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If structures with complex shapes have space limitations, vibration tests using an exciter or impact hammer for the excitation are difficult. Although measuring the auto frequency response function at an unexcited point may not be practical via a vibration test, it can be obtained by assuming that the inertia acting on a dummy mass is an external force on the target structure upon exciting a different excitation point. We propose a method to estimate the auto frequency response functions at unexcited points by attaching a small mass (dummy mass), which is comparable to the accelerometer mass. The validity of the proposed method is demonstrated by comparing the auto frequency response functions estimated at unexcited points in a beam structure to those obtained from numerical simulations. We also consider random measurement errors by finite element analysis and vibration tests, but not bias errors. Additionally, the applicability of the proposed method is demonstrated by applying it to estimate the auto frequency response function of the lower arm in a car suspension. [ABSTRACT FROM AUTHOR]

• We introduce the novel concept of decomposing the FRFs into paths. • The concept is based upon the FRFs, not upon transmissibilities as in GTDT. • The methodology can realize clear visualization of the contents of the FRFs. • It can evaluate the contributions of paths to the FRFs quantitatively. • The presented approach will promise to solve NVH problems. Frequency response functions (FRFs) lie within the framework of the linear response theory in elastic structures. In FRFs, the inputs/outputs relationships are strictly determined, but there is no way of knowing how waves are propagated and converted from the input signals into the output signals. Thus, the wave propagation between the inputs and outputs cannot be clearly understood by the FRFs. In this study, we succeeded in visualizing the contents of these FRFs by decomposing them into geometric paths using a signal flow graph. Moreover, we succeeded in quantitatively evaluating the contributions of the paths to these FRFs. In terms of application, when the noise or vibration of industrial products is loud and unpleasant, this analytical methodology can help identify the cause behind such nuisance by using paths in contribution to FRFs. This methodology is expected to pave the way for taking quantitative countermeasures on the basis of analytical results. [ABSTRACT FROM AUTHOR]