Exact solutions for the response of purely nonlinear oscillators: Overview

Abstract

This article provides an overview of the exact closed-form solutions for purely nonlinear oscillators. These solutions comprise the period of vibration and free and forced responses for one-degree-of-freedom systems. The use of special function for this purpose is demonstrated, which includes: beta function, gamma function, hypergeometric function, Ateb function, Jacobi amplitude and Jacobi elliptic function.