Vibration isolation performance of simply supported beam installed with a negative stiffness device

Abstract

A negative stiffness device composed of two horizontal pre-compression springs is proposed to isolate the vibration of the simply supported beam. The nonlinear vibration equation of simply supported beam installed with a negative stiffness device is established by using Hamilton principle first. The lower degree of freedom dynamic equation of the system is derived by using Galerkin truncation approach. The influence of support position and negative stiffness parameters on the natural frequency of the beam are obtained from the modal analysis of the free vibration system. According to the dynamic internal force of the beam, the force transmissibility at the support end is defined and the displacement transmissibility of any point on the beam is also defined to facilitate the analysis of the vibration isolation effect. The influence of negative stiffness support parameters on the amplitude–frequency curve and the transmissibility curve of the simply supported beam is discussed. The results show that the fundamental frequency of the system can be significantly reduced by the negative stiffness device, while the frequencies of high-order modes are changed a little bit only. Increasing the horizontal spring stiffness will reduce the first-order resonance frequency and the initial frequency of vibration isolation. Consequently, the aim of lower frequency vibration isolation for the simply supported beam can be achieved. This paper provides an effective approach to the vibration isolating design of flexible structures.