A mechanical relaxation test for the determination of the frequency dependent complex modulus of linear viscoelastic materials

Frequency-dependent elastic parameter determination for noise control materials remains challenging due to variable installation conditions. Material response depends on temperature, loading, and deformation, complicating test standardization. While multiple experimental methods exist, none are universally adopted. This study estimates the complex modulus of isotropic viscoelastic materials using stress relaxation tests. A sample between parallel plates undergoes fixed deformation while opposite-side stress is recorded. The stress-strain ratio (relaxation function) is calculated, then transformed via Laplace analysis and fractional derivative modeling to obtain frequency-dependent moduli (1 Hz–100 kHz). Results for various acoustic materials show reproducibility consistent with literature standards when compared to established techniques. The proposed method offers reliable characterization across broad frequency ranges under controlled strain conditions, addressing gaps in current testing approaches. Key advantages include simultaneous multi-frequency analysis and compatibility with typical laboratory equipment. Discrepancies with reference methods fall within expected variation ranges, validating the technique’s accuracy for engineering applications in material development and quality control.