Application of iteration perturbation method and Hamiltonian approach for nonlinear vibration of Euler-Bernoulli beams

This paper is devoted to the new classes of analytical techniques called the Iteration Perturbation Method (IPM)and Hamiltonian Approach(HA) for solving the equation of motion governing the nonlinear vibration of Euler-Bernoulli beams subjected to the axial loads. It has been found that theIPMand HAare very prolific, rapid, functional and do not demand small perturbation and are also sufficiently accurate to both linear and nonlinear problems in engineering. Comparison of the results of these methods with together and with the results of numerical solution reveals that the IPM and HA are very effective and convenient, and can be easily extended to other nonlinear systems so that can be found widely applicable in engineering and other sciences