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Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula
Institution:1. Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Belgrade, Serbia;2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11000 Belgrade, Serbia;1. Center of Advanced Systems and Technologies (CAST), School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran;2. Center of Excellence in Design, Robotics and Automation (CEDRA), Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran;1. Department of Mechanical Engineering, Technical University of Denmark, Nils Koppels Allé, Building 404, 2800 Kgs. Lyngby, Denmark;2. Institute of Problems in Mechanical Engineering RAS, V.O., Bolshoj pr. 61, St. Petersburg 199178, Russia;1. Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA;2. Mechanical and Aerospace Engineering, Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA;1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;2. Department of Engineering Mechanics, Hunan University, Changsha 410082, PR China;1. Department for Bio-medical Science, State University of Novi Pazar, Novi Pazar, Vuka Karadzica bb, 36 300 Novi Pazar, Serbia;2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11 120 Belgrade, Serbia;3. School of Medicine, University of Belgrade, Dr Subotica 8, 11 000 Belgrade, Serbia
Abstract: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:Fractional calculus  Rigid mulitibody dynamics  Spring  Spring-pot  Actuator  Adaptronic system
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