考虑初始荷载影响下梁动力特性的有限元分析

从非线性弹性理论出发，应用Hamilton原理，给出了考虑初始弯曲和轴向应力影响的一般形式的单元刚度矩阵，建立了考虑初始荷载影响时梁动力分析的有限元方法，编制了电算程序。通过与解析解结果的比较，验证了有限元公式。讨论了初始荷载的类型、大小及结构自身刚度（惯性矩、惯性半径、跨度）等因素在考虑初始弯曲应力影响时对不同约束情况下梁动力特性的影响。结果表明，荷载初始弯曲应力的存在提高了梁的自振频率，这种影响与荷载的大小及结构自身的刚度有关。

Finite element analysis for effect of initial load on dynamic characteristic of a beam

Based on nonlinear elastic theory and Hamilton’s principle,a generalized element stiffness matrix considering effects of initial bending and axial stresses induced by initial load was presented.A finite element method for dynamic analysis of a beam considering the effect of initial load was built with corresponding computer programs produced to facilitate the analysis.The formula was validated through comparing its results with the analytical solution.The effects of key physical factors including type and magnitude of initial load,and stiffness parameters,such as,cross-sectional inertia moment,inertia radius and span on the dynamic characteristics of the beam with various restraint conditions were discussed with the effect of initial flexural stress considered.The results suggested that the natural frequencies of the beam increase due to the existence of flexural stress induced by initial load and such an effect relates to the magnitude of initial load and stiffness parameters of the beam.