Frequency Driven Phasic Shifting and Elastic-Hysteretic Partitioning Properties of Fractional Mechanical System Representation Schemes

Based on the Louiville–Riemann fractional formulation of lumped hysteretic mechanical system simulations, asymptotic-type relationships are derived. These are employed to determine how such operators, which act as viscoelastic elements, partition system energy into conservative and nonconservative components. Special emphasis is given to: (a) determine how operator order serves to weigh such a splitting, (b) determine how partitioning affects system phasing and amplitude response, and (c) to establish how conservative and nonconservative effects modulate during a given system cycle. The generality of the undertaken approach is such that multi-element fractional Kelvin Voigt formulations subject to spectrally rich inputs can be handled, i.e., the multi-modal splitting of energies. As a result of the insights derived, improved frequency dependent simulations of system amplitude, phasing and energetics will be possible.