Active control impact analysis on shaped coupled beam structure

Vibration-based warning and sensing devices rely on compact nonlinear structures capable of operating reliably under combined parametric and harmonic disturbances. To address these engineering demands, we developed a two-degree-of-freedom (2-DOF) lumped-parameter model that captures the coupled dynamics of a mass-based multi-warning unit integrated into a host structure. An Ⅱ-shaped coupled beam was proposed as a practical realization of the concept, where an auxiliary "warning mass" interacts dynamically with a primary supporting beam through nonlinear oscillations. The governing nonlinear differential equations were analytically solved using the multiple-time-scale technique (MTST), with detailed emphasis on primary and internal resonance conditions ( ${\omega }_d\cong {\omega }_1,{\omega }_e\cong {\omega }_2$) that critically influence device functionality and stability. To mitigate large-amplitude oscillations and enhance robustness under strong nonlinearities, a new control law, Nonlinear Proportional-Derivative Control with Negative Cubic Velocity Feedback (NPDCVF), was introduced. This controller combines a nonlinear PD term with a cubic dissipative component to improve damping and suppress resonance amplification. Control performance was assessed using the worst-case resonance scenario of the primary mass. Comparative simulations against Integral Resonance Control (IRC), Positive Position Feedback (PPF), Proportional-Integral-Derivative (PID), and Nonlinear Integral PPF (NIPPF) showed that the NPDCVF controller achieves up to 35–60% reduction in vibration amplitude, ensures faster settling, and maintains stable operation even near low natural frequencies where conventional controllers deteriorate. Frequency-response-based stability analysis revealed the boundaries of safe operation and highlighted instability regions relevant for design considerations. Numerical simulations using MATLAB/Simulink confirmed that the NPDCVF controller significantly enhances vibration suppression and flexibility against nonlinear disturbances. These results demonstrated the potential of the proposed system and control strategy for engineering applications such as structural warning devices, precision actuators, robotic manipulators, and advanced motorcycle suspension systems.