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Semi-analytical solutions for stochastic response of non-classically damped linear structures to arbitrary time-frequency modulated seismic excitations

机译:用于非经典阻尼线性结构的随机响应的半分析解决方案,以任意时间频率调制地震激励

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摘要

This paper presents a semi-analytical method for stochastic response analysis of non-classically damped linear structures subjected to non-stationary seismic excitations modeled by arbitrary time-frequency modulating functions. In this method, the inherent randomness of seismic excitation process is characterized by a set of orthogonal random variables obtained using the spectral representation method. Then, by adopting piecewise polynomials to interpolate the time-frequency modulating function of seismic excitation, an explicit expression for the structural stochastic response in term of the orthogonal random variables is derived using the complex modal analysis. This expression can be used not only to efficiently predict the seismic response of structures subjected to an arbitrary excitation sample, but also to directly evaluate the structural response statistics in the time domain. Finally, a robust algorithm is proposed to determine the optimal locations of segmentation points for the piecewise polynomials, the computational efficiency can be further improved. In the numerical application, a typical non-classically damped structural system subjected to two models of non-stationary seismic excitations are studied. The classical evolutionary spectral method and the Monte Carlo simulation are used to verify the accuracy and efficiency of the proposed method. The effects of several parameters such as the order of polynomials on the performance of the proposed method are investigated.
机译:本文介绍了由任意时频调制功能模型的非经典阻尼线性结构的随机响应分析的半分析方法。在该方法中,地震激励过程的固有随机性的特征在于使用光谱表示方法获得的一组正交随机变量。然后,通过采用分段多项式来插入地震激励的时频调制功能,使用复杂的模态分析导出正交随机变量期间的结构随机响应的显式表达式。该表达不仅可以有效地预测经受任意激发样品的结构的地震响应,而且还可以直接评估时域中的结构响应统计。最后,提出了一种稳健的算法来确定分段多项式的分割点的最佳位置,可以进一步提高计算效率。在数值应用中,研究了经受两种非平稳地震激发模型的典型非经典阻尼结构系统。经典的进化光谱法和蒙特卡罗模拟用于验证所提出的方法的准确性和效率。研究了几种参数的影响,例如多项式阶数对所提出的方法的性能。

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