AN ALGORITHM FOR FAST DETERMINATION OF COMPLEX MODULI

Traditionally, the complex modulus is determined by Fourier analysis of steady state oscillatory data. However, steady state is not obtained immediately and data from the first period of oscillation must therefore be discarded. In the present work a recursive analysis algorithm for the determination of complex moduli from oscillatory data of the first period, which includes a transient response alongside the steady state response, is derived. The algorithm is based on Boltzmann's principle of superposition. At any given time, the analysis algorithm provides the best possible estimate of the complex modulus on the basis of the information available at that time, i.e., the stress and strain history. The analysis algorithm has been tested on simulated data from a mathematical model of an amorphous polymer. The tests show that the new analysis algorithm can determine the dynamic mechanical properties with very good accuracy from oscillatory data of the first period, where Fourier analysis fails. Thus, use of the new algorithm allows a reduction of the experiment time by a factor of 2 for experiments with a sufficiently high signal-to-noise ratio to avoid averaging over several periods. This reduction of the measurement time is particularly important for experiments at very low frequencies where the long measurement times seriously limit the number of runs per day.