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.

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Published

2012-11-22

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