# Periodic solution for strongly nonlinear oscillators by He's new amplitude-frequency relationship

## TL;DR

This paper utilizes He's new amplitude-frequency relationship to find periodic solutions of strongly nonlinear oscillators with odd nonlinearities, demonstrating effectiveness for both small and large amplitudes without discretization or linearization.

## Contribution

The paper introduces a direct method based on He's new relationship for solving strongly nonlinear oscillators, extending applicability to large amplitudes and complex systems.

## Key findings

- Effective for small and large oscillation amplitudes
- Applicable to a wide range of nonlinear systems with odd nonlinearities
- No discretization or linearization required

## Abstract

This paper applies He's new amplitude-frequency relationship recently established by Ji-Huan He (Int J Appl Comput Math 3 1557-1560, 2017) to study periodic solutions of strongly nonlinear systems with odd nonlinearities. Some examples are given to illustrate the effectiveness, ease and convenience of the method. In general, the results are valid for small as well as large oscillation amplitude. The method can be easily extended to other nonlinear systems with odd nonlinearities and can therefore be found widely applicable in engineering and other science. The method used in this paper can be applied directly to highly nonlinear problems without any discretization, linearization or additional requirements.