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Stochastic eigenfrequency and buckling analyses of plates subjected to random temperature distributions

机译：随机温度分布的板的随机特征频率和屈曲分析

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摘要

Many studies previously reported in the literature have demonstrated, both theoretically and experimentally, the influence of thermally-induced stresses on the static and dynamic behavior of structures, due to the so-called stress-stiffening effect. In most cases of practical interest, temperature variations associated to environmental and operational conditions are governed by rather complex combinations of conduction, convection and radiation mechanisms. As a result, the temperature values at different points of a structure are very difficult to control and can rationally be considered as random quantities. In this context, the present paper addresses the stochastic modeling and characterization of the influence of thermal stresses on the natural frequencies of thin rectangular plates, assuming space-dependent temperature fluctuations modeled as stationary two-dimensional Gaussian random fields. For this purpose, based on the hypotheses of the classical Kirchhoff plate theory, a Rayleigh-Ritz-based dynamic model is first derived for the bending vibrations of plates, accounting for the presence of thermal stresses. This model is combined with the Karhunen-Loeve expansion (KL), which is used to discretize the temperature random field, after which the statistics of the random natural frequencies are estimated by Monte Carlo sampling. Numerical simulations are performed for plates under free boundary conditions. Simulation results, which encompass sampling-based statistics for the thermal stresses and the first six natural frequencies of the plate, are presented and discussed. In addition, since thermal stresses can induce buckling, reliability has also been estimated considering this type of failure. Results enable to conclude that space-dependent temperature uncertainty can be significant upon the vibration and buckling behavior of plates, which justifies its consideration.
机译：本文在理论上和实验中据证明了本文报道的许多研究，由于所谓的应力加强效应，在理论上和实验中展示了热引起的应力对结构静态和动态行为的影响。在大多数实际兴趣的情况下，与环境和操作条件相关的温度变化是通过相当复杂的传导，对流和辐射机制的组合来控制。结果，结构的不同点处的温度值非常难以控制，并且可以合理地被认为是随机的量。在这种情况下，本文解决了热应力对薄矩形板的自然频率影响的随机塑造和表征，假设空间依赖于静止二​​维高斯随机场所呈现的温度波动。为此目的，基于经典柯克霍夫板理论的假设，首先推导出基于瑞利丽升的动态模型，用于板的弯曲振动，占热应力的存在。该模型与Karhunen-Loeve扩展（KL）相结合，用于将温度随机场分散，之后通过蒙特卡罗采样估计随机自然频率的统计数据。在自由边界条件下对板进行数值模拟。展示和讨论了仿真结果，其包括用于热应力的基于采样的统计数据和板的前六个自然频率。另外，由于热应力可以诱导屈曲，因此考虑到这种类型的故障也估计可靠性。结果可以得出结论，空间依赖性温度不确定度在板的振动和屈曲行为上可能是显着的，这证明了其考虑。

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