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Improvements to the Transfer Function Method for Determining the Complex Dynamic Modulus of Polymer Composites
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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The Materials Research Laboratory at The Pennsylvania State University fabricates diphasic transducer composites made from polymers and piezoceramic. It is desired to measure the loss factor of these materials over the audible frequency range. After consideration of a number of measuring systems, a decision was made to implement 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 dynamic modulus by two, coupled, transcendental equations derived by applying appropriate boundary conditions to the solution of the longitudinal wave equation. In theory, these equations can be solved at any frequency by an iterative procedure. In practice, convergence problems reduce the valid solutions to just those obtained at the longitudinal resonance frequencies. Improvements made during this study, enable the equations to be solved at any frequency except those where the phase of that ratio is zero. Plots of loss factor and storage modulus are presented for a number of composites. Several highdamping polymeric materials were also tested. A comparison between the present results and those quoted in other studies indicates that the improved method produces reliable results more quickly and with much less effort than previously required.
APPROVED FOR PUBLIC RELEASE