Complex wavenumber method for testing the Young’s modulus of viscoelastic rod

This study addresses the demand for the testing of complex Young’s modulus in viscoelastic materials across a continuous wide frequency range. To overcome the limitations that the resonance method only yields results at very few resonant frequencies and the incident wave extraction method involves complicated calculations for separately solving the amplitude and phase angle of the complex Young’s modulus, this study proposes complex wavenumber method. Through the analysis of the one-dimensional longitudinal vibration model of a slender rod, this study derives the principles underlying the complex wavenumber method and validates our approach using a finite element model. For a specific viscoelastic specimen, complex wavenumber method, the resonance method and the incident wave extracting method are used to process the same set of experimental data. Comparative results indicate that the complex wavenumber method effectively measures complex Young’s modulus across a continuous wide frequency range, with findings at resonance frequencies aligning with those obtained via the resonance method and agreeing well with the incident wave extraction method across the broadband frequency range.