在考虑参数不确定性的实际结构动力系统中,确定激励作用下的响应也必然具有随机性特征,其统计特征的获取是随机结构动力系统振动分析的难点问题。本文针对动力系统的随机响应,在系统不确定性特征参数均服从Gauss分布条件下,基于Fourier-Hermite多项式展开,通过广义模型降维、多重Gauss-Hermite数值积分的方法确定其展开系数,进而获得系统响应逼近的显式正交多项式函数形式,并嵌入局部MCS模拟,形成随机振动系统统计分析方法,以获得系统响应统计特征。进而针对板结构,利用FEM建模,并基于提出的方法开展原点振动响应统计分析,其数值仿真结果表明:提出的方法可获得与直接MCS模拟较一致的分析结果,能够获得随机板结构振动响应统计特征,并基于离散刚度边界的FEM网格细化预测连续刚度边界的随机板结构振动响应统计特征。
It is sure that the responses of practical structural dynamic systems considering parametric uncertainty under deterministic excitations also have characteristics of randomness. The acquisition of their statistical features is a difficult problem in vibration analysis of stochastic structural dynamic systems. Here, under the condition of a system’s uncertain characteristic parameters obeying Gauss distribution, based on Fourier-Hermite polynomial expansion, the stochastic responses of the dynamic system were solved using the generalized model dimension-reducing and the multi-dimensional Gauss-Hermite numerical quadrature to determine expansion coefficients, and obtain the system’s responses approximate solution in the form of explicit orthogonal polynomial function expansion. Then, the solution was embedded with the local Monte Carlo simulation (MCS) to form the statistical analysis method for random vibration systems, and acquire the statistical characteristics of the system responses. Furthermore, using FEM modeling, based on the proposed above method, the statistical analysis was conducted for plate structures’ vibration responses. Numerical simulation results showed that the statistical analysis results using the proposed method agree well with those using the direct MCS method to obtain statistical characteristics of random plate structures’ vibration responses; the statistical characteristics of random plate structures’ vibration responses under a continuous stiffness boundary condition can be predicted based on the FEM mesh refinement of a discrete stiffness boundary.