Stability and Bifurcation Effects in Nonlinear Vibratory Systems Under NIPPF Control

Purpose: This study aims to investigate the phenomenon of bifurcation in nonlinear dynamic systems and explores a Nonlinear Integral Positive Position Feedback (NIPPF) control strategy to reduce the vibration behavior and achieve more stability. Methods: The multiple time scales perturbation (MTSP) technique is used to solve the nonlinear differential equations of the modelling system via the NIPPF controller, and an analytical solution is produced. The Runge–Kutta technique of fourth order (RK4) is used numerically. Results and Conclusion: The NIPPF controller succeeded in reducing vibration amplitudes presented by the ratios of 98.5% for the first mode and approximately 100% for the second mode under the condition of a simultaneous primary, 2:1, and 1:1 internal resonance case. The influence of various parameters has been elucidated numerically using MATLAB. Finds a good match by comparing the approximate solutions to the numerical simulations. The analysis revealed that bifurcations significantly influenced the system's stability, with small parameter changes leading to dramatic shifts in the system's behavior, such as chaotic motion and large vibration amplitudes.