ANALYSIS OF MIMO MECHANICAL SYSTEMS USING THE VECTORIAL 4 POLE PARAMETER METHOD

Abstract

Formulas are derived to predict the frequency response characteristics of a multiple-input/multiple-output (MIMO) linear system consisting of several subsystems by using those of each subsystem. The method is called here the vectorial four pole parameter technique, since the basic concept and procedure are the same as for the conventional (scalar) four pope parameter method for a single-input/single-output (SISO) system. Compatibility of the formulas with Newtonian 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 measure all of the four poles directly from an excitation test. A method of indirect estimation of the two poles defined under boundary conditions which are difficult to realize is presented, in which the reciprocity and transmissibility theorems are used. Experimental results for a beam structure with two-input and two-output connections are presented as an illustration of the vectorial four pole parameter approach.