Sound Wave Propagation in Multilayered Two-dimensional Quasicrystal Cylindrical Shells with Internal and External Airflow

We present an analytical solution of sound transmission through a quasicrystal cylindrical shell to model the transmission of airborne sound into the aircraft interior. A state-space approach is employed to derive the governing equations of each layer. The propagator matrix is obtained by propagating the solution in each layer from the bottom of the layered plate to the top using the continuity conditions of the field variables across the interfaces. We make use of the imperfect interface conditions to capture the discontinuity of physical quantities across the interface, from which the displacements and stresses are further converted into the interface propagator matrix. The global propagator relation is assembled by propagating the solutions in each layer and each interface. The external and internal fluid mediums of the shell are used to simulate the air inside and outside the cabin and move with constant velocities. The Bessel and Hankel functions are introduced to characterize specific acoustic wave equations, and further to couple with the shell equations. An exact solution of the transmission loss is presented in a series form under satisfying the fluid-structure interaction boundary conditions. The numerical examples indicate that the flight altitude h, Mach number M, and incidence angle α change the distributions of transmission loss by influencing the axial and radial wave numbers during acoustic wave propagation. Other parameters have little effect on transmission loss.