The influence of coupling nonlinearities on the dynamic behavior of a beam-plate system

Abstract

Considering the wide application of beam-plate systems in engineering, this work studies the dynamic behavior of the beam-plate system connected by coupling nonlinearities. The governing equations of the beam-plate system are derived and then solved by employing the Galerkin truncation method (GTM). The correctness and stability of dynamic responses of the beam-plate system with coupling nonlinearities are studied, where a four-truncation number of the beam combined with a six-truncation number of the plate can guarantee the stability of the system's dynamic responses. Then, the influence of coupling nonlinearities on the dynamic behavior of the beam-plate system is studied. By analyzing the numerical results, the dynamic behavior of the beam-plate system with coupling nonlinearities can be effectively controlled by adjusting the parameters of coupling nonlinearities in a reasonable range. Complicated responses of the beam-plate system are motivated by coupling nonlinearities, where the working state of complex responses is quasi-periodic. The employment of coupling nonlinearities provides a possible way to control the frequency components of the vibration signal belonging to the beam-plate system. A reasonable use of coupling nonlinearities plays a positive effect on the vibration control of the beam-plate system.