An Analytical Study of Nonlinear Vibrations οf Buckled Euler-Bernoulli Beams

The current research deals with a way of using a new kind of periodic solutions called He's max-min approach for the nonlinear vibration of axially loaded Euler-Bernoulli beams. By applying this technique, the beam's natural frequencies and mode shapes can be easily obtained and a rapidly convergent sequence is obtained during the solution. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. To verify the results some comparisons are presented between max-min approach results and the exact ones to show the accuracy of this new approach. It has been discovered that the max-min approach does not necessitate small perturbation and is also suitably precise to both linear and nonlinear problems in physics and engineering.