Authors: Cajić, Milan 
Lazarević, Mihailo
Title: Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula
Journal: Mechanics Research Communications
Volume: 62
First page: 44
Last page: 56
Issue Date: 1-Jan-2014
Rank: M22
ISSN: 0093-6413
DOI: 10.1016/j.mechrescom.2014.08.009
Fractional order models of a spring/spring-pot and spring/spring-pot/actuator element connected into a multibody system are proposed in order to represent smart materials and components in adaptronic systems by introducing new tuning parameter. The models are introduced into dynamic equations via generalized forces and using the Lagrange's equations of the second kind in covariant form. Generalized forces are derived by taking into account fractional order derivatives in force-displacement relations and by using the principle of virtual work. The numerical scheme for solving fractional order differential equations proposed in Atanacković and Stanković (2008) is used in order to approximate fractional order derivative of a composite function appearing in the presented fractional order model. Numerical example for the multibody system with three degrees of freedom is presented. The results obtained for generalized forces are compared for different values of parameters in the fractional order derivative model.
Keywords: Actuator | Adaptronic systema | Fractional calculus | Rigid mulitibody dynamics | Spring | Spring-pot
Publisher: Elsevier
Project: Dynamics of hybrid systems with complex structures. Mechanics of materials. 
Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design 

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