High Frequency Vibroacoustic Analyses on VEGA Launch Vehicle

VEGA, the future European small launch vehicle, is a single-body launcher composed of three solid-propellant stages and a liquid propellant upper module. It is approximately 30 metres high, has a maximum diameter of 3 metres, and weights a total of 137 tons at lift-off. The acoustic loads applied to the launch vehicle upon the lift-off and the transonic flight, are broad band and random loads which may be dangerous for the payload and the equipment. A fast and cheap prediction may be obtained by numerical procedures rather than performing measurements on real prototypes. The classical numerical techniques (finite elements (FEM), boundary elements (BEM)) allow to predict the response of the mechanical systems at low frequency ranges, typically under 200 Hz. A high frequency problem happens when the ratio between the characteristic wave length and the characteristic dimension of the system is very little respect the unity. It happens, for example, when a broad-band load forces a large and lightweight structure. The classical numerical techniques fail to solve high-frequency dynamic problems, because the computational burden grows excessively, but also because the sensitivity of the numerical algorithms to uncertainties in the modal parameters increases with frequency so that the predicted response becomes meaningless. In this case a statistical approach is more appropriate. The Statistical Energy Analysis (SEA) is, at present, the most useful method for solving this kind of vibroacoustic problems, by providing information on the stored mechanical energy and on the dissipated mechanical power between modal subsystems. The energy of the subsystems is calculated by solving a set of algebraic energy-balance linear equations: the right-hand side quantities are the powers injected into each subsystem and the coefficients depend on the coupling loss factor (CLF) and the internal loss factor (ILF). These parameters depend on the kind of studied mechanical system and they are independent by the imposed forces