DIOPHANTINE TYPE FRACTIONAL DERIVATIVE REPRESENTATION OF STRUCTURAL HYSTERESIS .1. FORMULATION

Based on a diophantine representation of the operational powers, a fra ctional derivative modelling scheme is developed to simulate frequency dependent structural damping. The diophantine set of powers is establ ished by employing the curvature properties of the defining empirical data set. These together with a remezed least square scheme are employ ed to construct a Chebyschev like optimal differintegro simulation. Ba sed on the use of the rational form resulting from the diophantine rep resentation, a composition rule is introduced to reduce the differinte gro simulation to first order form. The associated eigenvalue/vector p roperties are then explored. To verify the robustness-stability accura cy of the overall modelling procedure, correlation studies are also pr esented. Part I of this series focuses on the diophantine representati on, its use in formulating a numerically more workable first order for m as well as formal representations of its transient and steady state solutions. This will include investigations of the asymptotic properti es of the various formulations. Part II will introduce the model fitti ng scheme along with a look at eigen properties and fitting effectiven ess.