A method to generate dynamic vibration absorber load combinations

Dynamic vibration absorbers (DVAs) in the form of tuned mass dampers (TMDs) and tuned sloshing dampers (TSDs) are commonly employed to reduce structural accelerations during common wind events. Since the loads are applied in multiple directions, and may be produced by multiple DVAs, the generation of load combinations that envelop all expected DVA loads applied to the structure is a challenging task. A method is presented that employs principal component analysis to transform the DVA loading time series into M orthogonal principal components (PCs). By normalizing the PC time series, the loading envelop can be represented as an M-sphere (M-dimensional hypersphere). M-dimensional geometric objects (polytopes) are required to envelop the M-sphere. The coordinates of the polytope’s vertices, when converted back into the original loading coordinates, represent the load combinations. The method is applied to wind tunnel test data as well as monitoring data collected from two anonymous buildings equipped with multiple DVAs. The method reduces the dimensionality of the problem by eliminating PCs that do not contribute significantly to the response. The results demonstrate that if efficient polytopes are chosen, the conservatism associated with the load combinations can be reduced by employing a larger number of load combinations.