Abstract
The presented work deals with nonlinear dynamics of a three degree of freedom system with a spherical pendulum and a damper of the fractional type. Vibrations in the vicinity of the internal and external resonance are considered. The system consists of a block suspended from a linear spring and a fractional damper, and a spherical pendulum suspended from the block. The viscoelastic properties of the damper are described using the Caputo fractional derivative. The fractional derivative of an order of 0 < alpha le 1 is assumed. The impact of a fractional order derivative on the system with a spherical pendulum is studied. Time histories, the internal and external resonance, bifurcation diagrams, Poincaré maps and the Lyapunov exponents have been calculated for various orders of a fractional derivative. Chaotic motion has been found for some system parameters.
Highlights
In this work, the nonlinear response of an autoparametric system of three degrees of freedom with a spherical pendulum and a damper of the fractional type is investigated
The investigated system comprised a spherical pendulum suspended from a mass block which was suspended from a vertical linear spring and a viscous dashpot
The examined system comprised a spherical pendulum suspended from a mass block which was suspended from a vertical linear spring and a magnetorheological damper
Summary
The nonlinear response of an autoparametric system of three degrees of freedom with a spherical pendulum and a damper of the fractional type is investigated. The examined system comprised a spherical pendulum suspended from a mass block which was suspended from a vertical linear spring and a magnetorheological damper They studied the impact of magnetorheological damper properties on the system vibration in the neighborhood of internal and external resonances. Leung and Kuang [8] presented an analytical and numerical analysis of a lightly damped spherical pendulum, whose suspension point was harmonically excited in both vertical and horizontal directions. They studied the bifurcation behavior of the pendulum taking into account third order terms in the amplitude in the vicinity of the resonance. In the authors’ opinion, the impact of damping described by a fractional derivative on the dynamic behavior of the system with a spherical pendulum should be analyzed, which is the purpose of this research
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