Analytical And Experimental Study Of Negative Stiffness In Structures

In many applications,passive vibration control is preferred mainly to avoid energy supply and cost.Meta-structure provides an excellent solution for passive low-frequency vibration isolation through negative effective mass density and modulus.However,the resonance nature restricts its application in a narrow frequency range.This thesis is devoted to the research on the new ways of eliciting linear/nonlinear negative stiffness and its application in manipulating acoustic and mechanical waves in structures.The main contributions are summarized as follows;1.A negative stiffness(NS)spring using repelling magnets is designed and the NS behavior is confirmed by experimental calibration.An air-track based platform is established for directly test of lumped-parameter model of coupled oscillators containing NS spring,for which the stability condition,the dynamics of free and forced vibration are examined.The anti-phase trajectory of masses due to the presents of NS is found by both the analytical and measurement.The Hamiltonian of systems containing NS element is clarified without violating the thermodynamic stability.2.A study of the dynamic characteristics of two examples mimicking high-static-lowdynamic-stiffness(HSLDS)isolator are carried out,taking different grade of nonlinearities of the NS spring into account by adjusting the gaps between the repelling magnets.The isolation behavior is analyzed by adopting the cubic approximation of the nonlinear NS,and good agreement on transmissibility spectrum is found by theoretical prediction and the experiments.The proposed platform proves to be a versatile test-bed for studying dynamic characteristics of one-dimensional NS system.3.An application of NS on the acoustic wave insulation is proposed and the sound transmission loss(STL)is analytically and experimentally investigated.The insulating layer consists of two thin plates connected by NS magnetic spring in order to reduce the interaction of the air in both sides and hence the transmission of sound.It is found that STL peaks are shifted to lower frequency,and the STL slightly increases for small negative stiffness achievable in experiment which is not enough to cancel the effect of air compressibility.However,parametric study shows that a significant enhancement of STL could be expected if NS can be made large enough in between the thin plates.