Analytical evaluation of the nonlinear vibration of a solid circular sector object

This paper applied a new class of critical technique for resolution of the cyclic solutions nonlinear called the HE’s variational approach method (VAM) to solve the nonlinear vibration of a solid circular sector object. In variational approach, only one repetition leads to high exactness of the solutions, as opposed to the other methods. It has been found that the variational approach is very prolific, rapid, functional and does not demand small perturbation and is also sufficiently accurate to both linear and nonlinear problems in engineering. The obtained consequences show that the approximate solutions are uniformly legitimate on the whole solution field in comparison with the numerical solution using Runge-Kutta method. VAM could simply be enlarged to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.