Alternate methods for characterizing spectral energy inputs based only on driving point mobilities or impedances

This article analyses three characterization methods for spectral energy inputs to a linear time-invariant system. Analytical frequency domain formulations are examined for discrete vibratory systems and one-dimensional continuous structure (undergoing longitudinal or flexural motions) given a harmonic force excitation. Two existing methods that have been proposed by prior researchers are first critically examined. In particular, the driving point transfer functions and their derivatives with respect to frequency are analyzed for an appropriate application to the energy characterization scheme and to determine the sources of error. Then, a new (third) scheme is proposed that is more suitable over low and mid frequency regimes, based on a proper interpretation of the driving point mobilities or impedances and their derivatives. The new method is found to be insensitive to the driving point mobility or impedance formulations, unlike the existing methods. It does yield consistent results, without requiring a prior knowledge of the transfer functions. Finally, the role of structural loss factor has been clarified in the context of the stated problem.