Improvement to the transfer function method for determining the complex dynamic modulus of polymer composites

Abstract

The Applied Research Laboratory, The Pennsylvania State University, University Park, PA 16802 Measurements of loss factor and storage modulus of diphasic transducer composites of polymers and piezoceramic were made using the transfer function method. This method consists of exciting a mass‐loaded rod into longitudinal vibrations. The complex acceleration ratio between its ends is related to the complex modulus by two coupled, transcendental equations derived from the solution of the longitudinal wave equation with appropriate boundary conditions. In theory, these equations can be solved at any frequency by an iterative procedure. In practice, convergence problems reduce the valid solutions to those just at the longitudinal resonance frequencies. Improvements made during this study enable the equations to be solved at any frequency, except where the phase of the acceleration ratio is zero. Plots of loss factor and storage modulus are presented for a number of these new composites and other high‐damping polymeric materials. A comparison between present results and those quoted in other studies indicates that this method produces reliable results. The improvements enable results to be obtained more quickly and with much less effort than previously required. [Work supported by ONR.]