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This paper outlines a method for computing the transfer functions of structures using their mass loaded responses. According to the method, scaled transfer functions are computed from the response of a structure and without any knowledge of the input forces. The paper outlines the analytical approach, develops the necessary equations for the computation of transfer functions between a mass loading point and other points on a linear dynamic system. A numerical example to show the validity, advantages and limitations of the method is also provided. Currently, the method can be applied to the responses obtained from analytical simulations where it may be necessary to compute coupled response of a simulated dynamic system with other dynamic systems that are not (or cannot be) included in a simulation. It is not uncommon that many dynamic simulations exclude certain coupling effects between the main and the auxiliary systems.

Critical speed induced by imbalance forces is a well-known dynamic behavior of rotating shafts. Such problems are typically found in flexible shafts or rigid shafts with flexible supports when the frequency of rotation reaches the natural frequencies of the shaft. This simple critical speed problem is well understood and formulated in many engineering texts. However, not all critical speed phenomena are induced by imbalance. A perfectly balanced shaft with certain inertial properties also reaches a critical speed condition at a rotational speed that is not equal to the natural frequency of the shaft. Several variables of the dynamic system play a role on the critical speed condition, which is mainly induced by the unstable gyroscopic moment acting on the shaft. The unstable gyroscopic moment forces the shaft bearings to deflect causing precession about the undeflected geometric centerline of the shaft, but the rotation and precession speeds remain synchronized at low speeds.