NONLINEAR VIBRATIONS OF CANTILEVER TIMOSHENKO BEAMS: A HOMOTOPY ANALYSIS

Authors

  • SHAHRAM SHAHLAEI-FAR INSTITUTO TECNOLóGICO DE AERONáUTICA - ITA
  • AIRTON NABARRETE INSTITUTO TECNOLóGICO DE AERONáUTICA - ITA
  • JOSÉ MANOEL BALTHAZAR INSTITUTO TECNOLóGICO DE AERONáUTICA - ITA

Keywords:

NONLINEAR VIBRATION, HOMOTOPY ANALYSIS METHOD, HAM, NONLINEAR NATURAL FREQUENCY, TIMOSHENKO BEAM

Abstract

THIS STUDY ANALYZES THE FOURTH-ORDER NONLINEAR FREE VIBRATION OF A TIMOSHENKO BEAM. WE DISCRETIZE THE GOVERNING DIFFERENTIAL EQUATION BY GALERKINÂS PROCEDURE AND THEN APPLY THE HOMOTOPY ANALYSIS METHOD (HAM) TO THE OBTAINED ORDINARY DIFFERENTIAL EQUATION OF THE GENERALIZED COORDINATE. WE DERIVE NOVEL ANALYTICAL SOLUTIONS FOR THE NONLINEAR NATURAL FREQUENCY AND DISPLACEMENT TO INVESTIGATE THE EFFECTS OF ROTARY INERTIA, SHEAR DEFORMATION, PRE-TENSILE LOADS AND SLENDERNESS RATIOS ON THE BEAM. IN COMPARISON TO RESULTS ACHIEVED BY PERTURBATION TECHNIQUES, THIS STUDY DEMONSTRATES THAT A FIRST-ORDER APPROXIMATION OF HAM LEADS TO HIGHLY ACCURATE SOLUTIONS, VALID FOR A WIDE RANGE OF AMPLITUDE VIBRATIONS, OF A HIGH-ORDER STRONGLY NONLIN-EAR PROBLEM.

Author Biographies

SHAHRAM SHAHLAEI-FAR, INSTITUTO TECNOLóGICO DE AERONáUTICA - ITA

PHD STUDENT

AIRTON NABARRETE, INSTITUTO TECNOLóGICO DE AERONáUTICA - ITA

PROFESSOR OF THE DEPARTMENT IEA-E (ESTRUTURAS AERONÁUTICAS)

JOSÉ MANOEL BALTHAZAR, INSTITUTO TECNOLóGICO DE AERONáUTICA - ITA

VISITOR PROFESSOR OF THE DIVISION IEM (MECHANICAL DIVISION)

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Published

2016-04-21

Issue

Vol. 13 No. 10 (2016)

Section

Articles

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