Wind vibration responses of structure with generalized Maxwell model viscoelastic dampers

Abstract

A new method for analysis of wind vibration response of structures with viscoelastic dampers is presented. Most existing studies focused on the numerical solution, and in this paper, an analytical method based on quadratic orthogonalized power spectral density function (QO-PSDF) was applied to obtain the closed-form solution of the structural dynamic responses with generalized Maxwell model (GMM) viscoelastic damper under Davenport spectral wind excitation. Firstly, the equations in motion of GMM viscoelastic dampers were coupled with the structural dynamic equation, which was decoupled into a linear combination of first-order vibration equations through complex mode method (CMM). Secondly, the frequency response eigenvalue function (FREF) was quadratic orthogonalized, which was combined with power spectral density function (PSDF) of Davenport spectral to obtain a QO-PSDF of the structural dynamic responses, and the exact closed-form solutions of the spectral moments and variances of the dynamic response were successfully acquired using the QO-PSDF. Finally, a 16-storey reinforced concrete building structure equipped with GMM viscoelastic dampers is taken as an example to validate the accuracy and applicability of the closed-form solution through a series of structural responses, including absolute displacements, inter-storey displacements, absolute velocities, inter-storey velocities.