An exact solution of three-dimensional elasticity for sound transmission loss through FG cylinder in presence of subsonic external flow

An exact elasticity solution is presented to study sound transmission loss through functionally graded cylinder in presence of subsonic external flow. This structure cylindrical is excited by an external plane wave with two angles of incidence, andy. The mechanical properties of the functionally graded material are assumed to vary uniformly and continuously with the change of volume fractions of the constituting materials across the thickness of the cylinder according to the power-law distribution. The functionally graded cylinder is approximated by a laminate model, whereas the solution is expected to gradually approach the exact one as the number of layers increases. The governing equations of motion for each layer are derived, based on 3-D elasticity theory. Then, the transfer matrix method is employed, which includes a global transfer matrix that composed as the product of the local transfer matrices by applying continuity of the displacement and stress components at the interfaces of neighboring layers. The transmission loss of the multi-layered functionally graded cylinder are presented for different incidence angles, Mach numbers, thicknesses, radii and distribution functions over a wide frequency range. Comparing the results of present study with those of previous models, particularly for thin shells, leads into good agreements as a result of ignoring the effects of shear and rotation terms on TL. The numerical results of positive Mach number show that TL decreases at the stiffness and coincidence controlled regions with increasing the Mach number but it behaves in opposite manner just in mass-controlled region. In addition, the results indicate that the TL is improved as consequences of decreasing the volume fractions through the thickness of FG cylindrical shells.