MATHEMATICAL-ANALYSIS OF RHEOMETER DYNAMICS USING MULTISEGMENT MODELS

Mathematical analysis of rheometer dynamics in terms of multi-segment models is discussed. It is shown that the algebra involved in the analysis most often can be simplified significantly if standing rather than propagating complex waves are used as trial functions for the displacement within each segment. The objective of this work is to demonstrate that a full analytical description of the diplacement of many dynamic rheometers is readily obtainable even when both inertia and viscoelasticity of the force and/or displacement transducers are taken into account. Using these analytical expressions and modern standard desktop computers the numerical analysis is shown to be nonproblematic.