Self-transformation approach for forced 2DOF damped nonlinear dynamical systems
Source abstract
Abstract
This study presents a robust analytical framework using the Harmonic Equivalent Linearization Method (HELM) to overcome limitations in existing analyses of two-degree-of-freedom nonlinear oscillatory systems. The use of HELM in system transformation enables the precise evaluation of stability boundaries, coupling effects, and the influence of critical parameters, offering analytical tractability and high accuracy through numerical simulations. This approach generates stability diagrams, revealing interactions between damping, coupling strength, and forcing parameters, allowing researchers to understand dynamic transitions and resonance phenomena in nonlinear coupled systems. This research presents a powerful, generalizable approach for analyzing complex nonlinear oscillators, addressing deficiencies in current methodologies, and enhancing engineering and applied physics applications.
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Research context
OpenAlex topics: Bladed Disk Vibration Dynamics · Vibration Control and Rheological Fluids · Model Reduction and Neural Networks
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, Ain Shams University 1 , Roxy, Cairo,
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University 2 , P.O. Box 84428, Riyadh 11671, a
Higher Teachers’ Training College, University of Maroua 3 , P.O. Box 55, Maroua,
Funding
Princess Nourah bint Abdulrahman University
References (35)
Show source-provided references
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