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. T hese are employed to determine how such operators, which act as viscoelasti c elements, partition system energy into conservative and nonconservative c omponents. Special emphasis is given to: (a) determine how operator order s erves to weigh such a splitting, (b) determine how partitioning affects sys tem phasing and amplitude response, and (c) to establish how conservative a nd nonconservative effects modulate during a given system cycle. The genera lity of the undertaken approach is such that multi-element fractional Kelvi n Voigt formulations subject to spectrally rich inputs can be handled, i.e. , the multi-modal splitting of energies. As a result of the insights derive d, improved frequency dependent simulations of system amplitude, phasing an d energetics will be possible. (C) 1999 The Franklin Institute. Published b y Elsevier Science Ltd.