MODELING AND DISTRIBUTED VIBRATION CONTROL OF BENDING-TORSION COUPLED VIBRATIONS IN RECTANGULAR CANTILEVER PLATES

Rectangular cantilever plates, commonly employed in aerospace structures such as straight wings and satellite solar panels, are susceptible to complex coupled bending-torsional vibrations under dynamic loads. These vibrations, particularly under resonance conditions, pose significant risks of structural damage or failure. While existing studies on resonance suppression for such systems have primarily addressed bending vibrations, the control of coupled bending-torsional interactions remains underexplored. This study investigates the efficacy of distributed nonlinear energy sinks (NES) in mitigating multi-modal coupled bending-torsional resonances, aiming to advance vibration control strategies for such geometrically flexible systems.A dynamic model for the coupled bending-torsional vibration of rectangular cantilever plates with distributed NES cells was developed using the generalized Hamilton’s principle and Newtonian mechanics. The governing equations incorporate nonlinear energy transfer mechanisms inherent to NES devices, enabling analysis of their energy dissipation effects. The Galerkin truncation method was applied to discretize the coupled partial differential equations into a reduced-order system, while the harmonic balance method was employed to compute steady-state responses. Numerical validation via the fourth-order Runge-Kutta method ensured solution accuracy and robustness. Parametric studies highlighted critical relationships between NES design parameters and vibration suppression performance. Under constant NES mass conditions, increasing the nonlinear stiffness coefficient significantly enhanced energy dissipation efficiency, particularly in higher-order resonance modes. Optimal damping ratios were identified to balance transient energy absorption and steady-state stability. Comparative analyses revealed that distributed NES configurations outperformed localized arrangements, achieving up to 60% reduction in resonance amplitudes across multiple coupled modes. Frequency-response curves demonstrated a broadening of effective vibration attenuation bandwidths, confirming the NES’s adaptability to multi-modal excitations.The results establish that strategically designed distributed NES systems can effectively decouple bending-torsional interactions and suppress multi-resonance phenomena. By leveraging nonlinear stiffness and optimized damping, the proposed approach addresses limitations of conventional linear absorbers in handling mode coupling and broadband excitations. This work provides a theoretical foundation for passive control strategies in lightweight aerospace structures, where simultaneous mass constraints and multi-axis vibration challenges exist. The findings offer practical guidelines for tuning NES parameters in applications ranging from satellite deployable mechanisms to high-aspect-ratio aircraft wings, paving the way for enhanced reliability in resonance-critical environments. Future research will explore transient vibration scenarios and stochastic loading effects to further validate the robustness of distributed NES configurations.