Abstract
•Extension version of the HA solving method for high order nonlinear oscillator is developed.•The high order approximate solution for oscillator with n-th order nonlinearity is obtained.•Procedure for analytical computing of the frequency of nonlinear is presented.•Analytically obtained frequency of the doubly clamped type N/MEMS agrees with numerical one.•Analytical and numerical diagrams for seventh order nonlinear oscillator agree well.
In this paper, Hamiltonian approach for solving vibration in the first approximation is extended into a high order Hamiltonian approach method for n order approximation. The method is applied for computation of the frequency of doubly clamped beam type N/MEMS subjected to the van der Waals attraction and the Duffing oscillator with seventh order nonlinearity. The obtained results are compared with numerically and other analytically obtained results. It is concluded that the solution in the third approximation gives the most appropriate solution in comparison to other analytical methods. The time history diagrams and the phase plane diagrams calculated analytically are on the top of the curves obtained numerically.