Reduced-order wavelet-Galerkin solution for the coupled, nonlinear stochastic response of slender buildings in transient winds

Abstract

A tall building is prone to wind-induced stochastic vibration, originating from complex fluid–structure interaction, dynamic coupling and nonlinear aerodynamic phenomena. The loading induced by extreme wind events, such as “downburst storms”, hurricanes and tornadoes is naturally transient and nonstationary in comparison with the hypothesis of stationary wind loads, used in both structural engineering research and practice. Time-domain integration methods, widely applied for solving nonlinear differential equations, are hardly applicable to the analysis of coupled, nonlinear and stochastic response of tall buildings under transient winds. Therefore, the investigation of alternative and computationally-efficient simulation methods is important. This study employs the wavelet-Galerkin (WG) method to achieve this objective, by examining the stochastic dynamic response of two tall building models subject to stationary and transient wind loads. These are (1) a single-degree-of-freedom equivalent model of a tall structure and (2) a multi-degree-of-freedom reduced-order full building model. Compactly supported Daubechies wavelets are used as orthonormal basis functions in conjunction with the Galerkin projection scheme to decompose and transform the coupled, nonlinear differential equations of the two models into random algebraic equations in the wavelet domain. Methodology, feasibility and applicability of the WG method are investigated in some special cases of stiffness nonlinearity (Duffing type) and damping nonlinearity (Van-der-Pol type) for the single-degree-of-freedom model. For the reduced-order tall building model the WG method is used to solve for dynamic coupling, aerodynamics and transient wind load effects. Computation of “connection coefficients”, effects of boundary conditions, wavelet resolution and wavelet order are examined in order to adequately replicate the dynamic response. Realizations of multivariate stationary and transient wind loads for the building models are digitally simulated in the numerical computations.