NON-LINEAR DYNAMICS OF A HANGING ROPE

Authors

  • PAWEL FRITZKOWSKI INSTITUTE OF APPLIED MECHANICS POZNAN UNIVERSITY OF TECHNOLOGY POLAND
  • HENRYK KAMINSKI INSTITUTE OF APPLIED MECHANICS POZNAN UNIVERSITY OF TECHNOLOGY POLAND

Keywords:

DISCRETE MODEL, ROPE, BIFURCATIONS

Abstract

TWO-DIMENSIONAL MOTION OF A HANGING ROPE IS CONSIDERED. A MULTIBODY SYSTEM WITH ELASTIC-DISSIPATIVE JOINTS IS USED FOR MODELLING OF THE ROPE. THE MATHEMATICAL MODEL BASED ON THE LAGRANGE FORMALISM IS PRESENTED. RESULTS OF SOME NUMERICAL SIMULATIONS ARE SHOWN FOR THE MECHANICAL SYSTEM WITH KINEMATIC EXCITATION. BASIC TOOLS ARE USED TO QUALIFY DYNAMICS OF THE ROPE: THE MAXIMUM LYAPUNOV EXPONENT (MLE) IS ESTIMATED NUMERICALLY BY THE TWO-PARTICLE METHOD, FREQUENCY SPECTRA ARE GENERATED VIA THE FAST FOURIER TRANSFORM (FFT) AND BIFURCATION DIAGRAMS ARE PRODUCED. INFLUENCE OF THE EXCITATION AMPLITUDE AND FREQUENCY ON BEHAVIOUR OF THE SYSTEM IS ANALYZED. THE WORK CAN BE TREATED AS THE FIRST STEP IN MORE ADVANCED ANALYSIS OF REGULAR AND CHAOTIC MOTION OF THE COMPLEX SYSTEM.

Downloads

Published

2012-11-22

Issue

Vol. 10 No. 1 (2013)

Section

Articles

License

Authors who publish with this journal agree to the following terms:

 

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).