Frequency Domain Method to Determine Peak Resultant Accelerations of Structure-DVA Systems

Abstract

Tall, slender buildings are often susceptible to excessive wind-induced motion during common wind events, which can lead to occupant discomfort. Traditionally, the structural response is computed through modal analysis and frequency domain methods using the auto-spectra of the dynamic wind loading. The peak spatial (X-, Y-, torsion, and resultant) accelerations are often estimated using the mode shapes, peak factors, and assumed coincidence factors, which are intended to account for the improbability of peak modal responses occurring simultaneously. While this methodology has been employed for decades, correlation among modal responses may result in erroneous predictions of accelerations for structures having nearly identical sway frequencies. Moreover, the rules that define how peak modal responses combine to create peak spatial peak accelerations are assumed. In this study, a frequency domain method is presented to determine the covariance matrix of the modal accelerations, which accommodates the correlation between modal responses. Subsequently, a Lagrangian multiplier technique is employed to determine the modal combinations that produce the largest spatial accelerations, without relying upon an assumed coincidence factor. The method is applied to a tall building, and the response is compared to results obtained from time domain analysis. The structure is then equipped with a TMD to demonstrate the performance of the TMD, and the ability of the proposed method to estimate peak responses of more complicated structure-TMD systems. The proposed method enables peak accelerations of linear systems to be determined using computationally-efficient frequency domain methods, rather than defaulting to more burdensome time domain analysis.