轴向荷载作用下梁结构动力特性的随机分析

传统梁结构动力特性分析方法由于忽略结构参数的不确定性而不能满足实际工程设计需要,因此,将响应面法(RSM)、有限元法(FEM)和蒙特卡罗法各自的优点相结合,提出一种新的结构随机动力特性计算方法-混合分析法。该方法的最大特点是有效地利用响应面法(RSM)、有限元法(FEM)和蒙特卡罗法(MCS)各自的优点,并将其充分地结合起来。然后,运用该方法分析一简支梁自振频率的统计值。结果表明基于确定性模型的梁结构频率响应分析仅能给出频率响应的均值,忽略结构随机参数对频率响应的影响。为获得准确的频率响应值,有必要在今后的结构动力特性分析中考虑结构参数随机性的影响。最后,进行梁结构随机动力特性计算的敏感性因素分析,并指明影响梁结构动力特性的主要随机因素。

Stochastic analysis of the dynamic characteristics of beams subjected to axial loads

Due to ignoring the effect of the randomness of structural parameters,conventional deterministic analysis cannot provide complete information regarding the dynamic characteristics of beams.A stochastic finite-element-based algorithm for probabilistic free vibration analysis of beams is proposed through combining the advantages of the response surface method,the finite element method and Monte Carlo simulations.Using the proposed method,a probabilistic free vibration analysis of a simply supported beam is performed.The results show that the free vibration analysis based on deterministic models gives only the mean natural frequency and misses the deviations present because of randomness in the structural parameters.For accurate natural frequency,it is necessary that the analysis technique incorporate the effect of structural parameter randomness.In addition,the effects of various parameters on the statistical moments of the frequency response of beams are investigated.