Galerkin method, ansatz method, and He’s frequency formulation for modeling the forced damped parametric driven pendulum oscillators

Haifa A Alyousef; Alvaro H Salas; Muteb R Alharthi; Samir A El-Tantawy

doi:10.1177/14613484221101235

journal article Open Access May 30, 2022

Galerkin method, ansatz method, and He’s frequency formulation for modeling the forced damped parametric driven pendulum oscillators

Haifa A Alyousef Alvaro H Salas Muteb R Alharthi Samir A El-Tantawy

Journal of Low Frequency Noise, Vibration and Active Control Vol. 41 No. 4 pp. 1426-1445 · SAGE Publications

View at Publisher Save 10.1177/14613484221101235

Abstract

The forced damped parametric driven pendulum oscillators are analyzed numerically via the Galerkin method (GM) and analytically using both ansatz method (AM) and He’s frequency formulation. One of the most important features of the obtained numerical approximation using GM is that it can recover a large number of different oscillators related to the problem under study. Moreover, the mentioned equation is solved analytically via both AM and He’s frequency formulation. Also, the analytical approximations can recover many different oscillators related to the problem under consideration. Both analytical and numerical approximations are compared with each other and with Runge–Kutta (RK) numerical approximation by estimating both maximum global distance and residual errors. The proposed method can help many authors interested in studying the dynamic problems to explain the mechanics of oscillating to different oscillators in physics, plasma models, engineering, and biological systems.

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References

33

[1]

10.1016/j.matcom.2021.12.014

[2]

10.1002/zamm.202100379

[3]

10.1007/s00419-021-02039-4

[4]

10.32604/sv.2022.014166

[5]

Nayfeth N (1973)

[6]

10.1142/s0218348x21502686

[7]

10.1016/j.rinp.2020.103403

[8]

10.1016/j.rinp.2018.06.015

[9]

10.3390/axioms10030191

[10]

10.22190/fume201205002h

[11]

10.1063/1.1761193

[12]

10.1088/1402-4896/ac0c57

[13]

10.5772/intechopen.97677

[14]

10.1140/epjp/s13360-020-00829-3

[15]

10.1080/00207176908905841

[16]

10.3390/math9040432

[17]

10.5890/jand.2021.03.007

[18]

Salas S Math Probl Eng (2020)

[19]

10.1016/s0375-9601(01)00580-1

[20]

10.1007/bf01178556

[21]

10.1115/1.3439423

[22]

10.1080/17455030.2021.1949072

[23]

10.1088/1572-9494/abda1b

[24]

10.1155/2021/8875589

[25]

10.1155/2021/6678102

[26]

10.1007/978-3-031-79645-6

[27]

Gabitov I (2014)

[28]

10.1088/0143-0807/35/3/035014

[29]

SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS

Ji-Huan He

International Journal of Modern Physics B 10.1142/s0217979206033796

[30]

10.1088/0143-0807/29/4/l02

[31]

10.1515/ijnsns.2008.9.2.211

[32]

10.1142/s0217979208048668

[33]

10.3390/axioms10040320

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Details

Published: May 30, 2022
Vol/Issue: 41(4)
Pages: 1426-1445
License: View

Authors

H

Haifa A Alyousef

Department of Physics, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia

A

Alvaro H Salas

Department of Mathematics and Statistics, FIZMAKO Research Group, Universidad Nacional de Colombia, Caldas, Colombia

M

Muteb R Alharthi

Department of Mathematics and Statistics, College of Science, Taif University, Taif, Saudi Arabia

S

Samir A El-Tantawy

Department of Physics, Faculty of Science, Port Said University, Port Said, Egypt; Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Saudi Arabia

Cite This Article

Haifa A Alyousef, Alvaro H Salas, Muteb R Alharthi, et al. (2022). Galerkin method, ansatz method, and He’s frequency formulation for modeling the forced damped parametric driven pendulum oscillators. Journal of Low Frequency Noise, Vibration and Active Control, 41(4), 1426-1445. https://doi.org/10.1177/14613484221101235

Galerkin method, ansatz method, and He’s frequency formulation for modeling the forced damped parametric driven pendulum oscillators

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