考虑参数不确定性的非线性梁随机振动分析

Random vibration analysis of non-linear beams with parameter uncertainties

非线性系统的随机振动分析一直是结构动力学领域中的难点,已有一些研究表明基于矩等效的线性化方法在功率谱预测上会得到不恰当的分析结果;另一方面,由于不确定性在实际工程中普遍存在,如果同时考虑非线性和不确定性,更是显著增加了问题难度。本文以具有非线性非理想边界梁为研究对象,基于梁模型的动力学微分方程推导了对应的广义频响函数,并应用Volterra级数理论建立了非线性系统随机振动的谱分析方法,最后,结合蒙特卡洛抽样方法计算了具有参数不确定性非线性梁响应功率谱的均值和方差,讨论了不确定性对结构随机振动响应统计特征的影响。

The analysis of random vibration of nonlinear systems has been a difficult area in the field of structural dynamics.Some studies have shown that linearization methods based on moment equivalence give inappropriate analytical results of power spectral density(PSD).On the other hand,since uncertainty is prevalent in practical engineering,it increases the problem difficulty significantly if both nonlinearity and uncertainty are considered.In this paper,beams with a nonlinear nonideal boundary are studied.The corresponding generalized frequency response function is derived based on the differential equation of the beam model.And the spectral analysis method of the nonlinear system with random vibration is established by the Volterra series theory.Finally,the mean and variance of the response PSD of the nonlinear beam with parametric uncertainty are calculated by combining the Monte Carlo method.The influence of uncertainty on the statistical characteristics of the random vibration response of the structure is discussed.The work in this paper is a reference for the prediction and control of stochastic vibration of practical nonlinear systems.