文章以动力学方程为基础，得出关于两端弹性固定纵向受压梁的横向固有频率与压力荷载的精确表达式；通过变分得出其近似表达式。两端弹性固定端选取四种典型刚性系数为例，辅以图示法将精确解与近似解进行比较，得到自由端附有质量的轴压悬臂梁的固有频率的平方与轴向力呈近似线性关系的结论。通过计算，近似解与精确数值解相差很小，精度满足工程上的要求。以此为依据，只要能够测出两种不同载荷下的固有频率，就可以通过近似线性的结论识别出两端弹性固定受压结构的弹性失稳荷载，因此文中提出了一种无损检测的分析方法。%Basing on the dynamics equation, the exact expression for horizontal natural frequency and pres-sure loads of the axis pressure beam fixed at both ends with allowed angel is obtained; the approximate ex-pression is derived from the variational method. Take four kinds of typical rigidity coefficients for example at both elastic fixed, graphic method as an auxiliary to compare the exact solution and approximate solution, the conclusion of the relationship between the square of the natural frequency and the axial force of the axis pressure beam fixed at both ends with allowed angel can be obtained, which is approximately linear re-lationship. By calculating, it is shown that the difference between the approximate solution and the exact nu-merical solution is small, and the accuracy can meet the engineering requirements. As a basis, as long as the natural frequency in two different load can be measured, the elasticity instability load of the compression structure fixed at both ends with allowed angel can be identified by approximately linear conclusion, and therefore an identification method of instability load is presented.
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