Work

Modified Lindstedt-Poincare transformation for fractal resonance approach in vibration 2-DOF heterogeneous system

Year: 2025

Type: article

Abstract: This study looks at the dynamics of a two-degree-of-freedom system subjected to a periodic force and describes it with fractal differential derivatives. The study applies a harmonic equivalent linearized approach (HELA) to convert nonlinear equations into linear systems, allowing for the derivation of analytical solutions and extensive numerical comparison. The study explores the use of analytical techniques in capturing complex dynamics, particularly in fractal resonance scenarios. It proposes novel techniques and compares analytical solutions with numerical methods, demonstrating high agreement. The research also investigates the fractal resonance phenomenon, providing analytical and visual evidence, and enhancing our understanding of its significance for system stability and behavior.

Source: Journal of low frequency noise, vibration and active control

DOI: 10.1177/14613484251335736

Authors: Yusry O El-Dib, Haifa A Alyousef

Institutions: Ain Shams University, Princess Nourah bint Abdulrahman University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,500

Funder: Princess Nourah Bint Abdulrahman University