NONLINEAR VIBRATION ANALYSIS OF EULER-BERNOULLI BEAMS BY USING CONTINUOUS GALERKIN-PETROV TIME-DISCRETIZATION METHOD

Authors

  • MUHAMMAD SABEEL KHAN DEPARTMENT OF APPLIED MATHEMATICS AND STATISTICS, INSTITUTE OF SPACE TECHNOLOGY, ISLAMABAD, 44000 ISLAMABAD, PAKISTAN
  • HAJRA KANEEZ DEPARTMENT OF APPLIED MATHEMATICS AND STATISTICS, INSTITUTE OF SPACE TECHNOLOGY, ISLAMABAD, 44000 ISLAMABAD, PAKISTAN

Keywords:

NONLINEAR VIBRATION, EULER-BERNOULLI BEAMS, TIME DISCRETIZATION, NUMERICAL METHOD

Abstract

IN THIS PAPER, WE PRESENT A NEW NUMERICAL METHOD FOR NONLINEAR VIBRATIONAL ANALYSIS OF EULER-BERNOULLI BEAMS. OUR APPROACH IS BASED ON THE CONTINUOUS GALERKIN-PETROV TIME DISCRETIZATION METHOD. THE EULER-BERNOULLI BEAM EQUATION WHICH GOVERNS ITS VIBRATIONS IS TRANSFORMED INTO SET OF ORDINARY DIFFERENTIAL EQUATIONS AND THE PRESENTED METHOD IS EMPLOYED IN ORDER TO INVESTIGATE THE VIBRATIONAL RESPONSE. A COMPARISON IS MADE BETWEEN PRESENT METHOD AND DIFFERENT OTHER METHODS AVAILABLE IN LITERATURE. IT IS OBSERVED THAT THE OBTAINED RESULTS ARE IN STRONG AGREEMENT WITH OTHER RESULTS IN LITERATURE. WE CONCLUDE THAT THE PRESENT METHOD HAS A GREAT POTENTIAL TO DEAL WITH NONLINEAR VIBRATION ANALYSIS PROBLEMS OF BEAMS AND RELATED STRUCTURES LIKE RODS AND SHAFTS.

Author Biographies

MUHAMMAD SABEEL KHAN, DEPARTMENT OF APPLIED MATHEMATICS AND STATISTICS, INSTITUTE OF SPACE TECHNOLOGY, ISLAMABAD, 44000 ISLAMABAD, PAKISTAN

ASSISTANT PROFESSOR

DEPARTMENT OF APPLIED MATHEMATICS AND STATISTICS

INSTITUTE OF SPACE TECHNOLOGY, ISLAMABAD PAKISTAN

HAJRA KANEEZ, DEPARTMENT OF APPLIED MATHEMATICS AND STATISTICS, INSTITUTE OF SPACE TECHNOLOGY, ISLAMABAD, 44000 ISLAMABAD, PAKISTAN

PHD SCHOLAR,

DEPARTMENT OF APPLIED MATHEMATICS AND STATISTICS

INSTITUTE OF SPACE TECHNOLOGY, ISLAMABAD PAKISTAN

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Published

2017-07-10

Issue

Vol. 14 No. 09 (2017)

Section

Articles

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