Piecewise convergence behavior of the condensed transfer function approach for mid-to-high frequency modelling of a panel-cavity system

The vibro-acoustic modelling of a panel-cavity system is of prime importance for the building industries, exemplified by the noise insulation of single or double skin façade. The vibro-acoustic analysis of such systems in the mid-to-high frequency range is computational costly and technically challenging due to the complex wavelength composition. In the present paper, the Condensed Transfer Function (CTF) approach is revisited to tackle this problem. It is demonstrated that the calculation efficiency of the CTF method can be greatly increased by properly selecting the Condensation Functions (CFs) and exploiting their physical characteristics. In particular, owing to their spatial wavy features, the complex exponential functions can better match the structural wavelength variations so that the velocity on the plate-cavity interface can be described by using a much reduced CF set as compared with the gate functions which are widely used in the previous works. Numerical results show a piecewise convergence behavior of the calculation which is further exploited for establishing a criterion for the truncation of the CFs. The proposed criterion allows the determination of a sub-set of the CFs for any prescribed frequency band for the calculation of the system response in a progressive and piecewise manner, resulting in a great increase in the computational efficiency.