Tsuji, H. and Nakano, K., "Transfer Path Analysis with the Coherent Operational Forces Estimated from the Responses," SAE Int. J. Passeng. Cars - Mech. Syst. 8(3):1142-1150, 2015, doi:10.4271/2015-01-2357.
This paper presents a new technique to estimate the coherent operational forces, with respect to the evaluation location, at the connections of separated passive substructures with reciprocity. Since transfer path analysis is conducted with respect to the evaluation location, the forces applied onto the substructures are, therefore, also required to estimate the coherent operational forces. In order to estimate the forces, the coherent impedance matrix, which is the projection of the impedance 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 reciprocity. The technique decomposes the acceleration responses into the output and input element vectors on the subspace. With those vectors, the coherent impedance matrix is constructed. The coherent operational forces at the passive substructure can be estimated by the operational accelerations pre-multiplied by the inverted coherent impedance 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 of the passive substructure.