A Condensed Transfer Function Method as a Tool for Solving Vibroacoustic Problems

Numerical methods are nowadays widely used to predict the vibroacoustic behavior of mechanical systems. Nevertheless, when the system is complex as for instance in the aerospace or naval industry, it is practically impossible to solve for the problem at once, more particularly at medium or high frequencies. That is why substructuring approaches have been developed to tackle complex systems and save computation costs. Some of these methods consist in dividing the system in several subsystems that can be studied separately and to deduce the response of the whole system by calculating the coupling forces at the interfaces between the subsystems. It is based on admittance, impedance or mobility frequency transfer functions at the coupling interfaces. Such methods have already been used intensively to couple subsystems linked by point contacts. In the case of subsystems coupled along lines, a Condensed Transfer Function (CTF) method is developed in the present paper. The admittances on the coupling line are condensed in order to reduce the number of coupling forces evaluated. Three variants of the method are presented, where the transfer functions are condensed using 3 different ways: (1) averaged on segments, (2) projected on exponential functions along the line and (3) projected on Chebyshev polynomials. After describing the principle of the CTF method, the case of a plate will be given as a test case for validation. In comparison with a classical Craig-Bampton method, which is used to reduce the size of finite element models, the CTF method has the advantage to be useable with several subsystems which vibrational behavior has not necessarily been described by the finite element method (FEM). For instance, it may be used to couple a submerged non-periodically stiffened shell described using the circumferential admittance approach (CAA) \cite{maxit2010prediction}, with internal substructures described by FEM that offers greater flexibility on their design. Way ahead to take into account non-axisymmetric internal substructures in an underwater structure will be given.