简支梁非线性响应的三维路径积分法分析

采用基于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；联立一阶滤波方程与简支梁一阶模态的振动模型，得到在过滤高斯白噪声激励下的简支梁随机振动模型，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与蒙特卡洛模拟值符合良好，即使在尾部区域也符合良好。三维路径积分法比等效线性化法的计算精度更高。

Three-dimensional path integration analysis of non-linear responses of simply-supported beams

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 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.