一种改进傅里叶级数方法的船舶轴系回旋振动动态特性研究

摘要

The gyroscopic vibration dynamic characteristics of a multi-span non-uniform shafting with arbitrary boundary conditions are presented based on an Improved Fourier Series Method. Firstly, the differential equation for the gyroscopic vibration of an uniform beam with lumped masses and gyroscopic effect is formulated. Then, the mass, stiffness and the force matrices for the shafting are derived using an Improve Fourier Series Method.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. The Newmark method is used to calculate the numerical result in time. Comparing with the results obtained by FEA software ANSYS and state standard results validates the correct of the method. And the dynamic characteristics of a shafting with the gyroscopic effect under the rating speed are described.%文章采用一种改进的傅里叶级数方法(Improved Fourier Series Method,IFSM)对弹性支撑边界条件下多跨距变轴颈轴系进行了回旋振动动态特性研究.首先推导了考虑集中质量及回旋效应的均匀梁回旋振动微分方程；其次应用一种改进的傅里叶级数方法推导了轴系的质量、刚度及激励力矩阵.在这一方法中,位移函数被表示为傅里叶余弦级数展开与一个辅助的多项式函数的叠加,进而成功地克服了弹性边界的不连续性.采用Newmark方法在时域内直接数值积分求解响应.通过与有限元软件ANSYS仿真结果及国家标准的结果对比,验证了文中分析方法的正确性.并研究了一轴系在额定转速下正逆回旋的动态特性.