Realization Of Negative Stiffness And Its Application In Vibration Control

The negative stiffness systems are rare in engineering practice.But it has become a research focus for many scholars due to its advantages,such as high bearing capacity,small deformation,good control performance and low natural frequency.Dynamic vibration absorber(DVA)is a useful device in vibration control,which is a subsystem attached to the primary system.A large number of viscoelastic materials are used in vibration control engineering and its mechanical model is more suitable for the Maxwell model.In this thesis,the negative stiffness system and Maxwell model is applied on DVA to improve the vibration control effect,and the work in this thesis is as follow:(1)A new type of piecewise negative stiffness(NS)mechanism is designed.On the basis of the negative stiffness function,the quasi-zero stiffness characteristic is added.The dimensionless stiffness curve of the piecewise negative stiffness mechanism under different system parameters is obtained by the statics analysis.It is proved that the proposed model in this thesis can realize the function of negative stiffness and quasi-zero stiffness by selecting specific system parameters.(2)The piecewise NS mechanism is applied to dynamic vibration absorber(DVA)to establish a dynamic vibration absorber model with the piecewise linearity.The approximate analytical solution and the amplitude frequency curve of the system with the piecewise NS are obtained by means of the averaging method.And the correctness of analytical solution is verified.It is proved that the model of DVA with the piecewise NS mechanism in this thesis can not only suppress the amplitude of the primary system in resonance region significantly,but also extend the efficient frequency range of vibration absorption under the condition of harmonic excitation.Furthermore,the dynamic vibration absorber model with piecewise NS characteristics has better vibration reduction effect than other traditional DVAs through comparison under random excitation.(3)The system parameters of the piecewise NS mechanism are adjusted and the quasi-zero stiffness part is omitted,so that the mechanism can only realize the negative stiffness function.The Maxwell model of the viscoelastic material is applied to dynamic vibration absorber(DVA)system to form a Maxwell model dynamic vibration absorber with negative stiffness part,and the parameters of the model are optimized in detail.Finally,it is proved that the model in this thesis has better vibration reduction effect by comparing with other traditional DVAs under the harmonic and random excitations.(4)The Maxwell model of viscoelastic material and negative stiffness spring are applied to dynamic vibration absorber(DVA)system in parallel to form a Maxwell model dynamic vibration absorber with multi-negative stiffness,and the parameters of the model are optimized in detail.The model has obvious effect on the vibration reduction of the main system,which is better than the three models of typical DVA.