Nonlinear vibration analysis of a 3DOF double pendulum system near resonance
The primary goal of this work is to analyze the energized motion of three-degrees-of-freedom (3DOF) dynamic system consisting of a coupled double pendulum with the damped mass under the external harmonic forces and moments. Lagrangian equations are employed to derive the differential governing equat...
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| Language: | English |
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Elsevier
2025-02-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824014431 |
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| author | Asmaa Amer W. Zhang T.S. Amer H. Li |
| author_facet | Asmaa Amer W. Zhang T.S. Amer H. Li |
| author_sort | Asmaa Amer |
| collection | DOAJ |
| description | The primary goal of this work is to analyze the energized motion of three-degrees-of-freedom (3DOF) dynamic system consisting of a coupled double pendulum with the damped mass under the external harmonic forces and moments. Lagrangian equations are employed to derive the differential governing equations of motion (GEOM) based on the system generalized coordinates. The approximate solutions (AS) of these equations are generated through the utilization of the multiple scales technique (MST) at the third-order level of approximation. These solutions are ascertained by contrasting them with numerical solutions (NS) that are derived utilizing the fourth-order Runge-Kutta algorithm (RKA-4). The modulation equations are constructed, and the principal external resonance cases are scrutinized concurrently based on the solvability constraints. The steady-state solutions are studied. Based on Routh-Hurwitz criteria (RHC), the stability and instability zones are examined and assessed in the line with the steady-state solutions. The amplitudes and phases over a specific period of time have been graphed to illustrate the movement at any given instant. Furthermore, in order to evaluate the advantageous effects of different values pertaining to the physical parameters on the system behavior, the graphed representations of the obtained results, resonance reactions and areas of the stability are provided. The significance of the research model stems from its numerous applications such as the gantry cranes, robotics, pump compressors, transportation devices and rotor dynamics. It may be applied to the study of these systems' vibrational motion. |
| format | Article |
| id | doaj-art-b3581b12fc564dcdb72a6eb9baec8552 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-b3581b12fc564dcdb72a6eb9baec85522025-02-07T04:47:01ZengElsevierAlexandria Engineering Journal1110-01682025-02-01113262286Nonlinear vibration analysis of a 3DOF double pendulum system near resonanceAsmaa Amer0W. Zhang1T.S. Amer2H. Li3Department of Mechanics, GuangXi University, GuangXi 530004, PR China; State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures, GuangXi University, GuangXi 530004, PR China; Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom, EgyptDepartment of Mechanics, GuangXi University, GuangXi 530004, PR China; State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures, GuangXi University, GuangXi 530004, PR China; Department of Mechanics, Beijing University of Technology, Beijing 100124, PR China; Corresponding author at: Department of Mechanics, GuangXi University, GuangXi 530004, PR China.Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, EgyptDepartment of Mechanics, Beijing University of Technology, Beijing 100124, PR ChinaThe primary goal of this work is to analyze the energized motion of three-degrees-of-freedom (3DOF) dynamic system consisting of a coupled double pendulum with the damped mass under the external harmonic forces and moments. Lagrangian equations are employed to derive the differential governing equations of motion (GEOM) based on the system generalized coordinates. The approximate solutions (AS) of these equations are generated through the utilization of the multiple scales technique (MST) at the third-order level of approximation. These solutions are ascertained by contrasting them with numerical solutions (NS) that are derived utilizing the fourth-order Runge-Kutta algorithm (RKA-4). The modulation equations are constructed, and the principal external resonance cases are scrutinized concurrently based on the solvability constraints. The steady-state solutions are studied. Based on Routh-Hurwitz criteria (RHC), the stability and instability zones are examined and assessed in the line with the steady-state solutions. The amplitudes and phases over a specific period of time have been graphed to illustrate the movement at any given instant. Furthermore, in order to evaluate the advantageous effects of different values pertaining to the physical parameters on the system behavior, the graphed representations of the obtained results, resonance reactions and areas of the stability are provided. The significance of the research model stems from its numerous applications such as the gantry cranes, robotics, pump compressors, transportation devices and rotor dynamics. It may be applied to the study of these systems' vibrational motion.http://www.sciencedirect.com/science/article/pii/S1110016824014431Nonlinear dynamicsperturbation techniquesvibration systemsstability/instability zones |
| spellingShingle | Asmaa Amer W. Zhang T.S. Amer H. Li Nonlinear vibration analysis of a 3DOF double pendulum system near resonance Alexandria Engineering Journal Nonlinear dynamics perturbation techniques vibration systems stability/instability zones |
| title | Nonlinear vibration analysis of a 3DOF double pendulum system near resonance |
| title_full | Nonlinear vibration analysis of a 3DOF double pendulum system near resonance |
| title_fullStr | Nonlinear vibration analysis of a 3DOF double pendulum system near resonance |
| title_full_unstemmed | Nonlinear vibration analysis of a 3DOF double pendulum system near resonance |
| title_short | Nonlinear vibration analysis of a 3DOF double pendulum system near resonance |
| title_sort | nonlinear vibration analysis of a 3dof double pendulum system near resonance |
| topic | Nonlinear dynamics perturbation techniques vibration systems stability/instability zones |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824014431 |
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