No abstract

This paper introduces mechanical networks as a tool for modeling complex unidirectional vibrations. Networks of this type have branches containing massless linear springs and dampers, with masses at the nodes. Tree and ladder configurations are examples demonstrating that the overall dynamics of infinite systems can be represented using implicitly defined integro-differential operators. Results from the proposed models compare well to numerical results from finite systems, so this approach may have advantages over high-order differential equations.

This abstract outlines recent results in two new applications for fractional-order modeling of engineering systems. First, fractional-order dynamics present in two types of multiagent systems are discussed; namely, a specific tree graph structure for a robotic formation control problem and fractional-order dynamics of a scale-free network of agents. Second, fractional-order dynamics present in modeling of the linear friction welding process are discussed.

The dynamics of many large-scale robotic formation systems, including structured systems as well as some random scale-free networks of agents, can be accurately described using fractional-order differential equations. A fractional-order differential equation can contain derivative terms with noninteger order, e.g., the one-half derivative. This paper demonstrates that the fractional order of the dynamics of a system may be a potentially powerful new way to monitor the operational status of such systems. When the order of the system changes, it can indicate an important change in the status of the system. Integer-order models will never exhibit a change in order because the order is dictated by a natural first principle and the structure of the system. For this reason, traditional health monitoring tools essentially focus on identifying parameter variations in a mathematical description of the system, but not changes in order. When fractional-order models are considered, the infinite number of possible real-valued orders between any two integer orders may capture essential changes in the system's dynamics. This paper provides an example of such changes, provides a theoretical justification for the approach, and explores possible limitations to the approach.

No abstract