Studying highly nonlinear oscillators using the non-perturbative methodology

GM Moatimid, TS Amer, AA Galal - Scientific Reports, 2023 - nature.com
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 …

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 …

Vibrational and stability analysis of planar double pendulum dynamics near resonance

TS Amer, GM Moatimid, SK Zakria, AA Galal - Nonlinear Dynamics, 2024 - Springer
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 …

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 …

Dynamical analysis of a damped harmonic forced duffing oscillator with time delay

GM Moatimid, TS Amer, WS Amer - Scientific Reports, 2023 - nature.com
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 …

Stability and analysis of the vibrating motion of a four degrees-of-freedom dynamical system near resonance

TS Amer, AI Ismail, MO Shaker… - Journal of Low …, 2024 - journals.sagepub.com
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 …

Dynamical analysis of a vertical excited pendulum using He's perturbation method

AA Galal, TS Amer, WS Amer… - Journal of Low …, 2023 - journals.sagepub.com
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 …

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 …

Analyzing the chaotic and stability behavior of a duffing oscillator excited by a sinusoidal external force

MK Abohamer, TS Amer, A Arab… - Journal of Low …, 2024 - journals.sagepub.com
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 …

[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 …