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针对梁结构振动在工程应用中的问题,以梁元件的弯曲振动为例,从梁元件弯曲振动的控制微分方程出发,推导了梁元件弯曲振动的边界元法解析公式,提出了局部区间步长细化的频率扫描方法,利用Matlab软件编制了梁元件振动问题求解的边界元法解析程序,最后给出了梁元件振动问题求解的相关算例。结果表明,边界元法对梁结构进行动态分析方便简单,局部区间步长细化频率扫描方法比常规扫描方法高效准确。
Aiming at the problem of beam structure vibration in engineering application, the bending vibration of beam element is taken as an example. Based on the governing differential equation of bending vibration of beam element, the analytical solution of boundary element method of bending vibration of beam element is deduced. A detailed frequency sweep method is presented. The Matlab software is used to develop the analytical solution of the boundary element method for solving the vibration problem of the beam element. Finally, the relevant examples of solving the vibration problem of the beam element are given. The results show that the boundary element method is very simple and convenient to analyze the beam structure dynamically. The frequency scanning method of the local interval step thinning is more efficient and accurate than the conventional scanning method.