AN ALGORITHM FOR FAST DETERMINATION OF COMPLEX MODULI

Traditionally, the complex modulus is determined by Fourier analysis o f steady state oscillatory data. However, steady state is not obtained immediately and data from the first period of oscillation must theref ore be discarded. In the present work a recursive analysis algorithm f or the determination of complex moduli from oscillatory data of the fi rst period, which includes a transient response alongside the steady s tate response, is derived. The algorithm is based on Boltzmann's princ iple of superposition. At any given time, the analysis algorithm provi des the best possible estimate of the complex modulus on the basis of the information available at that time, i.e., the stress and strain hi story. The analysis algorithm has been tested on simulated data from a mathematical model of an amorphous polymer. The tests show that the n ew analysis algorithm can determine the dynamic mechanical properties with very good accuracy from oscillatory data of the first period, whe re Fourier analysis fails. Thus, use of the new algorithm allows a red uction of the experiment time by a factor of 2 for experiments with a sufficiently high signal-to-noise ratio to avoid averaging over severa l periods. This reduction of the measurement time is particularly impo rtant for experiments at very low frequencies where the long measureme nt times seriously limit the number of runs per day.