简支梁动力有限元最后两阶自振频率的误差源

Error Sources of the Last Two Natural Frequencies of Simple Beam Obtained by Dynamic Finite Element

以一简支梁为例,用有限元计算的频率值与频率值的精确解进行比较,结果发现:不管划分多少单元,有限元算出来的最后两阶频率与精确解之间都相差巨大,从建立有限元法的运动方程和定解条件入手和数值拟合的角度详细分析了误差产生的原因。建议在采用有限元计算杆系结构动力反应时,应该对最后两阶自振频率进行相应的处理或者采用比较完善的频率精确解求解技术。

For simply supported beam a new phenomenon was discovered by comparing the frequencies obtained by dy-namic finite element method and by accurate analytical solution, i. e. , no matter how many elements the beam is divided into, the last two frequencies obtained by dynamic finite element method are significantly higher than that predicted by exact analytical solution. In this paper the source of the error is explored. The authors suggest that if structural dynamic finite element method is used to analyze dynamic response of girder structure, the last two natural frequencies of the structure should be removed or relatively perfect solution techniques for determining the precise frequencies should be a- dopted.