Volume 24, Issue 11 (November 2024)
Modares Mechanical Engineering 2024, 24(11): 11-16 |
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Application of the Modified Differential Transformation Method to Nonlinear Oscillations of a Magnetic Spherical Oscillator Considering the Damping Effect. Modares Mechanical Engineering 2024; 24 (11) :11-16
URL: http://mme.modares.ac.ir/article-15-79198-en.html
URL: http://mme.modares.ac.ir/article-15-79198-en.html
Abstract: (454 Views)
In this paper, nonlinear oscillations of a charged spherical oscillator under a magnetic field are examined. The oscillator is under the influence of gravity and magnetic fields, and air resistance is considered a damping effect. Using the Hamiltonian principle, the two-dimensional equations of motion are extracted, and by considering a constant velocity in one dimension, they are transformed into a one-dimensional nonlinear equation. To obtain an analytical solution, the differential transform method (DTM) is employed. Due to the oscillatory nature of the problem, the solution obtained by the DTM is improved using the Padé approximation technique. The proposed method is then applied to the oscillator for various system parameters and initial conditions. The obtained results are compared with the numerical fourth-order Runge-Kutta method, and good agreement is observed. The proposed method is simple in implementation and provides a high level of accuracy. Hence, the method is suggested for the vibration analysis of nonlinear oscillators including damping effect
Article Type: Original Research |
Subject:
Micro & Nano Systems
Received: 2025/01/27 | Accepted: 2024/10/22 | Published: 2024/10/22
Received: 2025/01/27 | Accepted: 2024/10/22 | Published: 2024/10/22
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