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Timoshenko梁的振动方程一般较为复杂,很难给出解的解析形式,尤其对于梁为变截面的情况。采用直接模态摄动法可将Timoshenko梁的振动微分方程组转化为一组非线性代数方程组,不仅可以简化计算过程,而且计算结果具有较高的精度。本文应用直接模态摄动法研究了变截面Timoshenko固端及简支梁的自由振动特性,并通过算例,讨论了这两种支撑条件下梁高的斜率及长细比对梁各阶主频率的影响,得到了相同条件下深梁效应对固端梁的影响要大于对简支梁的影响,且其影响随梁高的斜率增加而增大的结论。
The vibration equation of Timoshenko beam is generally complicated, and it is difficult to give an analytical form of the solution, especially for a beam with a variable cross section. The direct mode perturbation method can be used to transform the Timoshenko beam vibration differential equations into a set of nonlinear algebraic equations, which not only simplifies the calculation process, but also has high accuracy. In this paper, the free-vibration characteristics of Timoshenko fixed-end and simply supported beams with variable section are studied by using direct mode perturbation method. The slope and slenderness ratio of beam height under different supporting conditions are discussed. Under the same conditions, the effect of deep beam on solid beam is greater than that on simple beam, and the effect of beam depth increases with the slope of beam height.