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Stały URI dla kolekcjihttp://hdl.handle.net/11652/206

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20152

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  • Pozycja
    Identification of a non-linear damping coefficient characteristics in the free decay test of a single pendulum with friction.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Awrejcewicz, Jan; Olejnik, Paweł
    A pendulum in form of an equal arms angle body being a part of a two degrees-of-freedom mechanical system with friction is identified with respect to the observed in uence of some resistance of its rotational motion in ball bearings. It is damped in a much more complex manner, what could be considered as a non-linear damping. There is supposed between others, that the effective non-linear damping characteristics depends on a few effects such as fluid friction caused by vibrations of the pendulum with two springs in the air, as well as unknown kinds of a frictional resistance existing in ball bearings. The model under investigation finds its real realization on a laboratory rig designed for experimental investigations of viscous and structural frictional effects. A transient response oscillations of the pendulum are described by the explicitly state-dependent free decay. A free decay test of the pendulum with the state dependent non-linear parameters of damping and stiffness has been performed in this paper. It provided interesting observations that led to elaboration of a method of the overall damping coefficient identification. Effects of application of the proposed semi-empirical method of identification of the overall damping and stiffness coefficients have been illustrated and discussed.
  • Pozycja
    Double pendulum colliding with a rough obstacle.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Sypniewska-Kamińska, Grażyna; Starosta, Roman; Awrejcewicz, Jan
    The externally excited and damped vibrations of the double pendulum in the vertical plane are considered. The pendulum can collide with a rough obstacle many times during its motion. The pendulum is modeled as a piecewise smooth system. The differential equations govern the motion of the system in the relatively long time between the collisions. When a contact with the obstacle occurs, the pendulum exhibits a discontinuous behaviour. The velocities of both parts of the pendulum and the reaction forces are changing stepwise. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler’s laws of motion in the integral form. The equations are supplemented by the Poisson's hypothesis and Coulomb’s law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Furthermore, during the collision the dynamic behaviour may change. Therefore the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space.