The optimal design of dynamic systems with negative stiffness inertial amplifier tuned mass dampers

Abstract

The negative stiffness inertial amplifier tuned mass dampers (NSIA-TMD) are introduced in this paper. Another two novel tuned mass dampers such as negative stiffness tuned mass damper (NS-TMD) and inertial amplifier tuned mass damper (IA-TMD) are mathematically developed from the negative stiffness inertial amplifier tuned mass dampers (NSIA-TMD) and the static masses of these three novel dampers are retained constant. The exact closed-form expressions for optimized system parameters for these novel dampers are obtained using H2 and H∞ optimization techniques. The dynamic responses of the SDOF systems controlled by H2 and H∞ optimized novel tuned mass dampers subjected to base excitations are obtained analytically. The dynamic response reduction capacities of the novel tuned mass dampers are compared with the dynamic response reduction capacities of traditional tuned mass dampers (TMD). Therefore, the dynamic response reduction capacities of H2 optimized NS-TMD, NSIA-TMD, and IA-TMD are significantly 45.51%, 43.47%, 41.08% superior to the H2 optimized traditional tuned mass dampers. Furthermore, the dynamic response reduction capacities of H∞ optimized NS-TMD, NSIA-TMD, and IA-TMD are significantly 3.31%, 8.98%, 13.79% superior to the H∞ optimized traditional tuned mass dampers. The nonlinear negative stiffness inertial amplifier tuned mass dampers (NNSIA-TMD) are also introduced in this paper. As a result, the dynamic response reduction capacities of H2 optimized nonlinear negative stiffness tuned mass damper (NNS-TMD), NNSIA-TMD, and nonlinear inertial amplifier tuned mass damper (NIA-TMD) are significantly 24.54%, 21.92%, 19.12% superior to the H2 optimized traditional tuned mass dampers. Furthermore, the dynamic response reduction capacities of H∞ optimized NNS-TMD, NNSIA-TMD, and NIA-TMD are significantly 3.01%, 9.04%, 15.08% superior to the H∞ optimized traditional tuned mass dampers. The outcomes of this research are mathematically accurate and relevant to practical design applications.