Several techniques can be employed to predict dynamic characteristics of a large scale system consisting of various subsystems using those of each subsystem. When natural frequencies and damping ratios as well as detailed mode shapes are required for the assembled structure, general modal synthesis techniques will be essential. But when only a few natural frequencies and damping ratios or a few frequency response functions between specific points of interest in the assembled system are to be estimated, simpler approaches can be taken.
First, this paper reviews a simple and relatively old, but very practical, method called four pole parameter technique. In this approach, a system is characterized in terms of four frequency dependent functions between an input point and an output point. The advantage of this method is that the frequency response functions of a structure assembled in series and/or in parallel are obtained by simple matrix multiplications of those of subassemblies for the case of single-input and single-output connections. Also, application to the analysis of a passenger vehicle is presented.
So far the four pole parameter approach has been treated in case of single-input / single-output system, i.e. scalarly. This text presents the basic concepts as well as formulas to expand the scalar four pole parameter technique to multiple-input / multiple-output (MIMO) systems. The technique, called vectorial four pole parameter method here, keeps the properties and advantages that the scalar for pole parameter technique has. Compatibility of the formulas with the Newtonia mechanics is confirmed by two examples : one system constructed by two subsystems in series and another system in parallel.
Since two poles are defined under clamped conditions while the other two poles are under free boundary conditions, it is often difficult in practice to measur all of the four poles directly from excitation test. A method of indirect estimation the two poles defined under boundary conditions which are difficult to realize presented using the reciprocity and transmissibility theorems.. Experimental result for a beam structure with 2-input and 2-output connections are represented as an illustration of the vectorial four pole parameter approach to the frequency response prediction of structures with multiple connections.
