This study deals with two general solutions for a simply supported linear elastic Bernoulli–Euler beam with a stochastic bending flexibility, subjected to a deterministic loading. Two model problems are considered. The first problem is associated with a trapezoidally distributed load, whereas the second problem treats a sinusoidally distributed load. The importance of the solution for the trapezoidal load lies in its practicality. The derivation of stochastic characteristics for random beams under a sinusoidal load is useful due to the expandability to generally distributed loads by a Fourier sine series expansion. Numerical results are reported for various cases illustrating the effect of stochasticity of the beam’s properties on its flexural response.

这项研究针对具有确定性载荷的具有随机弯曲挠性的简单支撑线性弹性贝努利-欧拉梁提供了两种通用解决方案。考虑了两个模型问题。第一个问题与梯形分布的载荷有关，而第二个问题则与正弦分布的载荷有关。该解决方案对于梯形载荷的重要性在于其实用性。在正弦载荷下，随机梁的随机特性的推导是有用的，因为通过傅立叶正弦级数展开可将其扩展到一般分布的载荷。报告了各种情况的数值结果，这些结果说明了梁特性的随机性对其挠曲响应的影响。