Abstract: In this paper, an improved Fourier series method (IFSM) is employed to determine the transverse free vibration of a multi-span non-uniform shafting system with arbitrary boundary conditions. At first, the differential equation for the transverse free vibration of a uniform beam with lumped masses is formulated. Then, the mass and stiffness matrices for the shafting are derived using the IFSM, and then all the eigenvalues and eigenvectors are readily obtained by solving a standard matrix eigenvalue equation. In this method, the displacement function is expanded as a single Fourier cosine series plus an auxiliary polynomial function. The auxiliary function is used to overcome the discontinuities of the resilient boundary. Numerical results are presented to validate the correct of the method. And the stiffness effect of connecting flange is described.

Key words: vibration and wave, shafting, transverse vibration, improved Fourier series method, auxiliary function, resilient boundary

摘要： 采用基于改进傅里叶级数的方法（Improved Fourier Series Method，简称IFSM）对弹性支撑边界条件下多跨距变轴颈推进轴系进行横向自由振动分析。首先推导带集中质量点的均匀梁横向自由振动微分方程；其次应用IFSM导出轴系的质量与刚度矩阵，通过标准的特征值分解得到轴系固有频率及振型。在改进傅里叶级数方法中，位移函数被表示为一个傅里叶余弦级数展开与一个辅助的多项式函数的叠加，解决弹性边界的不连续性问题。通过数值仿真分析计算，分析中间连接法兰的刚度影响，验证分析方法的正确性与有效性。

关键词: 振动与波, 轴系, 横振, 改进傅里叶级数, 辅助函数, 弹性支撑边界