Approximate solutions to nonlinear oscillations via an improvedHe's variational approach

Abstract

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