Modelling and dynamic analysis of a coupled thin-beam system with distributed internal nonlinearities

Coupled thin beam systems (CTBS) find extensive applications in modern engineering fields such as aerospace structures, precision mechanical systems, and flexible robotic arms. The existing study mainly discusses the vibration control of parallel-coupled beam systems by using coupling nonlinear energy sinks and other nonlinear equipment. The lack of research on the nonlinear vibration control of non-parallel coupled beam systems limits the application of coupling nonlinear energy sinks and other nonlinear equipment in practical engineering. This research builds a vibration analysis prediction model of the coupled thin beam system enabled with the distributed internal nonlinearities (DIN), where the Galerkin truncation method (GTM) is chosen as the solution method. Based on the analysis as a whole, this research finds that the current method is effective at predicting the transverse vibration displacement responses of the CTBS enabled with the DIN. Core parameters (cubic nonlinear stiffness, viscous damping, and moving mass) of the DIN effectively impact the transverse vibration displacement responses of the CTBS. Reasonable design of the DIN’s parameters is necessary for the appropriate use of DIN. The distributed quantity of DIN is an attractive controlled parameter. A well-designed distributed quantity of the DIN can not only enhance its vibration control effect on the CTBS but also effectively eliminate or mitigate the CTBS’s nonlinear dynamic behavior induced by the introduction of cubic nonlinear stiffness. Overall, the reasonable use of DIN is effective for vibration control in the CTBS.