Studying highly nonlinear oscillators using the non-perturbative methodology
Due to the growing concentration in the field of the nonlinear oscillators (NOSs), the present
study aims to use the general He's frequency formula (HFF) to examine the analytical …
study aims to use the general He's frequency formula (HFF) to examine the analytical …
Dynamical system of a time-delayed ϕ6-Van der Pol oscillator: a non-perturbative approach
GM Moatimid, TS Amer - Scientific Reports, 2023 - nature.com
A remarkable example of how to quantitatively explain the nonlinear performance of many
phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current …
phenomena in physics and engineering is the Van der Pol oscillator. Therefore, the current …
Vibrational and stability analysis of planar double pendulum dynamics near resonance
The focus of this paper is to examine the motion of a novel double pendulum (DP) system
with two degrees of freedom (DOF). This system operates under specific constraints to follow …
with two degrees of freedom (DOF). This system operates under specific constraints to follow …
Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve
A Amer, TS Amer, HF El-Kafly - Scientific Reports, 2023 - nature.com
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 …
a plane as a vibrating system, in which its pivot point is constrained to move along a …
Dynamical analysis of a damped harmonic forced duffing oscillator with time delay
This paper is concerned with a time-delayed controller of a damped nonlinear excited
Duffing oscillator (DO). Since time-delayed techniques have recently been the focus of …
Duffing oscillator (DO). Since time-delayed techniques have recently been the focus of …
Stability and analysis of the vibrating motion of a four degrees-of-freedom dynamical system near resonance
This article investigates the impact of three harmonically external moments on the motion of
a four-degrees-of-freedom (DOF) nonlinear dynamical system composed of a double rigid …
a four-degrees-of-freedom (DOF) nonlinear dynamical system composed of a double rigid …
Dynamical analysis of a vertical excited pendulum using He's perturbation method
The current paper investigates the nonlinear dynamics of an excited pendulum by a crank-
shaft-slider mechanism (CSSM), in which it is restricted to move vertically. He's method of …
shaft-slider mechanism (CSSM), in which it is restricted to move vertically. He's method of …
Periodic solutions of strongly nonlinear oscillators using he's frequency formulation
G Ismail, G Moatimid, M Yamani - European Journal of Pure and Applied …, 2024 - ejpam.com
In this paper, we address several scientific and technological challenges with a novel non-
perturbative approach (NPA), simplifying processing time compared to traditional methods …
perturbative approach (NPA), simplifying processing time compared to traditional methods …
Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force
This paper delves into the dynamical, chaotic, and stability aspects of the Duffing oscillator
(DO) under sinusoidal external excitation, underscoring its relevance in various scientific …
(DO) under sinusoidal external excitation, underscoring its relevance in various scientific …
[HTML][HTML] Parametric excitation and chaos in a nonlinear forced Mathieu system: A comprehensive analysis
A Amer, W Zhang, TS Amer - Alexandria Engineering Journal, 2025 - Elsevier
The primary goal of this work is to examine the dynamic movement and chaos of a governed
system by the nonlinear forced Mathieu equation (NFME). The multiple-time-scales …
system by the nonlinear forced Mathieu equation (NFME). The multiple-time-scales …