A study of controlling the transverse vibration of a beam-plate system by utilizing a nonlinear coupling oscillator

•Establish the vibration suppression analysis model of the beam-plate system with a nonlinear coupling oscillator.•Find that the transverse vibration of the beam-plate system with a nonlinear coupling oscillator is correctly and stably predicted by the Galerkin truncation method.•Find two working modes of the nonlinear coupling oscillator in controlling the vibration of the beam-plate system.•Find the root reason for the change in linear elastic coupling stiffness of the beam-plate system influences the vibration suppression effectiveness of the nonlinear coupling oscillator.•Find the parameter influence regular of nonlinear stiffness, viscous damping, and motion mass of the nonlinear coupling oscillator on the transverse vibration of the beam-plate system. In the engineering field, prolonged exposure of complex structures to high-strength vibration environments can lead to various engineering challenges. This underscores the importance of effectively managing the vibration of complex structures. Given the extensive utilization of beams and plates in the construction of intricate structures, this study incorporates a nonlinear coupling oscillator into the beam-plate system and formulates a vibration analysis model for this system. The governing equations of the system are derived theoretically and solved numerically using the Galerkin truncation method. This study focuses on the operational modes of the nonlinear coupling oscillator based on accurate numerical results. Meanwhile, the influence of parameters belonging to the nonlinear coupling oscillator on the transverse vibration responses of the beam-plate system is systemically studied. Upon meticulous examination of the numerical results, the operational states of the nonlinear coupling oscillator encompass the normal vibration suppression mode and the quasi-periodic vibration suppression mode. The alteration in the linear elastic coupling stiffness of the beam-plate system impacts the effectiveness of vibration suppression in the nonlinear coupling oscillator. This influence stems from the fact that changes in the linear elastic coupling stiffness directly affect the nonlinear forces exerted on the beam-plate system within a nonlinear coupling oscillator. Within a feasible range, the nonlinear stiffness and viscous damping can be chosen as the adjustable parameters for the nonlinear coupling oscillator to regulate the vibration of the beam-plate system by adjusting the motion mass of the nonlinear cou