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| 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 |
| Concise and closed solution of random wind-induced vibration response of building structures based on Baskin wind speed spectrum |
| 投稿时间：2020-08-12 修订日期：2021-01-03 |
| DOI： |
| 中文关键词: 巴斯金风速谱 响应功率谱的二次正交式 谱矩 舒适度 简明封闭解 |
| 英文关键词:Baskin wind speed spectrum Quadratic orthogonal formula of response power spectrum Spectral moment Comfort Concise closed solution |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 针对巴斯金风速谱激励下的结构风振系列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、路面不平顺等各种随机激励，其采用有理式表示。本文首先利用留数定理给出巴斯金随机风速功率谱的二次正交式；其次运用复模态法将考虑多振型的结构系统解耦为一阶广义复模态的线性组合，并利用虚拟激励法获得了结构系列响应（绝对位移及其变化率、层间位移及其变化率）功率谱的统一形式的二次正交式；最后，根据谱矩定义，获得了建筑结构风振系列响应方差和0-2阶谱矩及绝对加速度方差的简明封闭解。运用本文方法对一10层建筑结构进行分析，并与虚拟激励法进行对比研究，研究表明本文方法所得方差和谱矩为巴斯金谱激励下结构风振响应的封闭解法，并可用于验证虚拟激励法在谱矩分析时的精度。此外，由于获得了响应的谱矩和方差，可用于基于动力可靠度和舒适度的优化分析。 |
| 英文摘要: |
| Aiming at the complex expression of wind-induced vibration response of structures under Baskin wind speed spectrum excitation, a simple closed solution is proposed. Baskin's random spectrum is widely used to describe various random excitation, such as pulsating wind, random ground vibration and uneven road surface. It is expressed in rational form. In this paper, the quadratic equivalent form of Baskin random wind speed power spectrum is given by using the residue theorem. Secondly, the structural system considering multiple modes is decoupled into a linear combination of first-order generalized complex modes by using the complex mode method, and the quadratic orthogonal formula of the unified form of the power spectrum of the structural series responses (absolute displacement and its rate of change, interlayer displacement and its rate of change) is obtained by using the virtual excitation method. Finally, according to the definition of spectral moments, the simple closed solutions of the response variance of the wind vibration series and the variance of 0-2 order spectral moments and absolute acceleration of the building structures are obtained. The results show that the variance and spectral moment obtained by this method are the closed solutions of wind-induced vibration of structures under Baskin spectral excitation, and can be used to verify the accuracy of the virtual excitation method in spectral moment analysis. In addition, the spectral moment and variance of the response are obtained, which can be used for optimization analysis based on dynamic reliability and comfort. |
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