Authors: | Hedrih, Katica (Stevanović) | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Dynamics of multi-pendulum systems with fractional order creep elements | Journal: | Journal of Theoretical and Applied Mechanics | Volume: | 46 | Issue: | 3 | First page: | 483 | Last page: | 509 | Issue Date: | 1-Jan-2008 | Rank: | M23 | ISSN: | 1429-2955 | Abstract: | A survey as a short review of author's research results in area of dynamics of hybrid systems and analytical dynamics of discrete material particle sys- tem containing creep elements described by fractional order derivatives, is presented. Free vibrations of a multi-pendulum system intercoupled by stan- dard light elements and different properties are considered. The correspon- ding system of an ordinary fractional order as well as integro-differential equations, described dynamics of the multi-pendulum system, are derived and analytically solved. For the case of one pendulum and two pendulum systems containing standard light creep elements with the stress-strain con- stitutive relation expressed by a fractional order derivative, ordinary diffe- rential equations are analytically solved. From the analytical solutions, for the case of the homogeneous two-pendulum system, it is visible that free vibrations under arbitrary initial conditions contain three modes, one pure periodic and two aperiodic expressed by time series expansions. The obta- ined analytical solution modes are numerically analysed and characteristic vibration modes for different kinetic parameters are graphically presented. |
Keywords: | Coupled dynamics | Coupled subsystems | Multi-pendulum system | Publisher: | Polish Society of Theoretical and Allied Mechanics |
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