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Vibro-impact dynamics of two rolling heavy thin disks along rotate curvilinear line and energy analysis

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Abstract

Construction of the phase trajectory portraits of a generalized rolling pendulum along rotate curvilinear line is presented. The generalized rolling pendulum containing a rolling thin heavy disk rotates along the curvilinear line consisting of three circle arches, with constant angular velocity around a vertical eccentric/central axis. Depending on system parameters, different possible forms of the phase portraits appear with different structures of the sets of singular points and forms of phase trajectories. Trigger of coupled singular points and homoclinic orbit in the form of deformed number “eight” appears. A mathematical analogy between nonlinear differential equations of the considered generalized rolling pendulum and motion of the heavy mass particle along rotate curvilinear line, which are same form, is pointed out. On the basis of the obtained different possible phase trajectory portraits, nonlinear phenomena in vibro-impact dynamics of two rolling thin disks on rotate curvilinear line are investigated. Energy transfer between rolling disks in each of the series of successive collisions is analyzed and presented on relative mechanical energy portraits for dynamics of each of the rolling disks in collision.

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Acknowledgements

Author is very grateful to reviewers and Guest Editors as well as to Editor-in-Chief of Journal, Walter Lacarbonara for the devoted time and effort to read and print all comments. Author expresses compliments to reviewers for expressed professional goodness in reading and understanding manuscript. Also, author is very grateful to young researcher and Ph.D student Stepa Paunovic, for valuable help in improvement in English of the manuscript.

Funding

Project ON174001 “Dynamics of hybrid systems with complex structures.”, partially supported by Ministry of Education, Science and Technology Republic of Serbia through Mathematical Institute of the Serbian Academy of Science and Arts, and Faculty of Mechanical Engineering University of Niš, as a researcher and Project leader without salary because is in age 75.

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  1. Department of Mechanics, Mathematical Institute of the Serbian Academy of Science and Arts, ul. Knez Mihailova 36/III, Belgrade, 11000, Serbia

    Katica R. (Stevanović) Hedrih

  2. Faculty of Mechanical Engineering, University of Niš, ul. Vojvode Tamkosića 3/V/22, Niš, 18000, Serbia

    Katica R. (Stevanović) Hedrih

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  1. Katica R. (Stevanović) Hedrih
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Correspondence to Katica R. (Stevanović) Hedrih.

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Dedicated to memory of Professor and important scientist ALY NAYFEH (December 21, 1933-March 27, 2017).

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Hedrih, K.R.(. Vibro-impact dynamics of two rolling heavy thin disks along rotate curvilinear line and energy analysis. Nonlinear Dyn 98, 2551–2579 (2019). https://doi.org/10.1007/s11071-019-04988-6

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