12 April 2017 Vibration analysis of discrete parameter systems using fractional order models
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Abstract
This study explores the use of fractional differential equations to model the vibration of single (SDOF) and multiple degree of freedom (MDOF) discrete parameter systems. In particular, we explore methodologies to simulate the dynamic response of discrete systems having non-uniform coefficients (that is, distribution of mass, damping, and stiffness) by using fractional order models. Transfer functions are used to convert a traditional integer order model into a fractional order model able to match, often times exactly, the dynamic response of the active degree in the initial integer order system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting differential models have both frequency-dependent and complex fractional order. The presented methodology is practically equivalent to a model order reduction technique that is able to match the response of non-uniform MDOF systems to a simple fractional single degree of freedom (F-SDOF) systems. The implications of this type of modeling approach will be discussed.
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John P. Hollkamp, Mihir Sen, Fabio Semperlotti, "Vibration analysis of discrete parameter systems using fractional order models", Proc. SPIE 10168, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2017, 101682V (12 April 2017); doi: 10.1117/12.2258736; https://doi.org/10.1117/12.2258736
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