APPROXIMATE SOLUTIONS OF LARGE AMPLITUDE VIBRATION OF A STRING

  • RAYEHE KARIMI MAHABADI Amirkabir University of Technology
  • MITRA DANESH PAZHOOH Amirkabir University of Technology
Keywords: NONLINEAR VIBRATION, STRING, AMPLITUDE-FREQUENCY FORMULATION, IMPROVED AMPLITUDE-FREQUENCY FORMULATION, MAX-MIN APPROACH

Abstract

IN THE PRESENT STUDY, THE RESPONSE OF A FLEXIBLE STRING WITH LARGE AMPLITUDE TRANSVERSE VIBRATION IS STUDIED UTILIZING AMPLITUDE-FREQUENCY FORMULATION, IMPROVED AMPLITUDE-FREQUENCY FORMULATION AND MAX-MIN APPROACH. IN ORDER TO VERIFY THE ACCURACY OF THESE APPROACHES, OBTAINED RESULTS ARE COMPARED WITH OTHER METHODS SUCH AS VARIATIONAL APPROACH METHOD, VARIATIONAL ITERATION METHOD, COUPLING NEWTON’S METHOD WITH THE HARMONIC BALANCE METHOD AND HAMILTONIAN APPROACH. IT HAS BEEN FOUND THAT FOR THIS PROBLEM, WHILE AMPLITUDE-FREQUENCY FORMULATION AND MAX-MIN APPROACH GIVE THE SAME RESULTS, IMPROVED AMPLITUDE FREQUENCY FORMULATION IS NOT AN APPROPRIATE CHOICE.
Published
2018-02-05
Section
Articles