Sound transmission into an axisymmetric enclosure

A method to compute the power spectral density of sound transmitted on the axis of an axisymmetric enclosure for a wide frequency band is presented. This method is very easy to program. hen the driving excitation is not axisymmetric, the method only requires the in vacuo structural modes to be calculated. This can be achieved by a finite element calculation, since the density of these modes tends to zero while the frequency tends to infinity. sults improve as the frequency increases, but generally they are already valid at the first resonance of the elastic shell. oblem comprises three coupled domains: external acoustics, internal acoustics, and structural vibrations. The internal acoustics is formulated with acoustic dissipation, modelled by locally reacting wall impedance superimposed onto the motion of the elastic structure. be solved through three original arguments:• int use of an integral representation and a modal decomposition of the Helmholtz equation results in an integral relation between the pressure inside the cavity, the wall acceleration and the acoustic and structure damping. ntegral expression can be developed with the stationary phase method since the axisymmetric modes of most aeronautical structures are acoustically fast, even below the coincidence frequency, and only these modes are needed to compute the pressure on the axis. As a result, the structure zones which contribute to the pressure on a specific point of the axis are very localized. Generally, there is only one zone: the parallel constituted by the points nearest to this axis point. pressure jump formulation provides a second equation for the pressure on the axis point; the equality of both pressure expressions leads to a local relation between the pressure jump expression and the wall acceleration: the fluid–structure coupling for axisymmetric modes is quite local. he modal coupling terms are known, the wall acceleration, and therefore the internal pressure on the axis, can be computed by using only the structural modes.