Analytical H2 optimization for the design parameters of lever-type stiffness-based grounded damping dynamic vibration absorber with grounded stiffness

A novel lever-type stiffness-based grounded damping dynamic vibration absorber with grounded stiffness is presented in this paper, and the analytical design parameters are derived in detail. At the first, the equations of motion are established and the analytical solution of the primary structure displacement is obtained. It is found that with the introduction of grounded stiffness, the coupled system could be unstable and the stability condition is established. Then, the optimum stiffness ratio, the optimum damping ratio and the optimum grounded stiffness ratio are expressed as the function of mass ratio and lever ratio by minimizing the mean squared displacement response of the primary structure previously established. From the results analysis, the system stability is verified, and it is found that with the change in the lever ratio when the mass ratio is selected, there are three cases for the optimum grounded stiffness ratio, i.e., negative, zero and positive. Thus, for the vibration reduction of primary structure, the proposed dynamic vibration absorber (DVA) with positive grounded stiffness has the best control performance among the three cases. Compared with some typical designed DVAs under harmonic and random excitation, the results show that with the proposed optimum DVA the resonance amplitude and the frequency band of vibration reduction can greatly reduce and broadened, respectively, and the random vibration mitigation can be greatly increased. According to the existing literature, the proposed lever-type stiffness mechanism is justified, which means that the proposed DVA is practical and can be used in many engineering applications.