Model-free sequential design of absorbers for customized vibration control

Optimal design of distributed vibration absorbers for controlling broadband vibration of structures is challenging, mainly because of the modal coupling incurred inside the structure as well as the interplay among multiple absorbers. Without analytical solutions, absorber design usually resorts to numerical optimizations over the full parameter space, which is computationally intensive alongside the risk of being trapped into local optima. Meanwhile, most existing methods are model based, mostly numerical ones, thus adding additional difficulties when the structure is complex with uncertain parameters which are difficult to be accurately apprehended. In this paper, based on the structural response (either simulated or experimentally measured), we propose a model-free and sequential approach for the design of distributed absorbers over an arbitrarily given thin-walled structure to achieve pre-defined target vibration reduction. The proposed approach involves a systematic three-step procedure. Upon identifying the Excitation-Dependent Representative Basis (EDRB) of the primary structure, locations of the absorbers are first determined to ensure their strong coupling with the targeted and higher-frequency EDRB while minimizing the interaction with the lower-frequency ones. Subsequently, absorber masses are determined through an inverse design approach, followed by the optimization of their uncoupled frequencies and damping coefficients through an iteration procedure in which only two parameters are involved. The effectiveness of the proposed approach is validated through both numerical simulations on representative cases and experiments on a complex structure.