M.S. Thesis Presentation by David B. Copeland
Friday, December 21, 2001

(Dr. Jacek Jarzynski, advisor)

"Measurement of the Complex Shear Modulus and Its Frequency Dependence for Viscoelastic Materials"

Abstract

Viscoelastic materials, both homogeneous and composite, are used for vibration damping and for absorbing and decoupling sound.  To model and predict the acoustic performance of these materials it is necessary to know the complex elastic moduli of the material.  The objective of this study is to develop a method for measuring the complex shear modulus, and its frequency dependence, for high-loss (large loss tangent) viscoelastic materials.  The sample material used in this study is neoprene rubber.  The shear modulus is determined by measuring the amplitude and phase of harmonic torsional vibrations of the sample.  The sample is a rod with a square cross-section, 9.78 x 9.78 x 67.5 mm.  Measurements are made over a frequency range of 200 - 1500 Hz, and two methods are used to detect the torsional vibrations at the two ends of the sample.  One method uses a non-contact optical probe, and the second method uses a magnetic drive and pickup configuration.  In each case a transfer function is determined, which relates the amplitude and phase of the vibrations at the two ends of the sample.  Two numerical root search procedures are tested - a downhill Simplex and a Newton-Raphson algorithm - to determine the complex shear modulus, G', which gives the best fit, at each frequency, between the theoretical and measured transfer functions.  The values of G' are compared with values estimated from measurements, for the same material, of the complex Young's modulus, using a resonant bar technique.