Acoustic Radiation from Two Concentric Cylindrical Shells with Periodic Supports and a Viscoelastic Perforated Outer Coating

A solution is developed for the acoustic radiation from two concentric cylindrical shells which are connected by a set of periodic annular plates, and the outer of which is coated with a viscoelastic perforated layer. All the perforations in the coating have an identical cavity configuration with variable (thickness-dependent) cross-sections. The classical theory of Kennard type and the linear acoustic field equation are employed to simulate the two shells and their entrained fluid, respectively. It is assumed that only membrane motions exist in the annular plates, based on which a two dimensional membrane theory is employed to derive their reactive forces. The viscoelastic perforated coating is divided into many sub-layers each has an equivalent complex wave number by using a thick walled cylinder model. Transfer matrix method is then used to develop the relation between the quantities (velocity and pressure) at the inner and outer surfaces of the coating. The solution is found by using Fourier wave number transforms, and the stationary phase approximation is used to find an expression for the far field pressure. Comparison of numerical results for the two concentric infinite cylindrical shells without the outer coating to measured data from a cabin model is in good agreement. Far field acoustic pressure results are presented for two cylindrical shells with and without the viscoelastic perforated coating, which indicate that the viscoelastic perforated coating can effectively reduce the radiated sound pressure at middle and high frequency ranges. The influences of the coating parameters on far field acoustic pressure are also discussed.