Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve
Abstract This study examines the motion of a spring pendulum with two degrees-of-freedom (DOF) in a plane as a vibrating system, in which its pivot point is constrained to move along a Lissajous curve. In light of the system’s coordinates, the governing equations of motion (EOM) are obtained utilizi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-12-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-48523-5 |
| _version_ | 1827590591350833152 |
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| author | Asmaa Amer T. S. Amer H. F. El-Kafly |
| author_facet | Asmaa Amer T. S. Amer H. F. El-Kafly |
| author_sort | Asmaa Amer |
| collection | DOAJ |
| description | Abstract This study examines the motion of a spring pendulum with two degrees-of-freedom (DOF) in a plane as a vibrating system, in which its pivot point is constrained to move along a Lissajous curve. In light of the system’s coordinates, the governing equations of motion (EOM) are obtained utilizing the equations of Lagrange’s. The novelty of this work is to use the approach of multiple scales (AMS), as a traditional method, to obtain novel approximate solutions (AS) of the EOM with a higher degree of approximation. These solutions have been compared with the numerical ones that have been obtained using the fourth-order Runge–Kutta algorithm (4RKA) to reveal the accuracy of the analytic solutions. According to the requirements of solvability, the emergent resonance cases are grouped and the modulation equations (ME) are established. Therefore, the solutions at the steady-state case are confirmed. The stability/instability regions are inspected using Routh–Hurwitz criteria (RHC), and examined in accordance with the steady-state solutions. The achieved outcomes, resonance responses, and stability areas are demonstrated and graphically displayed, to evaluate the positive effects of different values of the physical parameters on the behavior of the examined system. Investigating zones of stability/instability reveals that the system’s behavior is stable for a significant portion of its parameters. A better knowledge of the vibrational movements that are closely related to resonance is crucial in many engineering applications because it enables the avoidance of on-going exposure to potentially harmful occurrences. |
| first_indexed | 2024-03-09T01:18:58Z |
| format | Article |
| id | doaj.art-d42fe85a51fa44f0ad3fc7a80c669ce0 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-09T01:18:58Z |
| publishDate | 2023-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-d42fe85a51fa44f0ad3fc7a80c669ce02023-12-10T12:17:42ZengNature PortfolioScientific Reports2045-23222023-12-0113112110.1038/s41598-023-48523-5Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curveAsmaa Amer0T. S. Amer1H. F. El-Kafly2Department of Mathematics and Computer Science, Faculty of Science, Menoufia UniversityMathematics Department, Faculty of Science, Tanta UniversityTanta Higher Institute of Engineering and TechnologyAbstract This study examines the motion of a spring pendulum with two degrees-of-freedom (DOF) in a plane as a vibrating system, in which its pivot point is constrained to move along a Lissajous curve. In light of the system’s coordinates, the governing equations of motion (EOM) are obtained utilizing the equations of Lagrange’s. The novelty of this work is to use the approach of multiple scales (AMS), as a traditional method, to obtain novel approximate solutions (AS) of the EOM with a higher degree of approximation. These solutions have been compared with the numerical ones that have been obtained using the fourth-order Runge–Kutta algorithm (4RKA) to reveal the accuracy of the analytic solutions. According to the requirements of solvability, the emergent resonance cases are grouped and the modulation equations (ME) are established. Therefore, the solutions at the steady-state case are confirmed. The stability/instability regions are inspected using Routh–Hurwitz criteria (RHC), and examined in accordance with the steady-state solutions. The achieved outcomes, resonance responses, and stability areas are demonstrated and graphically displayed, to evaluate the positive effects of different values of the physical parameters on the behavior of the examined system. Investigating zones of stability/instability reveals that the system’s behavior is stable for a significant portion of its parameters. A better knowledge of the vibrational movements that are closely related to resonance is crucial in many engineering applications because it enables the avoidance of on-going exposure to potentially harmful occurrences.https://doi.org/10.1038/s41598-023-48523-5 |
| spellingShingle | Asmaa Amer T. S. Amer H. F. El-Kafly Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve Scientific Reports |
| title | Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve |
| title_full | Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve |
| title_fullStr | Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve |
| title_full_unstemmed | Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve |
| title_short | Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve |
| title_sort | dynamical analysis for the motion of a 2dof spring pendulum on a lissajous curve |
| url | https://doi.org/10.1038/s41598-023-48523-5 |
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