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EN
Dynamic properties of the three degrees of freedom autoparametric system with spherical pendulum including the magnetorheological (MR) damper are investigated. It was assumed that the spherical pendulum is suspended to the oscillator excited harmonically in the vertical direction. The influence of damping force described by Bingham’s model on the energy transfer can be modified by magnetic field. The equation of motion have been solved numerically. In this type system one mode of vibration may excite or damp another one, and for except different kinds of periodic vibrations there may also appear chaotic vibration. Results show that MR damper can be used to change the dynamic behavior of the autoparametric system with spherical pendulum giving semiactive control possibilities.
EN
In the paper, the dynamics of a three degree of freedom vibratory system with a spherical pendulum in the neighbourhood of internal and external resonance is considered. It has been assumed that the spherical pendulum is suspended to the main body which is then suspended to the element characterized by some elasticity and damping. The system is excited harmonically in the vertical direction. The equation of motion has been solved numerically. The influence of initial conditions on the behaviour of the spherical pendulum is investigated. In this type of the system, one mode of vibration may excite or damp another one, and for different kinds of periodic vibrations there may also appear chaotic vibrations. For characterization of an irregular chaotic response, time histories, bifurcation diagrams, power spectral densities, Poincar´e maps and the maximum Lyapunov exponents have been calculated.
EN
The nonlinear response of a three degree of freedom vibratory system with spherical pendulum in the neighbourhood internal and external resonance is investigated. It was assumed that spherical pendulum is suspended to the main body which is suspended by the element characterized by elasticity and damping and is excited harmonically in the vertical direction. The equation of motion have bean solved numerically. In this type system one mode of vibration may excite or damp another one, and for except different kinds of periodic vibrations there may also appear chaotic vibration.
4
Content available remote Oscillations of an Autoparametrical Systems with the Spherical Pendulum
EN
Dynamic properties of the three degrees of freedom autoparametric system with spherical pendulum in the neighbourhood internal and external resonance are investigated. It was assumed that the spherical pendulum is suspended in the main body which is suspended by the element characterized by elasticity and damping and is excited harmonically in the vertical direction. The spherical pendulum is similar to the simple pendulum, but moves in 3-dimensional space, so the model with spherical pendulum is more similar to the real systems than the model with simply pendulum. In this paper the position of the main body is described by coordinate z and position of the pendulum is describe by the coordinate z and two angles: θ and φ in the vertical planes. This system has three degrees of freedom. Dynamic properties of the system described by three differential equations containing strongly nonlinear terms are investigated numerically. In autoparametric system one mode of vibration may excite or damp another one, and for except periodic or quasi-periodic vibrations there may also appear chaotic vibration. For characterizing an irregular chaotic response, time histories, bifurcation diagrams, power spectral densities, Poincaré maps and maximal exponents of Lyapunov have been developed.
EN
A mathematical model of spherical pendulum with moving pivot is suggested and developed. Such a model allows studying the influence of the different kinematic excitations applied at the pivot point upon the kinematical and dynamical parameters of the pendulum which also determine the force in the rope. A numerical simulation for spatial curvilinear and planar with straight line motions trajectories is performed.
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