Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance

Dynamic vibration absorbers (DVAs) serve as critical passive control devices. However, their conventional designs are characterized by high directional sensitivity and large additional mass, failing to meet the rigorous demands of modern equipment for multi-directional coupled vibration suppression and lightweighting. To address these challenges, this study establishes an isotropic dynamic model of coupling spring and shell stiffnesses. This model shows that the isotropy degrades with the lightweight design due to a failure mode of shear deformation. Then, by constraining the shear stiffness, a collaborative design framework integrating topology optimization and parameter optimization is constructed to lighten the DVA. Using a 50 Hz DVA as a case study, prototype designs, simulations, and experiments are conducted. The results indicate that the isotropic natural frequencies agree well with the design targets. The shell mass is reduced by 79.8% compared to the conventional rigid shell design. Moreover, in vibration reduction simulations under the same total mass, the optimized absorber further reduces the vibration response by 7.4 dB compared to the rigid shell design.