Absolute and relative path measures in a discrete system by using two analytical methods

This paper analytically examines two vibration paths rank ordering methods and critically investigates several path identification issues. One method is the indirect interfacial path force estimation procedure that is employed in the well known experimental transfer path analysis. The other method is path disconnect scheme that has been historically utilized in industry to empirically find a dominant or defective path. In this article we utilize simplified, but pedagogical, discrete vibratory systems to clarify the underlying principles of both methods and to assess the path rank orders. Our analysis is limited to a linear time-invariant system (with only translating motions) under harmonic excitation and three distinct parallel paths (with or without masses) are considered. Alternate formulations of the interfacial path forces, based on direct and indirect methods, are derived. The indirect, yet exact, interfacial (path) force expressions could be used to estimate time-averaged dissipated power and Lagrangian energy spectra in various sub-systems. Estimations using only the driving point frequency response functions are emphasized, since they would ease the experimental burden. Next, the path disconnect method is analytically formulated and related to the path connect scheme (assuming one path at a time). This analysis reveals some useful relations among the path measures and the way a particular path could be connected or disconnected. A laboratory experiment validates the simplified massless path model, which yields asymptotic trends. Finally, all of the path rank orders are quantified and compared using many absolute and relative measures (based on interfacial force, receiver motion and sub-system energy relationships). Direction for future work is briefly discussed.