Data for publication: Analysis of a parametrically excited 2DOF oscillator with nonlinear restoring magnetic force and rotating rectangular beam

DescriptionThis dataset accompanies the publication: “Analysis of a parametrically excited 2DOF oscillator with nonlinear restoring magnetic force and rotating rectangular beam,” which was accepted in Nonlinear Dynamics.The dataset contains numerical simulations, analytical results, and computational materials related to the study of a nonlinear two-degree-of-freedom mechanical oscillator subjected to parametric excitation, nonlinear magnetic restoring forces, and dry friction.The investigated system consists of two coupled oscillators connected through a rotating rectangular beam producing time-periodic stiffness variation. The dynamic response was analysed using analytical and numerical approaches, including complexification-averaging (CxA) method and Runge–Kutta simulations.Dataset contentsThis repository includes:Mathematica computational codesystem parameter filesanalytical model outputsnumerical simulation resultsamplitude–frequency response databifurcation diagramsLyapunov exponent calculationsPoincaré mapstime-series and phase-space plotsfigures used in the articleOverviewThe Mathematica scripts implement the governing equations of motion of a parametrically excited nonlinear 2DOF oscillator and perform analytical and numerical dynamic analysis. The dataset allows reproduction of:modulation equations derived using the CxA methodamplitude–frequency responsesstability and bifurcation analysisLyapunov exponent evaluationtime-domain and phase-space responsesThe results demonstrate periodic, quasiperiodic, and chaotic dynamics of the considered nonlinear mechanical system.Software requirementsMathematica (14.2 recommended)Maple for symbolic computationsExecution workflowDefine system parametersImplement nonlinear governing equationsApply the CxA analytical methodRun numerical simulationsGenerate amplitude-frequency responsesCompute bifurcation diagramsEvaluate Lyapunov exponentsProduce figures and visualizationsRelated publicationPrimary article: Analysis of a parametrically excited 2DOF oscillator with nonlinear restoring magnetic force and rotating rectangular beam, which is accepted for publication in Nonlinear Dynamics (Springer Nature).Keywordsnonlinear dynamics, 2DOF oscillator, parametric excitation, magnetic restoring force, rotating beam, bifurcation analysis, Lyapunov exponent, Poincaré mapsFunding informationThis research has received funding from the National Science Centre, Poland, under the grant PRELUDIUM 23 No. DEC-2024/53/N/ST8/00400. This article was completed while the first author, Muhammad Junaid-U-Rehman, was a PhD student at the Interdisciplinary Doctoral School of Lodz University of Technology, Poland.