The transverse dynamic behavior study of a beam system coupled through a local nonlinear coupling layer

Abstract

In engineering, some complex systems can be reduced to the beam system connected by serval coupling elements. To explore the potential application of local coupling nonlinearity on the transverse dynamic behavior of beams, this work establishes the physical model of a beam system coupled by a local nonlinear coupling layer. On the basis of ensuring the validity of the results, studies the effect of the nonlinear coupling layer on the transverse forced vibration of the beam system. Exploring the characters and reason for complex responses of the beam system coupled through a local nonlinear coupling layer. After discussing the numerical results, it can be found that the beam system presents complex responses within some parameters of the local nonlinear coupling layer, including amplitude jumping, quasi-periodic state, and targeted energy transfer, in which the change of the nonlinear restoring force is the reason for the appearance or disappearance of complex responses. For single-frequency responses, complex responses of the beam system can be motivated by changing the parameters of the local nonlinear coupling layer. With the simultaneous variation of the nonlinear stiffness and viscous damping, responses of the beam system contain both amplitude-sensitive regions and amplitude-jumping regions, in which the amplitude-sensitive region provides an effective parameter range for controlling the vibration by adjusting the local nonlinear coupling layer. On the whole, a suitable combination of nonlinear stiffness and viscous damping of the local nonlinear coupling layer can effectively reduce the vibration at the boundaries of the beam system.