Experimental and Theoretical Analysis of Frequency- and Temperature-Dependent Characteristics in Viscoelastic Materials Using Prony Series

This study comprehensively investigates the frequency- and temperature-dependent viscoelastic properties of two elastomer materials, focusing on the comparison between experimental results and theoretical models derived from Prony series coefficients. Dynamic Mechanical Analysis (DMA) was performed across a broad temperature range of 0–100 °C and frequency range of 0.1–100 Hz to generate storage modulus and relaxation modulus data for both materials. Relaxation tests were conducted at 25 °C to further characterize the time-dependent behavior. Time–Temperature Superposition (TTS) was applied to the resultant shift factors used to fit both Williams–Landel–Ferry (WLF) and Arrhenius equations. Additionally, sinusoidal sweep tests were carried out at 0 °C, 25 °C, 50 °C, and 80 °C, with frequencies ranging from 1 Hz to 1000 Hz, to experimentally determine the natural frequencies of the elastomers. The findings demonstrate that Prony series coefficients derived from storage modulus data offer a more accurate prediction of the viscoelastic response and natural frequencies compared to those derived from relaxation modulus data. The storage modulus data closely match the experimentally observed natural frequencies, while the relaxation modulus data exhibit larger deviations, particularly at higher temperatures. The study also reveals temperature-dependent behavior, where increasing temperature reduces the stiffness of the materials, leading to lower natural frequencies. This comprehensive analysis highlights the importance of selecting appropriate modeling techniques and data sources, particularly when predicting dynamic responses under varying temperature and frequency conditions.