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

Version 1.0

Junaid-U-Rehman, Muhammad; Kudra, Grzegorz; Polczyński, Krystian; Dekemele, Kevin; Awrejcewicz, Jan, 2026, "Data for publication: Analysis of a parametrically excited 2DOF oscillator with nonlinear restoring magnetic force and rotating rectangular beam", https://doi.org/10.18150/731YEC, RepOD, V1

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Description

Description

This 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 contents

This repository includes:

  • Mathematica computational code
  • system parameter files
  • analytical model outputs
  • numerical simulation results
  • amplitude–frequency response data
  • bifurcation diagrams
  • Lyapunov exponent calculations
  • Poincaré maps
  • time-series and phase-space plots
  • figures used in the article

Overview

The 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 method
  • amplitude–frequency responses
  • stability and bifurcation analysis
  • Lyapunov exponent evaluation
  • time-domain and phase-space responses

The results demonstrate periodic, quasiperiodic, and chaotic dynamics of the considered nonlinear mechanical system.

Software requirements

  • Mathematica (14.2 recommended)
  • Maple for symbolic computations

Execution workflow

  • Define system parameters
  • Implement nonlinear governing equations
  • Apply the CxA analytical method
  • Run numerical simulations
  • Generate amplitude-frequency responses
  • Compute bifurcation diagrams
  • Evaluate Lyapunov exponents
  • Produce figures and visualizations

Related publication

Primary 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).

Keywords

nonlinear dynamics, 2DOF oscillator, parametric excitation, magnetic restoring force, rotating beam, bifurcation analysis, Lyapunov exponent, Poincaré maps

Funding information

This 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.

(2026-02-13)
Subject
Engineering
Keyword

2DOF Magnetic oscillators, parametric excitation, magnetic interaction, CxA method, variable stiffness

CC0 Creative Commons Zero 1.0 CC0 Creative Commons Zero 1.0

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draft_pdf_version.pdf
Adobe PDF - 9.8 MB - Mar 3, 2026 - 0 Downloads
MD5: f0e711fbcdf903aad52d7b1132c86e11
License: CC0 Creative Commons Zero 1.0
PDf file of the draft which is accepted for publication in nonlinear dynamics.
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latex_version_of_published_draft.zip
ZIP Archive - 11.0 MB - Mar 3, 2026 - 0 Downloads
MD5: c0a5b070ade51d0a13ac736a5e29d43b
License: CC0 Creative Commons Zero 1.0
LaTeX source files for nonlinear 2DOF oscillator with magnetic restoring force.
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parametric_2DOF.nb
Unknown - 11.4 MB - Mar 3, 2026 - 0 Downloads
MD5: a109657eb87a427702d94f0ed3638064
License: CC0 Creative Commons Zero 1.0
Mathematica simulation data for nonlinear 2DOF oscillator with magnetic restoring force
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parametric_2DOF.txt
Plain Text - 16.5 KB - Mar 3, 2026 - 0 Downloads
MD5: 209a9bc338d3331b081fd6d348b1d385
License: CC0 Creative Commons Zero 1.0
text file from Mathematica
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complexification_method_2DOF.mw
Unknown - 184.4 KB - Mar 3, 2026 - 0 Downloads
MD5: 35816388324ab33a8db5097219ff2f70
License: CC0 Creative Commons Zero 1.0
CxA Method calculations in Maple file to calculate the analytical results.
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complexification_method_2DOF.tex
Unknown - 28.9 KB - Mar 3, 2026 - 0 Downloads
MD5: 529a05b8d89f4db5de0140def032bb6e
License: CC0 Creative Commons Zero 1.0
CxA Method calculation by using Maple, LATEX version.
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complexification_method_2DOF.pdf
Adobe PDF - 984.3 KB - Mar 3, 2026 - 0 Downloads
MD5: acc3fd8a6de5253ef96bc0bf31ae7687
License: CC0 Creative Commons Zero 1.0
PDF format of the code from Maple to find the analytical solutions for the considered system.
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time_phase_poincare_plots_for_same_masses_section_mathematica_code.tex
Unknown - 43.3 KB - Mar 3, 2026 - 0 Downloads
MD5: c83481dc2a5f7bc1dbf2ac4c5227feb4
License: CC0 Creative Commons Zero 1.0
Time, Phase, and Poincare plots for same masses section LaTeX version.
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time_phase_poincare_plots_for_same_masses_section_mathematica_code.pdf
Adobe PDF - 7.7 MB - Mar 3, 2026 - 0 Downloads
MD5: 4a30703f93de76f712722239289be2e2
License: CC0 Creative Commons Zero 1.0
PDF format of code from Mathematica to plot time, phase, and Poincare graphs.
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mathematica_code_analytical_numerical_results_for_same_masses_bif_plots.tex
Unknown - 35.3 KB - Mar 3, 2026 - 0 Downloads
MD5: 75908e39ea4fb031993ff9c84aafb2a7
License: CC0 Creative Commons Zero 1.0
Bifurcation plots code from Mathematica. Analytical and numerical results for same masses bif plots LaTeX version.
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