中文摘要：

文章分析了非均质变截面弹性杆轴向自由振动问题，该类杆件的弹性模量、横截面面积和单位杆长质量是截面位置的函数，对于函数的具体形式无任何限制条件。运用插值矩阵法可一次性地计算出各阶振动固有频率，它们具有同阶精度，并可同时获取相应的振型函数。数值计算结果与现有结果对比表明了文中方法的有效性和良好的计算精度。

英文摘要：

This paper deals with the longitudinal vibration problems of functions of section location of elastic straight bar including elasticity modulus, section area and mass per unit length under the nor- mal conditions. There is no restriction to the specific form of function. By applying the interpolating matrix method to solving the established equations, all the natural frequencies of longitudinal vibra- tion companying with the corresponding vibration mode functions of bar with variable cross-section are calculated at a time. All the calculated natural frequencies of longitudinal vibration have the same high accuracy. The numerical results show that the computed results from the presented method have very high accuracy compared with the existing solutions.