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简支梁非线性响应的三维路径积分法分析
Three-dimensional path integration analysis of non-linear responses of simply-supported beams
投稿时间:2018-04-05  修订日期:2018-06-05
DOI:
中文关键词:  三维路径积分法  过滤高斯白噪声  简支梁  非线性  非平稳
英文关键词:three-dimensional path integration method  filtered Gaussian white noise  simply-supported beam  non-linear  non-stationary
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)
作者单位E-mail
潘鑫凯 天津大学 panxinkai@tju.edu.cn 
王小盾 天津大学  
朱海涛 天津大学 htzhu@tju.edu.cn 
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中文摘要:
      本文采用了基于Gauss-Legendre积分公式的三维路径积分法,分析了在过滤高斯白噪声激励下的简支梁非线性随机振动响应的概率密度函数。在过滤高斯白噪声激励下的简支梁随机振动模型采用一阶滤波方程与简支梁一阶模态的振动模型联立得到。本文通过基于Gauss-Legendre积分公式的积分法和短时高斯近似法求解响应的概率密度函数值。结果表明,三维路径积分法计算值能够很好地与蒙特卡洛模拟值符合,即使在尾部区域也符合良好。三维路径积分法能比等效线性化法提供更高的计算精度。
英文摘要:
      This paper analyzes the probability density functions of non-linear random vibration responses of simply-supported beams under filtered Gaussian white noise by three-dimensional path integration method based on the Gauss-Legendre integration scheme. The random vibration model of simply-supported beams under filtered Gaussian white noise is obtained by considering the formulas of one-dimensional filter equation and the first-order vibration mode of simply-supported beams. This paper adopts the integration method based on Gauss-Legendre integration scheme and short-time Gaussian approximation to obtain the probability density functions of responses. The results show that the obtained values of the three-dimensional path integration method can agree well with the Monte Carlo simulation results, even in the tail regions. Three-dimensional path integration method can provide higher accuracy than equivalent linearization method.
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