The coupling dynamic characteristics and vibration suppression of a double-beam structure with two linear oscillators installed separately

This paper investigates the coupling dynamic characteristics of a double-beam structure with two linear oscillators that generate harmonic concentrated excitation and the vertical elastic support boundary, including the Sommerfeld effect and the synchronization behavior. The governing equations of motion with boundary conditions are developed using Hamilton's principle. The Sommerfeld effect near the resonance region is characterized by transient power balance analysis, and the critical power of the motor is given to allow the system to pass through the resonance region. The theoretical condition for the synchronous behavior of two linear oscillators is derived using the average method, and its stability is also determined. The synchronization characteristics are analyzed and compared with the numerical steady-state response of typical physical parameters. Results show good agreement. Further, on the condition of the linear oscillators exhibiting synchronous behavior, sensitive working regions and parameters are sought to suppress the dynamic loads transmitted from the system to the foundation. The parameter optimization results show that the stable phase difference plays a crucial role in vibration suppression within the appropriate range of sensitive parameters. This study effectively extends the theoretical criteria for synchronous behavior on complex structures and is expected to provide ideas for vibration suppression strategies of multi-driving sources acting on multi-groups of elastic structures.