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The frequency response functions of discretely connected structures, such as a vehicle system, are determined by inverting the spectral-based sub-structuring equation in dynamic compliance form, which is classically used to compute coupled system response in terms of the characteristics of the free sub-structures. The resulting formulation backs out the response spectra of the free sub-structures including the dynamic stiffness terms of the coupling elements. When analysing the vibration response of one sub-structure due to an externally applied harmonic excitation on an adjacent sub-structure, the proposed theory can express the force transmissibility and structural path contribution functions directly in terms of the coupled system response. This provides a convenient way to identify the critical elements of a physical structure containing multiple coupling points without having to disconnect the individual sub-structures. The salient features of this approach are demonstrated using an idealised lumped parameter dynamic system.

The spectral-based inverse sub-structuring theory formulated in Part 1 is applied here to investigate the vibration transmissibility and frequency response characteristics of motor vehicle structures. Analysis assumes a vehicle model that comprised of two sub-structures representing the body and chassis/suspension. Measured structural-acoustic and vibration spectra acquired from a relatively direct experimental setup are utilised to compute the relevant force transmissibility and path contribution functions at the discrete coupling points. Furthermore, the free sub-structure response characteristics and mount dynamic stiffnesses are expressed directly in terms of coupled system responses. These studies are performed using four real-life vehicles. For each case, the constructed system response functions are shown to match well with experimental data. Comparisons of the results derived from these vehicle examples reveal useful relationships between coupled system responses, free sub-structure characteristics and coupling compliances.