas sound power radiated for the corresponding unbaffled configuration is obtained using COMSOL multiphysics. With the help of these scaling factors, the sound power from an unbaffled plate due to any arbitrary excitation can be obtained. The sound power from a baffled and an unbaffled plate is compared and it is observed that the influence of baffle is significant in lower frequencies. The results obtained through the scaling
approach are noted to be in good agreement with the simulation for the unbaffled plate implemented in COMSOL multiphysics.