用二阶共轭方程近似解研究楔形杆振动及屈曲  

Study on Vibration and Buckling of Wedge Shaped Rod with Approximate Solutions of Second-Order Conjugate Equation

作　　者：吴晓 肖珍 WU Xiao;XIAO Zhen(Furong College,Hunan University of Arts and Science,Changde 415000,China)

机构地区：[1]湖南文理学院芙蓉学院,常德415000

出　　处：《湖南师范大学自然科学学报》2024年第3期137-142,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(52008164)。

摘　　要：证明了任意二阶变系数线性方程都可以转化为二阶共轭线性方程。利用自变量变换、因变量变换求得了含有大参数二级共轭线性方程的近似解,此近似解即为楔形杆固有纵振、扭振、剪切振动及屈曲的模态函数。利用模态函数结合边界条件推导出确定固有纵振、扭振、剪切振动频率及屈曲载荷的特征方程,解此特征方程便可以求得固有纵振、扭振、剪切振动频率及屈曲载荷。与有关文献采用Bessel函数法求得的固有纵振、扭振、剪切振动频率及屈曲载荷进行比较,二阶共轭线性方程近似解法不但计算过程简便,而且计算精度也很高,更适合工程设计人员掌握应用。It was proved that any second-order linear equation with variable coefficients could be transformed into second-order conjugate linear equation.Approximate solutions of the second-order conjugate linear equation with large parameters were obtained by using the transformation of independent variable and dependent variable.And they are the modal function of the natural longitudinal vibration,torsional vibration,shear vibration and buckling of the wedge shaped rod.The characteristic equations for determining the frequencies of natural longitudinal vibration,torsional vibration,shear vibration and buckling load were derived by combining the modal function with the boundary conditions.The frequencies of natural longitudinal vibration,torsional vibration,shear vibration and buckling load could be obtained with solving the characteristic equation.Compared with Bessel function method in relevant literatures,the natural longitudinal vibration,torsional vibration,shear vibration frequency and buckling load obtained by approximate solutions of second-order conjugate linear equation,the method is simpler in the calculation process with high calculation accuracy,which is more suitable for engineering designers to master for application.

关 键 词：共轭方程 楔形杆 固有频率 屈曲载荷 

分 类 号：O321[理学—一般力学与力学基础] TU323.1[理学—力学]