孙攀旭, 杨红, 刘庆林. 基于动力特性的混合结构地震响应复模态叠加法[J]. 工程力学, 2020, 37(11): 69-82. DOI: 10.6052/j.issn.1000-4750.2019.12.0723
引用本文: 孙攀旭, 杨红, 刘庆林. 基于动力特性的混合结构地震响应复模态叠加法[J]. 工程力学, 2020, 37(11): 69-82. DOI: 10.6052/j.issn.1000-4750.2019.12.0723
SUN Pan-xu, YANG Hong, LIU Qing-lin. COMPLEX MODE SUPERPOSITION METHOD OF HYBRID STRUCTURE SEISMIC RESPONSES BASED ON DYNAMIC CHARACTERISTICS[J]. Engineering Mechanics, 2020, 37(11): 69-82. DOI: 10.6052/j.issn.1000-4750.2019.12.0723
Citation: SUN Pan-xu, YANG Hong, LIU Qing-lin. COMPLEX MODE SUPERPOSITION METHOD OF HYBRID STRUCTURE SEISMIC RESPONSES BASED ON DYNAMIC CHARACTERISTICS[J]. Engineering Mechanics, 2020, 37(11): 69-82. DOI: 10.6052/j.issn.1000-4750.2019.12.0723

基于动力特性的混合结构地震响应复模态叠加法

COMPLEX MODE SUPERPOSITION METHOD OF HYBRID STRUCTURE SEISMIC RESPONSES BASED ON DYNAMIC CHARACTERISTICS

  • 摘要: 混合结构由不同阻尼特性的材料组成,确定其阻尼矩阵存在困难。分块Rayleigh阻尼模型由于数学上的简易性,被广泛用于构建混合结构的阻尼矩阵,但分块Rayleigh阻尼模型的计算精度与参考频率的选择方法直接相关。针对参考频率的选择问题,依据结构动力响应的组成和特点,提出了一种确定Rayleigh阻尼系数的计算方法,进而实现基于分块Rayleigh阻尼模型的复模态叠加法。求解结构的瞬态反应时,根据结构前两阶振型的自振频率确定阻尼系数;求解结构的稳态反应时,选择结构的基频、与外激励频率接近的结构自振频率确定阻尼系数。依据地震波的频谱特性,提出了基于地震波卓越频率的分块Rayleigh阻尼模型,并结合地震加速度的分段线性假定,建立了混合结构的复模态叠加法。在此基础上,利用三角级数展开得到组成地震波的谐波频率,进一步提出了基于谐波频率的分块Rayleigh阻尼模型和对应的复模态叠加法。算例分析结果表明:所提方法误差更小,且克服了传统方法因振型选择不唯一导致的计算结果具有不确定性的问题;与基于地震波卓越频率的复模态叠加法相比,基于谐波频率的复模态叠加法计算量更大,但计算精度更高、适用范围更广。

     

    Abstract: The damping matrix of a hybrid structure of different material damping characteristics is difficult to determine. By the aid of mathematical simplicity, Rayleigh damping model is widely used in the construction of damping matrix of a hybrid structure. But the calculation precision of Rayleigh damping model is affected by the choice of reference frequencies. Thusly, a calculation method of Rayleigh damping coefficients is proposed based on the characteristics of structural dynamic responses. The corresponding complex mode superposition method is also realized. The damping coefficients are determined based on the natural frequencies of the first two modes when the structural transient responses are calculated. The damping coefficients are determined based on fundamental frequency and certain frequency when the structural steady state responses are calculated. The certain frequency is the natural frequency close to external excitation frequency. According to the spectrum characteristics of seismic wave, a Rayleigh damping model is obtained based on the predominant frequency of seismic wave. Combined with the linear assumption of earthquake acceleration, a complex mode superposition method of hybrid structure is realized. The harmonic frequencies of seismic wave could be obtained by trigonometric series. Another Rayleigh damping model is developed based on the harmonic frequencies, and the corresponding complex mode superposition method is proposed. The cases show that the proposed method could avoid the arbitrariness of selective modes based on traditional methods. The calculation error of the proposed method is small. Compared with the complex mode superposition method based on the predominant frequency of seismic wave, the computational amount of complex mode superposition method based on the harmonic frequencies is larger, but with higher calculation accuracy and wider range of application.

     

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