Tsuji, H. and Nakano PhD, K., "Road Noise Transfer Path Analysis with Operational Force Estimated from the Responses," SAE Technical Paper 2014-01-2049, 2014, doi:10.4271/2014-01-2049.
This paper presents new technique to estimate the projected operational forces, which is the operational forces with respect to the evaluation location, at the connections of the separated passive substructures with reciprocity. Since the transfer path analysis (TPA) is conducted with respect to the evaluation location, the forces for the substructures are, therefore, also required only to estimate the projected operational forces. In order to estimate the forces, the projected inertance matrix, which is the projection of the inertance matrix onto the subspace with respect to the evaluation location, is estimated without measuring it directly. The acceleration responses at the connections of the passive substructure are measured by the excitation at the evaluation location with the reciprocity. The technique decomposes the acceleration responses into the output and input element vectors on the subspace. With those vectors, the projected inertance matrix is constructed. The projected operational forces at the passive substructure can be estimated by the operational accelerations pre-multiplied by the inverted projected inertance matrix. As a result, the transfer path contribution with respect to the evaluation location is calculated with these estimated forces and the noise transfer functions (NTF) of the passive substructure.