Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

Abstract

This article proposes a simple energy-based criterion developed to characterize four commonly identified responses, namely: linear, weakly nonlinear, moderately nonlinear and strongly nonlinear regimes. The response of the nonlinear simple pendulum was used for benchmarking the boundary conditions for each of the four response regimes and the test criterion was demonstrated using relevant examples. The test presented in this article is important for clarifying the obscurity surrounding the accuracy and range of validity of recent approximate analytical schemes used to investigate strong nonlinear oscillators. Furthermore, it is meant to create awareness of the need to develop more robust testing criteria.

Keywords: strong nonlinear oscillation; periodic oscillation; approximate analytical solution