Passive vibration suppression in a coupled linear-bistable continuous module excited near resonance

Vibration suppression for marine structures has been an important concern for a long time. In this paper, a specifically designed continuous module that consists of an Euler beam, a preloaded bimorph beam and a coupled spring unit produces self-increasing damping and strongly suppresses the steady-state response near resonance. Based on Hamilton's principle, we derive a two-degree-of-freedom coupled linear-bistable (CLB) model of this module. Utilizing the harmonic balance method and a numerical simulation, we analyze the proposed CLB model under a harmonic excitation. When the preloaded beam moves toward the critical amplitude of the saddle point of the system potential, the unstable equilibrium greatly increases the velocity phase difference between the Euler and preloaded beams and spontaneously enhances the dissipation power of the system. The self-increasing damping decreases the amplitude of the steady-state vibration of the coupled module excited near resonance by an order of magnitude. Numerical results demonstrate the essential roles of the damping ratio and the shape of the potential function in determining how this module can better suppress vibrations. This investigation provides opportunities to suppress dynamical responses using a continuous CLB module.