Development of a Negative Stiffness Bistable Damper for Structural Vibration Control

Abstract

Linear dampers have been widely applied for suppressing the dynamic responses of structures to mitigate their damage. However, the primary disadvantage of the classical linear damper is that it is vulnerable to detuning, which has become an issue of great importance recently due to a great reduction in vibration control performance. To overcome the shortcoming, this study develops a negative stiffness bistable damper (NSBD) composed of a simple assembly consisting of a bistable buckling beam with a mass. Energy is dissipated through the transformation between the bistable states. The constitutive equation of the NSBD is derived to analyze the effects of the stiffness ratio, the arch-span ratio, and the damping ratio on its restoring capabilities. The vibration reduction effect of the NSBD is experimentally evaluated under different sinusoidal and seismic excitations in shaking table tests. The obtained results reveal that the NSBD can effectively restrain structural displacements.

Equivalent Linearization and Parameter Optimization of the Negative Stiffness Bistable Damper

“…A linear SDOF structure equipped with an NSBD was introduced in our previous study [34]. For the dynamic analysis of beam-like structures, the Galerkin-assumed modal approach [45][46][47][48] has been applied in practical applications [48][49][50] and has led to remarkable results.…”

“…According to a study by Qiu et al [51], based on the assumption of a small deformation, the bending deformation of the buckling beam is considered, while because the shear deformation has a relatively small impact on the buckling beam's direction of motion, the shear deformation is ignored. Then, the mechanical constitutive equation for the displacement of the buckling beam (as illustrated in Figure 1) under the external force is as follows: As derived in our previous study [34], the mechanical constitutive equation for the bistable buckling beam is…”

“…The NSBD has been proposed in our previous study [34] to reduce the structural dynamic responses, inspired by the properties of the negative stiffness and bistable structure, which benefit the passive control. Based on previous experimental research, this paper further studies and proposes a detailed optimization design method to achieve the excellent vibration control of high-rise structures.…”

A review on reprogrammable bistable structures

“…Bistable buckled beams, which undergo pre-buckling deformation under horizontal force, are among the most common bistable structures. The bistable characteristics of bistable buckled beams are influenced by a geometrical parameter Q = H/t, where H and t represent the arch height and thickness of the beams, respectively, as shown in figure 2(A) [20][21][22]. As the parameter Q increases, the beam transitions from the simple stability to monostability with snap-through instabilities, and ultimately to bistability.…”