Evaluation of Modal Correlation Effects on Peak Spatial Accelerations of Structure-Dynamic Vibration Absorber Systems

It has been challenging to predict the peak spatial accelerations of tall buildings experiencing wind-induced motion. Frequency domain solution techniques using modal analysis are typically employed for wind tunnel studies, in which it is necessary to combine the modal responses statistically to estimate the peak spatial responses. An improved solution technique is presented that treats the determination of the peak accelerations as an optimization problem with a closed-form solution. The peak X, Y, and torsional accelerations are solved using matrix multiplication of the modal response covariance matrix and mode shapes. The peak resultant acceleration is determined by solving an eigenvalue problem. The proposed solution method accommodates correlation between modal responses, which existing methodologies have neglected. A case study is presented in which significant correlation exists between a building's modal responses due to a strong across-wind loading exciting two modes simultaneously. A tuned mass damper (TMD) is incorporated into the building design to reduce wind-induced motions. The TMD transfers energy between structural modes of vibration and increases the correlation between modes considerably. Neglecting modal correlation effects results in a considerable overestimation of some spatial responses and a considerable underestimation of other spatial responses. While a bidirectional TMD decreased the modal responses by a similar amount, due to the strengthened modal correlation not all directions of motion were decreased as much as would be expected if the correlation was not present. It is therefore necessary that DVA systems designed for tall buildings properly account for modal correlation.