Power operator dimensional reduction to obtain the useful intensity in rectangular plates with several boundary conditions

Abstract

This work investigates the acoustical intensity generated by the sound radiated from rectangular baffled plates in eight cases with distinct combinations of classical boundary conditions. The primary objective is to identify the regions of these plates that effectively contribute to the radiated sound power into the far-field, especially when the driven frequency occurs below the critical coincidence frequency. This identification is done by filtering the non-propagating waves, both using the (analytical) supersonic intensity method and the (numerical) useful intensity model. The spectral decomposition of the sound energy operator is applied, becoming possible the dimensional reduction of this operator to remove the components that do not propagate. Brief theoretical formulations, both for the plates vibration and the resulting acoustical field, are discussed. The closed form solution of the normal velocity field for the eight cases is given. Then, the supersonic intensity is estimated. On the other hand, a summary of the useful intensity technique is discussed and it is computed for the same cases. In the numerical examples, the comparison of the supersonic intensity, the useful intensity and the classical acoustic intensity is shown. The edge and corner modes are clearly identified and the useful intensity plots showed to fit well with the supersonic intensity ones.