Comparing different data processing methods for determining a Prony series from Dynamic Mechanical Analyzer frequency data

Abstract This study focuses on using a dynamic mechanical analyzer (DMA) for obtaining frequency domain data suitable for constructing an accurate Prony series for a viscoelastic material. Polymethyl methacrylate (PMMA) specimens were used in each experiment, following the ASTM D4000 and ASTM D5023 standards. The experiments were completed using a frequency range of 1 to 100 Hz at multiple temperatures to capture the long‐term behavior via time–temperature superposition. Prony series were fit to the data from these experiments, and used to establish the time domain viscoelastic modulus of PMMA. The effect of the fitting function, material soak time, noise, and reference temperature selection were each investigated for their effect on the Prony series. The raw data may be processed via four paths, which are then compared for statistical error. The most accurate path resulted in a cumulative error of 2.1% for the storage modulus and 26% for the loss modulus. The impact of these errors on the tip displacement of a reference cantilever beam subject to axial loading for 15 years is a variation of over 25%.