Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula
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 Atanackovic and Stankovic (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 o...rder derivative model.
Keywords:
Spring-pot / Spring / Rigid mulitibody dynamics / Fractional calculus / Adaptronic system / ActuatorSource:
Mechanics Research Communications, 2014, 62, 44-56Publisher:
- Pergamon-Elsevier Science Ltd, Oxford
Funding / projects:
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
- Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design (RS-MESTD-Technological Development (TD or TR)-35006)
DOI: 10.1016/j.mechrescom.2014.08.009
ISSN: 0093-6413
WoS: 000347129300007
Scopus: 2-s2.0-84908426100
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Cajić, Milan AU - Lazarević, Mihailo PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1860 AB - 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 Atanackovic and Stankovic (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. PB - Pergamon-Elsevier Science Ltd, Oxford T2 - Mechanics Research Communications T1 - Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula EP - 56 SP - 44 VL - 62 DO - 10.1016/j.mechrescom.2014.08.009 ER -
@article{ author = "Cajić, Milan and Lazarević, Mihailo", year = "2014", 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 Atanackovic and Stankovic (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.", publisher = "Pergamon-Elsevier Science Ltd, Oxford", journal = "Mechanics Research Communications", title = "Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula", pages = "56-44", volume = "62", doi = "10.1016/j.mechrescom.2014.08.009" }
Cajić, M.,& Lazarević, M.. (2014). Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula. in Mechanics Research Communications Pergamon-Elsevier Science Ltd, Oxford., 62, 44-56. https://doi.org/10.1016/j.mechrescom.2014.08.009
Cajić M, Lazarević M. Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula. in Mechanics Research Communications. 2014;62:44-56. doi:10.1016/j.mechrescom.2014.08.009 .
Cajić, Milan, Lazarević, Mihailo, "Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula" in Mechanics Research Communications, 62 (2014):44-56, https://doi.org/10.1016/j.mechrescom.2014.08.009 . .