连续多跨梁结构振动特性分析

Vibration Analysis of Multi-Span Beam System

以连续多跨梁结构为计算模型,对其自由振动特性进行计算分析。首先将梁的弯曲位移函数以改进傅立叶级数进行表示,在结构两端边界与耦合边界处引入横向位移弹簧和旋转约束弹簧,通过改变其刚度值大小来模拟任意边界条件与耦合条件。此外,正弦函数的引入能够改善以往求解过程在边界处存在的不连续或者跳跃现象。在求解框架中,先通过能量原理对整个结构进行能量描述,然后结合瑞利-里兹法对其进行求解。最后进行数值仿真验证,仿真对比结果表明文中方法是合理的,并且具有良好的计算精度与收敛速度。

In this investigation, the free vibration analysis model of multi-span beam system is constructed based on Bernotdli-Euler beam theory. Firstly, the beam displacement funetion is generally sought as improved Fourier cosine series, and four sine terms were introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. The linear and rotational springs are arranged along the boundary edges and coupling edges. The various boundary supports and coupling conditions are realized by setting linear displacement and rotational spings with different stiffness constants. In the current solution framework, the beam system is described based on the energy principle. Then the solution is determined using the Rayleigh-Ritz method. Finally, numereous numerical examples are carried out to validate the current method. The compariorts show that the presented approach has good computation accuracy and convergence speed.