Approximate solutions to nonlinear oscillations via an improved He's variational approach

This study investigates accuracy of the He's variational approach with a rational trial function to obtain the frequency of conservative nonlinear oscillations. This method utilizes a semi-inverse method to establish variational principles from the governing equations. Four illustrative examples are considered, the restoring force of the studied cases has non-integer and cubic power terms as well as discontinuities. The last case considers the mathematical model of nonlinear oscillations of an elevator cable. The results demonstrate the usefulness and merit of the algorithm.