Enhanced Method for Forced Strongly Nonlinear Two-Degree-of-Freedom Nonlinear Systems Using an Integro-Differential Equation Approach

Lewis, Andrew (2025) Enhanced Method for Forced Strongly Nonlinear Two-Degree-of-Freedom Nonlinear Systems Using an Integro-Differential Equation Approach. Nonlinear Dynamics. ISSN 0924-090X

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In this paper, a method based on an integro-differential equation approach for investigating the response of a strongly nonlinear two-degree-of-freedom system subject to sinusoidal forcing is presented and applied to a set of equations based on an aeroelastic model of an all-moving control surface with a nonlinearity in its root support in supersonic flow. The method is shown to be able to accurately determine primary and subharmonic resonances together with symmetry-breaking and period-doubling responses. Additionally, their stability has been investigated using a Harmonic Balance-based implementation of Floquet theory which is a modification of a method previously used for autonomous systems. This method was validated by comparison with time domain derived Floquet multipliers, and comparisons between the two sets of values showed very close agreement. The study also highlighted several areas for further investigation.

Item Type	Article
Identification Number	10.1007/s11071-025-11290-1
Additional information	© 2025 The Author(s), under exclusive licence to Springer Nature B.V. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11071-025-11290-1
Keywords	forced nonlinear systems, primary resonance, subharmonic resonance, symmetry-breaking, period-doubling, floquet multipliers, primary resonance, forced nonlinear systems, subharmonic resonance, symmetry-breaking, period-doubling, floquet multipliers, engineering(all), mathematics(all), control and systems engineering, aerospace engineering, ocean engineering, mechanical engineering, electrical and electronic engineering, applied mathematics
Date Deposited	19 Jun 2025 07:37
Last Modified	08 Jun 2026 00:03