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

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.