TY - JOUR
ID - 16236
TI - The Rank Upgrading Technique for a Harmonic Restoring Force of Nonlinear Oscillators
JO - Journal of Applied and Computational Mechanics
JA - JACM
LA - en
SN -
AU - El-Dib, Yusry Osman
AU - Matoog, Rajaa. T
AD - Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
AD - Department of Mathematics, Faculty of Applied Science, Umm Al-Qura University, Makkah, Saudi Arabia
Y1 - 2021
PY - 2021
VL - 7
IS - 2
SP - 782
EP - 789
KW - Homotopy perturbation method
KW - Frequency Expansion
KW - Periodic solution
KW - Restoring Force
KW - Nonlinear Oscillation
DO - 10.22055/jacm.2020.35454.2660
N2 - An enhanced analytical technique for nonlinear oscillators having a harmonic restoring force is proposed. The approach is passed on the change of the auxiliary operator by another suitable one leads to obtain a periodic solution. The fundamental idea of the new approach is based on obtaining an alternative equation free of the harmonic restoring forces. This method is a modification of the homotopy perturbation method. The approach allows not only an actual periodic solution but also the frequency of the problem as a function of the amplitude of oscillation. Three nonlinear oscillators including restoring force, the simple pendulum motion, the cubic Duffing oscillator, the Sine-Gordon equation are offered to clarify the effectiveness and usefulness of the proposed technique. This approach allows an effective mathematical approach to noise and uncertain properties of nonlinear vibrations arising in physics and engineering.
UR - https://jacm.scu.ac.ir/article_16236.html
L1 - https://jacm.scu.ac.ir/article_16236_253376b40bcdc06729c05105d69e3a0a.pdf
ER -