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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.

Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method