【摘要】 利用递推随机有限元方法研究了具有随机参数结构的重特征值问题。采用随机收敛的非正交多项式展式表示未知的随机重特征值和随机特征向量,建立了和摄动法类似的一系列确定的递推方程,通过求解这些递推方程,得到了重特征值的统计值。算例表明,同基于二阶泰勒展开的摄动随机有限元法相比,递推随机有限元法的结果能在较宽的随机涨落范围内更好地逼近蒙特卡洛模拟结果。更多还原

【Abstract】 Based on recursive stochastic finite element method(RSFEM),the problem on repeated eigenvalues of structures with random parameters is studied in this paper.The repeated eigenvalues and eigenvectors of random structures are expressed as the expansions of nonorthogonal polynomials.To deal with random eigenvalues problems,a set of deterministic recursive equations is set up using perturbation techniques.After the coefficients of nonorthogonal polynomial expansions are obtained,statistics of the repeated eigenvalues are given.Numerical examples show that compared with perturbation stochastic FEM,the results of RSFEM are closer to those of Monte-Carlo simulation in a wide range of random fluctuation.更多还原