附加集中质量块悬臂梁路径积分法分析

Path Integration Analysis on a Cantilever Beam with a Lumped Mass

对在高斯白噪声激励下附加集中质量块悬臂梁的随机振动响应进行了研究。利用泰勒公式展开法,替换系统振动方程中加速度非线性项。根据替换后的等效非线性振动方程,运用路径积分法(PIS)求解悬臂梁响应的稳态概率密度函数数值解,将所得结果与蒙特卡罗模拟法(MCS)及等效线性化法(EQL)所得结果进行比较。结果表明:所提出的方法能用于求解该类型悬臂梁响应的稳态概率密度函数。

This paper presents a path integration analysis on random vibration of a cantilever beam with a lumped mass under Gaussian white noise. Using the Taylor series expansion method, the nonlinear governing modal equation of motion is simply modified by an equivalent nonlinear equation without the nonlinear modal acceleration term. According to the e quivalent nonlinear equation, a path integration solution （PIS） procedure is adopted to obtain the stationary probability density function （PDF） of the response of the cantilever beam. The results are compared with the ones given by Monte Carlo simulation （MCS） and the equivalent linearization （EQL） method. Comparison shows that the proposed solution procedure can present a satisfactory stationary PDF solution for this kind of cantilever beam.