Vibration behavior and control study of an interlaced coupled beam system equipped with a nonlinear internal oscillator

Interlaced coupled-beam systems are widely used in engineering applications, including rigid mechanical arms, frame-type offshore platforms, shield machine support structures, and others. To demonstrate the potential of nonlinear oscillators for suppressing longitudinal, transverse, and total vibration in interlaced coupled-beam systems, this work introduces a nonlinear internal oscillator (NIO) into an interlaced coupled-beam system and establishes its physical model. It is worth noting that there are differences between NIOs and nonlinear energy sinks. Both ends of NIOs are respectively connected to the controlled substructure through nonlinear springs, while only one end of NES is connected to the main structure through nonlinear springs. The dynamic control equations for the interlaced coupled beam system equipped with the NIO are derived using the Hamiltonian principle and variational procedures, with the Galerkin truncation method (GTM) chosen to solve them. Introducing NIO enables the interlaced coupled-beam system to achieve a local vibration-suppressing effect at the coupled interface, while concurrently suppressing the longitudinal, transverse, and total vibrations of HB and IB across multiple resonance regions. The suppression states of NIO include multispectral linear and nonlinear vibration-suppression states. The total vibration control effect and nonlinear behavior of the interlaced coupled-beam system are effectively regulated by adjusting NIO parameters. A suitable NIO still exhibits acceptable vibration-suppression characteristics under changes in the coupled angles of HB and IB when suppressing the interlaced coupled beam system’s vibration. Overall, this work reveals the working and parameter influence mechanisms of the NIO, providing a feasible way to concurrently suppress the vibration of sub-beams in an interlaced coupled-beam system.