Acoustic scattering by finite composite plates

Abstract

Trailing edge scattering is a significant source of sound, and elasticity is known to decrease the radiated sound by a process involving coupled acoustic and bending waves. Most of the analysis available in the literature to deal with this problem is limited to structures of isotropic material. A numerical method is extended, based on the solution of a boundary element method with boundary conditions given by the structural problem, to account for anisotropic composite plates, restricted to symmetric laminates. These conditions are recast in terms of the vibration modes of a rectangular plate. To obtain these modes, the hierarchical finite element method is used to model an elastic flat plate. Expressions for bending waves propagating in such plates are derived, and how the solution of the problem is modified to account for these effects is shown. Results show modifications in the scattered sound as a function of ply orientation and stacking sequence. Composite materials are shown to be advantageous, since laminates lead to lower acoustic scattering when compared to structurally equivalent metallic plates. This is due to a lower specific mass, leading to higher coupling between fluid and solid, and thus to more significant elasticity effects, decreasing substantially the radiated sound.

Effects of structural damping on acoustic scattering by flexible plates

“…In this subsection, we present results for a plate with thickness h equals to 0.2% of its chord, which contrasts with the preceding parametric study, where changing Ω with fixed k 0 amounts to modifying h. Here, with a fixed thickness the parameters k 0 and Ω are related by Ω = [k 0 (h/l)/(ω c h/c 0 )] 1/2 [19]. When considering elasticity, we refer to an aluminium plate immersed in the air, and under these conditions, the fluid loading parameter = 0.0021 and ω c h/c 0 = 0.22, according to the literature [20].…”

“…Finite-plate effects are seen to lead to structural resonance, which affects the sound radiation by the plate. When compared to theoretical results for semi-infinite plates, it is seen that finite flexible plates lead to lower sound reductions with respect to the rigid case; the use of lighter, composite materials may then be of interest, as they lead to higher fluid loading and hence to more significant decreases of trailing-edge noise [19].…”

“…The plate model used by Jaworski & Peake [13], Cavalieri et al [17] and Nilton et al [19] was developed by Howe [20], it is written in terms of transverse displacement of the plate and the displacement of the fluid through apertures that mimic the porosity. This equation has explicit terms for the plate stiffness and inertia; however, it does not take into account the structural damping.…”