弹性地基上Euler-Bernoulli梁的热屈曲模态跃迁特性

Characteristics of thermally buckling mode transition of Euler-Bernoulli beams resting on an elastic foundation

采用解析方法研究了置于线性弹性地基上的Euler-Bernoulli梁在均匀升温载荷作用下的临界屈曲模态跃迁特性;分别在两端不可移简支和夹紧边界条件下,给出了弹性梁屈曲模态跃迁点的地基刚度值以及屈曲载荷值的精确表达式,并分析了模态跃迁特点。结果表明:随着地基刚度参数值的增大临界屈曲模态通过跃迁点从低阶次向高阶次跃迁;两端简支梁的模态跃迁具有突变特性,而两端夹紧梁的模态跃迁则是一个缓慢变化过程,它是通过端截面的弯矩或曲率的正负号改变实现的。

Behaviors of transitions of the buckling mode shapes of Euler-Bernoulli beams resting on a linear elastic foundation and subjected to a uniform temperature rise are investigated by analytical method.For the beams with both of the ends immovably simply supported or clamped,analytical solution for the transition values of the elastic foundation stiffness and the critical buckling loads corresponding to the transition points are obtained and the characteristics of the mode transition are analyzed.The results show that the critical buckling modes changes from the lower orders to the higher ones with the increase in the values of the stiffness of the elastic foundation.The mode transition of the beams with simply ends occurs abruptly,but that with clamped ends changes continuously through the variation of the sign of the end bending moment,or the curvature.