Re-designing strategy to enable a sub-system to function as a dynamic vibration absorber

Abstract

In the design of a typical dynamic absorber, the components corresponding to the dynamic vibration absorber (DVA) should be reduced to a lumped constant system model comprising a mass, spring, and damper. The equivalent mass and stiffness must be determined and linked to design coefficients. However, no studies on the dynamic design of a main structure (main system) and an attached DVA (sub-system) based on an FE model without constructing a reduced-order equivalent model with a few DOFs have been conducted. This study proposes a new method of extracting and simplifying the design of a sub-system to function as a DVA using the state of a finite element (FE) model. We established the relationship between the condition of the sub-system functioning as a DVA and the modal parameter of the entire system. According to a survey, the modal kinetic energies, which were calculated from the partial mass matrix and mode vectors, of the main system and sub-system are approximately equal. We used this relationship to redesign the sub-system. As the modal kinetic energy was used as a design index, the FE model could be redesigned without constructing an equivalent lumped parameter model consisting of two or three degrees of freedom (DOFs) as in the conventional DVA design. We demonstrated the relationship between the modal kinetic energies of the main system and sub-system when it functions as a DVA for a 2-DOF lumped mass model and discussed how to distinguish the sub-system from the entire system (multi-DOF system). Considerable improvement was found in re-designing at FE model, validating the proposed method. The proposed method can be used to redesign components that behave similarly to dynamic absorbers to effectively reduce vibration from the results of FE analysis, without modeling the system as a lumped constant system.