分段轴压阶梯梁自由振动及稳定性分析的传递函数方法

采用分布传递函数方法,分析任意多段分段常轴压阶梯梁的自由振动和稳定问题,得到形式统一的封闭解析解。根据梁横截面几何尺寸、梁材料和轴压沿梁轴线的变化,将梁分成多段子梁,对每一子梁采用传递函数方法得到其解析解,通过各子梁间的位移连续和力平衡条件,得到分段常轴压阶梯梁的各阶自由振动频率和失稳载荷及其相应的模态形状。通过三阶梯梁的算例验证本文方法的正确性,并以四阶梯梁为例,计算分段轴压多阶梯梁自由振动的固有频率。

Free Vibration and Stability of Multiple-step Beams under Stepped Axial Pressure by Distributed Transfer Function Method

With the distributed transfer function method,a closed-form solution is obtained for free vibration and stability of a multiplestep beam under stepped axial pressures.According to variations of the geometry of the cross-section,the material and the axial pressure in axial direction,the beam is divided into multiple sub-beams whose closed-form solution is obtained with the distributed transfer function method.The natural frequencies and buckling loads along with their mode shapes are obtained by using the displacement continuity conditions and force balance conditions between the sub-beams.The method was validated through numerical examples of three-step beams.The natural frequencies of multiple-step beams under different axial pressure in each section were calculated with the example of four-step beams.