Closed-form solutions to optimal parameters of dynamic vibration absorbers with negative stiffness under harmonic and transient excitation

In this present paper, two configurations of dynamic vibration absorber in conjunction with negative stiffness (NSDVA) are investigated and their parameter optimization is conducted according to two tuning methodologies: the fixed points theory and the stability maximization criterion. Closed-form solutions to the optimal parameters of NSDVAs are analytically derived and are expressed in terms of ratio between the negative stiffness and mechanical stiffness of primary system. Allowable bounds on negative stiffness are specified with the consideration of stability requirement, based on which the ultimate control performance of NSDVAs could be imagined. Furthermore, an optimal negative stiffness ratio is defined within the stable region when the NSDVAs are tuned by the fixed points theory. Finally, numerical simulations are carried out in both harmonic and free vibration scenarios. Simulation results suggest that the inclusion of negative stiffness in the coupled system can significantly improve the vibration control performance in terms of broadening the frequency bandwidth of vibration suppression, decreasing the peak vibration amplitude of primary system and confining the stroke length of NSDVAs. Meanwhile, the negative stiffness can enhance the damping capability of coupled system, engendering an accelerated convergence of transient disturbances.