Modeling and analysis of a system of two self-balancing pendulums is presented in this paper. Such systems are commonly used as elements of automotive door latch mechanisms that can be subjected to oscillatory excitation or vibratory inertia forces occurring during crash events. In order to avoid an unwanted behavior such as opening of the door, the considered mechanism should be properly designed and its dynamical response well understood and predictable. One pendulum of the double-pendulum system, playing the role of a counterweight (CW), is used to reduce the second (or main) pendulum motion under inertia loading. The interaction force between the pendulums is defined as the reaction of a holonomic constraint linking the rotations of both pendulums. Another reaction force acts between one of the pendulums and the support, reinforced by the action of a preloaded spring. An important aspect of the model is its discontinuous nature due to the presence of a gap in the interface area. This may result in impacts between both pendulums and between one of the pendulums and the support. High-frequency/high-acceleration amplitude vibratory motion of the base part provides inertia input to the system. Classical multibody dynamics approach is adopted first to solve the equations of motion. It is shown that the considered system under certain conditions responds with a high-amplitude irregular motion. A special methodology is used in order to study the regions of chaotic motion, with the goal to gain more understanding of the considered system dynamics. Bifurcation diagrams are presented together with quantitative and qualitative analysis of the motion. The sensitivity of solutions to variation of system parameters and input characteristics is also analyzed in the paper.
Skip Nav Destination
Article navigation
July 2016
Research-Article
Dynamics of a Self-Balancing Double-Pendulum System
Andrzej Mitura,
Andrzej Mitura
Department of Applied Mechanics,
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: a.mitura@pollub.pl
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: a.mitura@pollub.pl
Search for other works by this author on:
Jerzy Warminski
Jerzy Warminski
Department of Applied Mechanics,
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: j.warminski@pollub.pl
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: j.warminski@pollub.pl
Search for other works by this author on:
Krystof P. Jankowski
Andrzej Mitura
Department of Applied Mechanics,
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: a.mitura@pollub.pl
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: a.mitura@pollub.pl
Jerzy Warminski
Department of Applied Mechanics,
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: j.warminski@pollub.pl
Lublin University of Technology,
Nadbystrzycka 36,
Lublin 20-618, Poland
e-mail: j.warminski@pollub.pl
1Corresponding author.
Manuscript received February 2, 2015; final manuscript received October 13, 2015; published online December 11, 2015. Assoc. Editor: D. Dane Quinn.
J. Comput. Nonlinear Dynam. Jul 2016, 11(4): 041012 (9 pages)
Published Online: December 11, 2015
Article history
Received:
February 2, 2015
Revised:
October 13, 2015
Citation
Jankowski, K. P., Mitura, A., and Warminski, J. (December 11, 2015). "Dynamics of a Self-Balancing Double-Pendulum System." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041012. https://doi.org/10.1115/1.4031978
Download citation file:
Get Email Alerts
Cited By
A Nodal-Lie-Group Beam Element for Absolute Nodal Coordinate Formulations
J. Comput. Nonlinear Dynam (March 2025)
Modal Analysis for Localization in Multiple Nonlinear Tuned Mass Dampers Installed on a Structure
J. Comput. Nonlinear Dynam (March 2025)
Free wave propagation in pretensioned 2D textile metamaterials
J. Comput. Nonlinear Dynam
Reduced-Order Modeling and Optimization of a Flapping-Wing Flight System
J. Comput. Nonlinear Dynam
Related Articles
Analytical and Numerical Investigations of Stable Periodic Solutions of the Impacting Oscillator With a Moving Base and Two Fenders
J. Comput. Nonlinear Dynam (November,2017)
Path-Following Bifurcation Analysis of Church Bell Dynamics
J. Comput. Nonlinear Dynam (November,2017)
Nonlinear Responses of Dual-Pendulum Dynamic Absorbers
J. Comput. Nonlinear Dynam (January,2011)
Response Scenario and Nonsmooth Features in the Nonlinear Dynamics of an Impacting Inverted Pendulum
J. Comput. Nonlinear Dynam (January,2006)
Related Proceedings Papers
Related Chapters
Smart Semi-Active Control of Floor-Isolated Structures
Intelligent Engineering Systems Through Artificial Neural Networks, Volume 17
Implementation of an Internet-Based Tele-Operation for the Control of an Inverted Pendulum
Intelligent Engineering Systems through Artificial Neural Networks
Design and Performance of PD and LQR Controller for Double Inverted Pendulum System
International Conference on Software Technology and Engineering (ICSTE 2012)