Nonlinear Vibration of an Euler–Bernoulli Beam Using Variational Iteration Procedure

The accurate prediction of nonlinear dynamic characteristics of a beam is essential for its dynamic design. Strong geometric nonlinearity in the Euler–Bernoulli beam arising out of mid-plane stretch is employed to investigate its nonlinear free vibration characteristics by the variational iteration procedure as against classical first-order perturbation method, for the three boundary conditions with immovable ends. It is noted for both the approaches that the error in nonlinear frequency estimate shows an increasing trend with rise in nonlinear frequency ratio. However, the error in frequency prediction by variational iteration procedure is significantly lower than that from first-order perturbation method. The response from variational iteration procedure shows superior prediction capability compared to the first-order perturbation method.