A modal expansion analysis of noise transmission through circular cylindrical shell structures with blocking masses

This paper covers the development and application of a modal interaction analysis (MIA) to investigate the plane wave transmission characteristics of a circular cylindrical sandwich shell of the type used in the aerospace industry for satellite launch vehicles. The model is capable of handling many high order structural and acoustic modes, and can be used to investigate the sensitivity to different structural stiffness configurations, angles of incidence, damping and cavity absorption. The model has been developed to predict the structural response and transmitted noise when a number of discrete masses are applied to the shell. The study presented considers a set of cases where blocking masses, having a total weight equal to 8% of the cylinder weight, are attached to the cylinder. The simulations carried out show a substantial reduction of the sound transmission in many of the first 15 one-third octave frequency bands (frequency range 22.4-707 Hz). The blocking masses act on the shape of the cylinder normal modes and their orientations with respect to the plane of the incident wavenumber vector. In particular, the circumferential re-orientation reduces the coupling between the incident acoustic field and the structural modes of the cylinder. The modification of the structural mode shapes, both in axial and circumferential directions, also reduces the coupling between the cylinder modes and the acoustic modes of the interior. Simulations show the effect of the number of structural and acoustic modes included on the calculated frequency response, and indicate the number necessary for an accurate prediction of the resonant and non-resonant sound transmission through the structure. In particular, the effect of neglecting off-resonance acoustic and structural modes is investigated. It is shown that restricting the acoustic and structural modes to those having natural frequencies within an interval of ± 40 and ± 60 Hz, respectively, of the excitation frequency produces acceptably small errors in the transmission estimate. The simulations also show that in order to represent accurately the coupling effect between the structural and acoustic modes, for each acoustic mode of order ma, na, pa (axial, circumferential and radial order, respectively), it is necessary to account only for the structural modes with ns = na and ms = ma ± α with α = 1, 3, 5, ..., αmax. It is found that the time required to compute the sound transmission in a frequency range of 0-3123 Hz, using the minimum number of acoustic and structural modes required to compute an accurate response at each frequency, is 3% of that necessary for the computation of the full response using all the structural and acoustic modes with natural frequencies within the frequency range considered in the analysis.