Output-only acoustic analysis of a rigid enclosure

The knowledge of vibration behaviour of real structures during their operational life is more and more important in many engineering applications in order to get their best performance. In operating conditions loads are typically unknown and the estimation of structure’s modal parameters has to be based on the output data only. Output-only techniques have been successful applied to many structural dynamic fields; herein the idea is to apply these algorithms to interior acoustic data. An in-house code that implements Data Driven (DD) and Covariance Data Driven (CDD) algorithms for Stochastic Subspace Identification has been developed and validated via a simulation of simple numerical systems whose analytical results were available. The applicability of output-only techniques to acoustic data in order to easily estimate effects of installation and operational conditions on cavity sound field has been assessed. Starting from time histories recorded in different acoustic volumes, modal characteristics of the cavities in terms of frequencies, damping and mode shapes have been identified. 440 IOMAC'09 – 3 International Operational Modal Analysis Conference with classical testing facilities, in-operation modal analysis remains the only technique which may help in structural identification. It is an approach which, by definition, is able to properly take into account the environmental influences on the system behaviour (e.g. pre-stress of suspensions, load-induced stiffening, aero-elastic interaction, and so on) and its non-linearity (Van der Auweraer et al. 1990, Wyckert et al. 1994) and it may result extremely important for the structural monitoring, together with the classical purposes of the experimental modal analysis (validation of numerical models, structural modification or optimization). The drawback of this approach is that the real operating structure is needed and, in some cases, it is unrealistic to believe that the results of an operational modal campaign may affect the design approach. The paper briefly recalls the supporting theory (Juang and Pappa 1985, Hermans and Van der Auweraer 1999), based on Stochastic Subspace model, on which an in house developed MATLAB code was available (Marulo et al. 2005), then discusses some experimental applications to interior acoustic problems. Three different test setups have been employed in order to evaluate the performance of the output only algorithms implemented to acoustic data. Encouraging results have been achieved for two of them whereas for the last one, that is an aircraft fuselage barrel, the high number of acoustic modes even in the low frequency range did not allow a modal identification. Vice versa in other cases the realization obtained with this program highlight some specific behaviour of the structure coupled with the acoustic cavity, hidden by the frequency response data that could be analysed during a standard laboratory test. 2 THEORETICAL BACKGROUND The purpose of operational modal analysis is to determine modal parameters of a real system, which is assumed to be Linear Time Invariant (L.T.I.), measuring only its response at specific locations, being the exciting load unknown. If considering an n masses lumped mechanical system with springs and dampers and indicating with [M], [C], [K] the mass, damping and stiffness matrices, the dynamical equilibrium equation can be described by the following matrix differential equation: [ ] ( ) { } [ ] ( ) { } [ ] ( ) { } ( ) { } [ ] ( ) { } t u D t F t x K t x C t x M = = + + (1) where {F(t)} is the input forcing vector, {x(t)} the resulting displacement vector and [D] is the matrix of the input {u(t)}. The approach of stochastic methods is very common in the practical engineering applications because the signal (displacement, velocity or acceleration) given by the sensors can be sampled at discrete time intervals depending on the characteristic of the computer processing. In the output-only modal analysis environment, the main assumption is that the input force comes from a white noise or time impulse excitation; under this hypothesis a discrete-time stochastic state-space model may be written as: