Targeted vibration control of flexible structures through positive position feedback

This investigation focuses on the nonlinear interaction of a structural framework with six degrees of freedom (DOF) when it is excited externally. The response is significantly influenced by several critical zones of internal resonance arising from the system’s nonlinearity. The multiple time scales perturbation method (MSPM) is employed to derive analytical solutions and examine all resonance cases. Frequency response equations corresponding to the most critical resonance scenarios are developed for stability analysis. MATLAB software (ode45) is used to analyze the system both before and after incorporating a positive position feedback (PPF) controller. For the vibrating system and controller, the effects of various parameters are examined numerically, and the obtained results confirm the accuracy of the approximate analysis. Finally, comparisons with previously published work demonstrate the consistency of the proposed approach. The novelty of this work lies in integrating MSPM-based analytical modeling with a PPF control strategy to achieve near-complete vibration suppression in nonlinear multi-DOF systems, providing a validated and practical framework for advanced structural vibration control.