Abstract
There is considered a system of a spatial double pendulum with rigid movable obstacle, consisting of two links connected to each other and suspended on a shaft performing rotational motion about its horizontal axis according to a given function of time (kinematic driving). The links are connected by the use of two universal joints. The second link ends with a ball which can come into contact (impacts and permanent contact) with a planar and rotating obstacle situated below the pendulum. There is presented mathematical model of dynamics based on the Lagrange formulation. In this work, we use and expand our earlier developed models of contact forces (resulting friction force and rolling resistance). The friction models are based on the integral model developed assuming developed sliding on a planar contact area, where at each point, the classical Coulomb’s friction law is valid. The integral models are then replaced by special approximations being more suitable for fast numerical simulations. In the present work, we model impacts with non-point frictional contacts assuming Hertzian compliance of the obstacle. The constructed models of 3D dynamics of a rigid body and the planned experimental investigations allow us to perform the tests of importance of the particular individual elements of the models and may lead to general conclusions about modelling and effective computer simulations of mechanical systems with 3D frictional contacts. We report bifurcation dynamics using bifurcation diagrams, Poincaré sections as well as the largest Lyapunov exponent.
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Awrejcewicz, J., Kudra, G. (2021). Modelling of Frictional Contacts in 3D Dynamics of a Rigid Body. In: Herisanu, N., Marinca, V. (eds) Acoustics and Vibration of Mechanical Structures—AVMS 2019. Springer Proceedings in Physics, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-030-54136-1_1
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DOI: https://doi.org/10.1007/978-3-030-54136-1_1
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