Journal of the Franklin Institute
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.
Sawicki, J.T. and Padovan, J. (1999) Frequency Driven Phasic Shifting and Elastic-Hysteretic Partitioning Properties of Fractional Mechanical System Representation Schemes. Journal of the Franklin Institute, 336(3), 423-433, doi: 10.1016/S0016-0032(98)00036-2.
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of the Franklin Institute. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of the Franklin Institute, 336, 3, (04-01-1999); 10.1016/S0016-0032(98)00036-2