Vibroacoustic subtractive modeling using a reverse condensed transfer function approach

Substructuring methods are a very common and efficient way to solve complex vibroacoustic problems. The Condensed Transfer Function (CTF) approach is a substructuring method based on the concept of subsystem condensed transfer functions (corresponding to admittances or impedances) that allows assembling acoustical or mechanical subsystems coupled along lines or surfaces. For certain practical applications, it may be more efficient to subtract or to decouple a subsystem to a global system rather than assembling different subsystems. In this paper, a reverse formulation of the CTF method is proposed. This formulation allows us to predict the behavior of a subsystem that is part of a larger system, from the knowledge of the condensed transfer functions (CTFs) of the global system and of the residual subsystem that must be removed. For purposes of validation, the scattering problem of a rigid sphere in an infinite water domain impacted by an acoustic plane wave is considered. Comparisons with theoretical calculations are used to validate the formulation proposed and permit studying its accuracy for two types of condensation functions defining the CTFs.