Dynamic Responses Analysis of Bridges With Uncertain Parameters Under Moving Loads
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摘要:
针对具有不确定参数桥梁在移动荷载作用下的动力响应分析，首次建立了移动荷载作用下桥梁响应分析的多项式维数分解法。将结构的不确定参数视为独立的随机变量，构造了结构动力响应关于不确定参数的随机函数；进而采用一组变量数目逐次增加的成员函数实现结构动力响应的维数分解，并利用Fourier多项式展开推导成员函数的近似显式表达。通过降维积分方法降低概率空间内的积分维度，高效地实现了展开系数的计算。在数值算例中，进行了具有不确定参数桥梁在移动荷载作用下的响应估计，并与Monte-Carlo模拟进行对比，验证了该文方法的精确性和效率。
Abstract:The dynamic responses of bridges with uncertain parameters under moving loads were analyzed, and a polynomial dimensional decomposition method for the analysis of structural responses induced by moving loads was proposed for the first time. The uncertain parameters were regarded as independent random variables, and the random response function about these uncertain parameters was constructed. The dimensional decomposition of the function was further performed with a group of component functions with a gradually increasing number of variables, and the approximate expressions of the component functions were derived through the Fourier polynomial expansion. Then, the expansion coefficients were efficiently calculated through the introduction of the dimension-reduction integration method. The numerical examples give response estimation of bridges with uncertain parameters under moving loads, which in comparison with those from the Monte-Carlo simulation, verify the accuracy and efficiency of the proposed method.
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图 4
$ t=0.8\;\mathrm{s} $ 时跨中位移的概率密度Figure 4. The probability density of displacement at
$ t=0.8\;\mathrm{s} $ 
图 9
$ t=10.60\;\mathrm{s} $ 时的概率密度Figure 9. The probability density at
$ t=10.60\;\mathrm{s} $ -
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