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Open access
Sep 2026
Comparative analysis of homotopy perturbation and power series solutions for strongly nonlinear oscillators with cubic restoring forces
We studied the behavior of a strongly nonlinear oscillator characterized by cubic nonlinearity, which commonly occurs in engineering, mechanical, and physical systems. Additionally, we also utilized two semi-analytical approaches, namely the Homotopy Perturbation Method (HPM) and the Power Series Method (PSM), to obtai...
Aya Raddad, Taqwa M. Al-Khader, J. Asad
· Advances in Mechanical Engin... · 0 citations
Open access
Aug 2026
Fractional-Order State Feedback Controller to Suppress the Nonlinear Self-Excited Oscillations: Accurate Analytical and Numerical Solution
In this work, an accurate analytical solution is developed for a harmonically excited self-excited nonlinear oscillator under fractional-order state feedback control using a modified version of the Traditional Multiple Scales Method (TMSM), termed the Detuned Multiple Scale Method (DMSM). In contrast to the TMSM, which...
N. Saeed, Lei Hou, Turki J. Alqurashi
· Mathematics · 0 citations
Open access
Aug 2026
A highly accurate and explicit analytical approximation of the frequency–amplitude relationship for symmetric non-natural oscillators
Non-natural oscillators represent a class of nonlinear dynamical systems characterized by kinetic energy that is non-squared in velocity. Such systems commonly appear in engineered applications and in predictive models used to describe certain natural phenomena. The frequency–amplitude relationship is central to both q...
Baisheng Wu, Wei-Jia Liu, C. W. Lim et al.
· Physica Scripta · 0 citations
Open access
Sep 2026
Taylor-map-based polynomial approximation of non-homogeneous dynamical systems
The paper addresses the construction of a polynomial approximation of the flow of a dynamical system governed by autonomous ordinary differential equations with polynomial right-hand sides that contain non-homogeneous (constant) terms, in the case when the initial state is not close to the origin. The existing matrix T...
Timofei Y. Gladyshev, Anna Golovkina, V. Kozynchenko
· Cybernetics and Physics · 0 citations
Open access
Aug 2026
Stability of the inverted pendulum system: An optimized equivalent linearization approach
A unified framework for analyzing nonlinear vibrations in a two-degree-of-freedom (2DOF) system comprising an inverted pendulum (IP) mounted on a cart is proposed. Unlike existing approaches that rely on direct numerical integration or restrictive small-angle assumptions, this work introduces a novel combination of the...
Y. El-Dib, W. Albalawi, E. Elbeshir
· Journal of Low Frequency Noi... · 1 citation
Preprint
Sep 2026
Fractional oscillators with fractional damping in the presence of external forces
We investigate how a fractional oscillator reacts to external forces when the dynamic law includes a damping term that is explicitly fractional. The corresponding three-parametric fractional differential equation (in the Caputo sense) admits exact solution. Two of the fractional parameters are associated with the intri...
F. Olivar-Romero, O. Rosas‐Ortiz
· 0 citations