Universal simplified spectral models and closed form solutions to the wind-induced responses for high-rise structures

Abstract

High-rise structures are characterized as wind-sensitive vertical structures, estimating the wind-induced vibration response is a key to the structural design procedure. This study presented universal wind load spectral models for high-rise structures, including tri-para and κ model for along-wind load characterized by power dissipating with frequency and analog filter model for cross-wind load dominant by power concentration induced by vortex excitation. The spectral models appear to provide good agreement with wind tunnel data of buildings with various configurations. With analog filter approach, the along-wind spectra can be approximated by a linear filter polynomial and the cross-wind spectra is expressed by a quadratic filter polynomial. Thus forming a simple differential equation for the along- and cross-wind excitation based on a pseudo idea white noise. The closed form solutions to the wind-induced responses are derived based on analog filter approach. The Lyapunov equations are also provided in the state-space for high-rise structures with and without extra damping devices. The presented closed form solutions can provide a powerful tool in codification and vibration control optimization.