Wavelet-Galerkin analysis to study the coupled dynamic response of a tall building against transient wind loads

Abstract

The wavelet-Galerkin analysis approach is explored for the solution of the stochastic structural dynamic response of a tall building under transient nonstationary winds. The approach is obtained by combining the Galerkin expansion method with basis-functions selected from discrete orthonormal wavelets (namely, the compactly supported Daubechies wavelets). The expansion transforms the stochastic dynamic problem of the tall building, subjected to time-dependent turbulent-induced forces and motion-induced forces, into a system of random algebraic equations in the domain of the wavelet coefficients. A reduced-order model of a benchmark tall building is employed as a numerical example. Nonstationary wind time histories, simulating the loading of a downburst, are artificially generated at discrete points along the vertical axis of the building by using the notions of evolutionary power spectral density of the turbulence and time-dependent amplitude modulation function. Important aspects such as the treatment of boundary conditions are examined. The paper also aims at investigating the influence of the order of the wavelets and the wavelet resolution on the numerical accuracy of the building response. Even though the primary purpose of the study is to examine the feasibility of the proposed analysis method for studying the transient stochastic response of the tall building, a “frozen” thunderstorm downburst model (a first approximation of a slowly-varying time-dependent wind velocity profile with constant wind direction and negligible thunderstorm translation velocity) is also employed. Two time-independent synoptic wind velocity profiles (power-law models) and one non-synoptic downburst wind velocity profile (“Vicroy’s model”) are considered.