Some relationships for coupled structures and their application to measurement of structural dynamic properties in situ

Three relationships are presented for indirect determination of the structural dynamic properties of substructures, namely the blocked force, mobility and free velocity. First, it is shown that the blocked force of a vibration source can be obtained from measurements made in situ, i.e. when the source is connected to a receiver structure. This potentially removes the need for special test rigs employing blocked terminations. A corollary of this relationship is that a theoretically exact transfer path analysis can be made on a fully assembled structure, such as a vehicle. Next, a relationship for indirect measurement of substructure mobility is derived. In this case, it is necessary to separate the substructures, but the advantage is that excitation is only required at user defined points on the substructures; excitation at the contact points is not required, so commonly encountered measurement difficulties can be avoided. Finally, it is shown that the free velocity of a vibration source can be obtained indirectly from measurements made in the installed condition; the need for a free suspension, which is impossible in practise for many important vibration sources, is thus avoided. The relationships are validated using semi-analytical simulations of rods and beams, and errors are briefly discussed.