Analytical Solution for Nonlinear Oscillation with Sinusoidal Nonlinearity by Using of Chebyshev Polynomials and Variational Approach

In this study large amplitude oscillation of a nonlinear pendulum attached to a rotating structure is solved using an analytical method called variational approach. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting is solved by the variational Method.Illustrative examples are selected and compared to those exact solutions to demonstrate the accuracy and correctness of the approximate analytical approach. The results show that the proposed variational method offered an accurate analytical closed form solution forthe nonlinear problems as well as it is simple and rapid analytical method

Keywords:

Nonlinear oscillation , Variational method , Rotational pendulum system , Chebyshev polynomials , Cubic-quintic Duffing equation