Speaker
Description
Continuous relaxation spectra accurately describe how vibrating materials dissipate energy across scales. The fractional wave equation models this behaviour, yet engineering practice often collapses damping into a single structural parameter, obscuring its intrinsic multi-scale nature. Herein, we present a discrete approximation of continuous relaxation spectra based on a superposition of relaxation functions with characteristic time scales. The associated stress–strain relation is derived from Ludwig Boltzmann’s Theory of Elastic After-Effects, which was published during his professorship in experimental physics at the University of Graz in 1876. We establish the conditions that ensure convergence of the discrete spectra to their continuous counterparts in a theoretical consideration. Variational mode decomposition and Hilbert-Huang spectral analysis are used to determine the discrete relaxation functions. Free vibration measurements on a cantilever beam validate the approach using nonlinear regression analysis to determine the decay behaviour of the relaxation functions. The methods enable robust time-domain damping identification, including nonlinear damping, where frequency-domain techniques are inapplicable. Finally, we demonstrate applicability to more complex materials and structures, exemplified by a wooden rod, highlighting the method’s practicality for the engineering of vibrating structures.