轴向受载多跨弹性支撑连续梁的模态分析

Modal Analysis of Multi-span Beam with Intermediate Elastic Eearing under Axial-loaded

以轴向受载的多跨连续等截面Bernoulli-Euler梁为研究对象,将多跨连续梁的自由振动转化为单跨梁在支座反力下的受迫振动。采用Laplace变换求解振动微分方程。根据连续梁的边界条件及弹性支撑处的变形相容条件得出频率特征方程。由频率特征方程得出自振频率,及其相应模态。结合数值算例,验证了理论推导与计算程序的正确性。最后分析了在不同边界下,中间弹性支撑刚度对连续梁稳定临界轴压的影响。

The model analysis of multi-span uniform Bernoulli-Euler beams with intermediate elastic bearing un- der axial force is studied. For the equivalent system of continued beams which support reaction force substituted for elastic bearing, Laplace transformation to obtain the frequency characteristic equations under the boundary condi- tions of continued beams and the deformation compatibility conditions at the elastic bearing are used. It is obtained frequency from the frequency characteristic equations, and corresponding mode of continued beams. According to numerical example, between the result and the result from theoretical value are conducted for the validity. The effects of axial force on critical axial compressive of continued beams under different boundary conditions are dis- cussed.