建筑结构基于巴斯金风速谱的系列风振响应的简明封闭解

针对巴斯金风速谱激励下的建筑结构顺风向振动响应表达式复杂的问题,提出了一种简明封闭解法.巴斯金随机谱广泛应用于描述脉动风、随机地震动和路面不平顺等各种随机激励,本文基于留数定理给出巴斯金风速功率谱的二次正交式.综合运用复模态法和虚拟激励法获得了建筑结构系列响应(位移、层间位移及其变化率)功率谱的统一形式的二次正交式,并根据谱矩的定义获得了建筑结构系列响应的方差和谱矩及绝对加速度方差的简明封闭解.运用本文方法对一8层建筑结构进行分析,并与传统虚拟激励法进行对比研究,表明本文所得封闭解正确,并可用于验证虚拟激励法在谱矩和方差分析时的精度和效率.由于本文方法含有复模态法,故可用于各类线性结构基于巴斯金谱的随机响应分析和基于动力可靠度及舒适度的动力优化分析.

Concise closed-form solutions of random wind-induced vibration response of building structure based on Baskin wind speed spectrum

In order to solve the problem that the expression of the along-wind vibration response of a building structure excited by Baskin wind speed spectrum is complex,a concise closed-form solution is proposed.Baskin spectrum is widely used to describe various random excitations such as fluctuating wind,random ground motion and road surface irregularity.Based on the residue theorem,the quadratic orthogonal formula of Baskin wind spectrum is given.By using the complex mode method and the pseudo excitation method,the unified quadratic orthogonal expressions of the power spectrum density function of the series response (absolute displacement,inter-story displacement and their change rates) of the building structure is obtained.According to the definition of the spectral moment,the concise closed-form solutions of the variance and spectral moments of the series response and the acceleration variance of the structural floor are obtained.This method is used to analyze an 8-storey building structure and is compared with the traditional pseudo excitation method.The results show that the closed-form solutions obtained in this paper is correct and can be used to verify the accuracy and efficiency of the pseudo excitation method in spectral moment and variance analysis.Since the complex modal method is included in this method,it can be used for stochastic response analysis based on Baskin spectrum and dynamic optimization analysis based on dynamic reliability and comfort of various linear structures.