Model for Active Control of Flow-Induced Noise Transmitted Through Double Partitions

Abstract

The results are presented of a study concerned with the prediction of the air ow noise transmitted through an element of the fuselage structure: a double panel of nite extent that consists of a pair of thin elastic plates containing a light insulating material separated from the inner skin by an air gap. This con guration is representative of typical compound sidewalls in large commercial aircraft. A solution based on modal coupling is obtained and validated by comparisons with other solutions on various test cases. A physical interpretation is given for the calculated vibroacoustic response of a double partition system excited by a turbulent boundary layer, and the effect of an air gap between the insulation facing bag and the trim panel is analyzed. It is shown that the levels of the inwardly radiated sound power are mainly determined by the contribution of the rst skin panel-controlled mode, and the added damping effect due to the insulating material has little effect below this resonance. To achieve sound reduction in the very low-frequency domain, the performance of various active control strategies are examined and compared. It is found that the most ef cient strategy is the suppression of the low-order skin panel structural modes. However, we note that signi cant reductions in the sound power radiated can also be achieved by the active suppression of the low-order structural modes of the trim panel. Nomenclature A s , A t = skin and trim panel surfaces a = vector of cavity modes amplitudes C = damping modal matrix C e = cospectrum of the wall-pressure eld c a = sound speed of the equivalent uid into the cavity c e = external sound speed c i = sound speed of the internal uid c j = equivalent uid coef cients, j D 1; : : : ; 8 D s = skin panel exural rigidity d = cavity depth F = vector of the cavity modes F n = rigid wall cavity modes f c = hydrodynamic coincidence frequency k = wave number vector L s;nm , L t;nm = modal coupling coef cient between the nth cavity mode and the mth skin or trim panel mode l x , l y = respectively, spanwise and streamwise dimensions of the panels M = mass modal matrix M i;m , M a;n = generalized masses associated to the mth panels mode and to the nth cavity mode N a = number of cavity modes accounted for in the simulations N s , N t = number of skin and trim panels modes accounted for in the simulations P i = amplitude of the incident pressure eld p a = cavity pressure eld p t = sound pressure radiated by the trim panel on its surface p t = vector of complex acoustic pressure at the trim panel surface Q = eigenvector matrix of <[Z] Q e = vector of generalized forces Q e s;m = generalized external force associated to the mth skin panel mode q fs;tg = vector of complex structural modes amplitudes <[Z]= modal radiation resistance matrix of the trim panel r x , r y = separation distances, respectively, in the spanwise and in the streamwise directions S = stiffness modal matrix t = time U c = convection velocity U 1 = freestream velocity V = cavity volume W i = incident sound power ...

Active control of turbulent boundary layer-induced sound transmission through the cavity-backed double panels

“…Under this assumption, it is possible to model the excitation term for the source panel as a 'blocked pressure', i.e. the wall pressure fluctuations that would be observed on a rigid wall [34]. Further hypothesis on the nature of the turbulent boundary layer are listed in Section 2.1.…”

“…To this end, the modal expansion method is used [37]. Simply supported boundaries of the two panels, and rigid cavity walls are assumed [34,37]. The rectangular coordinates (x, y, z) are chosen, z being normal to the panel, and x in the direction of mean flow, as seen in Fig.…”

Vibration and Bandgap Behavior of Sandwich Pyramid Lattice Core Plate with Resonant Rings

“…Nevertheless, the elastic wave propagates at lower frequencies due to the open cell sandwich structure and high stiffness to mass ratio, leading to poor vibration attenuation and acoustic performance [ 8 , 10 ]. The low-frequency mode contributes the most to sound power, and thus, effective reduction in sound power can be achieved by suppressing vibrations in the low-frequency range [ 15 ]. Therefore, it is still a challenge for lattice sandwich structures to simultaneously achieve the balance of vibration suppression and light weight.…”