Fractionally damped mechanical systems are described by differential equations including fractional-order derivatives, i.e. of arbitrary real order. In mechanics, these take the form of force elements called “springpots”, whose behavior lies in between that of ideal springs and dashpots. These models are especially relevant for describing the behavior of viscoelastic materials, providing a good mapping of short- and long-term behavior.
The aim of this project is to develop a method for stability analysis of periodic solutions of said systems, which is characterized by linear time-periodic dynamics. In the well-known case of first-order differential equations, various approaches are available and understood quite deeply. In order to provide a method for the fractional-order case, we propose a frequency-based approach analogous to the classical Hill method, enabling the extraction of stability information in systems with fractional damping.
To validate the developed method, we will implement it in an experimental setup. The material exhibiting fractional behavior is a synthetic resin applied in civil engineering composite materials as a corrosion-resistant reinforcement alternative to steel. In order to minimize the influence of external energy dissipation, we use a laser vibrometer for contactless measurements and an air bushing, minimizing energy dissipation through friction.
In the joint research project MuSiK (Modellierungsmethoden und Simulationswerkzeuge für faserverstärkte Kunststoffe) supported by the Federal Ministry of Education and Research, we are collaborating with Prof. Kai Diethelm’s research group at THWS, as well as with industry partners GNS Gesellschaft für numerische Simulation mbH in Braunschweig and Deutsche Basalt Stab GmbH in Stuttgart.
Paul-Erik Haacker
M.Sc.
Remco I. Leine
Prof. Dr. ir. habil.director