A Criterion for Piece-wise Mid-Frequency Vibro-acoustic Modelling Using the Condensed Transfer Function Approach

Analyses of vibro-acoustic systems in the mid-to-high frequency range is technically challenging due to the complex wavelength composition involved in different vibroacoustic components. The problem needs to be tackled in order to cope with the crying need in various applications fields such as vehicles and buildings. In the present paper, an improved condensed transfer function (CTF) approach is proposed to model a plate-cavity system. In the improved CTF approach, the uncoupled subsystems are firstly modelled separately, by decomposing the force and velocity on the coupling surfaces between subsystems over a set of CTFs. The entire coupled system can then be assembled and solved by applying the force equilibrium and velocity continuity conditions over the coupling surfaces. The modelling efficiency is shown to be greatly increased by properly selecting the condensation functions in terms of their type and size. It is shown that a better spatial match between the wavy feature of the condensation functions and the wavelength of the system would allow more efficient modelling within a prescribed frequency range. Given a set of truncated CTF series, a piece-wise convergence behaviour is observed, leading to the proposal of a convergence criterion. The proposed convergence criterion allows the entire system to be modelled in any prescribed frequency band, one at a time in a piece-wise manner, thus resulting in a great reduction in the computational time. The proposed criterion is then tested using various excitation and damping configurations in one-third octave bands.