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Transverse Vibration Analysis of Shafting Based on an Improved Fourier Series Method
ZHOU Hai-jun;LV Bing-lin;DU Jing-tao;Wen L. Li;LI Wan-you
2011, 31 (4):
68-72.
DOI: 10.3969/j.issn.1006-1355-2011.04.016
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.
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