Study On Passive Control Of Vibration Of Beam With Additional Negative Stiffness Supports

The beam is a commonly used structure in aerospace,mechanical and civil engineering.In practical applications,it often has to withstand different types of external excitations,which causes large structural vibrations.Therefore,its active and passive control problems have been affected by scientists and engineers.Negative stiffness supporting structure can decrease the dynamic stiffness of the system without changing the system's load-bearing capacity,and reduce the natural frequency of the system.However,in the past studies,they have been applied to discrete systems for vibration isolation.In this paper,the negative stiffness supporting structure is used for the beam's vibration control.In this paper,the negative stiffness supporting structure composed of two horizontal preload springs is used to isolate and suppress the vibration of the beam.The nonlinear dynamic models of cantilever beam with additional negative stiffness structure and simply supported beam with additional negative stiffness structure under the excitation of simple harmonic force and base displacement are studied.The change law of the natural frequency of the system with the negative stiffness parameter is studied and adopted.The Hamilton principle and Galerkin method are used to obtain the nonlinear vibration equation of the system.By studying the natural frequency,modal and nonlinear vibration response of the system,the vibration suppression effect of negative stiffness components on cantilever beams and simply supported beams is explained.The effects of horizontal spring stiffness,preload ratio,system equivalent linear damping and nonlinear damping on the vibration isolation bandwidth are analyzed.The results show that(1)increasing the horizontal spring stiffness can reduce the first-order natural frequency of the cantilever beam and the simply supported beam-with negative stiffness supports,ensuring that the second-order natural frequency remains almost unchanged;(2)when the beam structure is subjected to simple harmonic force excitation,the first-order formant peak of the system moves forward,the peak value increases,the second-order formant peak remains intact and the amplitude of the non-resonant area does not change significantly;(3)When the beam structure is subjected to displacement excitation of the base,increasing the horizontal spring stiffness or decrease the preload ratio,the system first-order resonance peak moves forward,but the peak value becomes smaller,when the system natural frequency is zero,the first-order resonance peak disappears;(4)when the horizontal spring stiffness is large,the system superharmonic resonance occurs in the low-frequency region.The research results in this paper show that the negative stiffness supporting structure can increase the non-resonant area of the beam structure and expand the working frequency band of the beam structure by changing the resonance frequency of the system.