Exact forced torsional vibration solution of a shaft with multiple discontinuities and arbitrary boundary conditions

• Main Authors: Meilong Chen, Shuying Li, Hongliang Li, Siyuan Liu
• Format: Article
• Language: English
• Published: JVE International 2020-06-01
• Series: Journal of Vibroengineering
• Subjects: analytical solution; forced torsional vibration; integral transformations; arbitrary boundary conditions
• Online Access: https://www.jvejournals.com/article/20938

In this paper, the method based on Laplace transform and Fourier transform and their inverse transforms is developed to give an exact solution to the forced torsional vibration of a shaft subjected to multiple inertias, multiple elastic supports, arbitrary boundary conditions and arbitrary excitation forces. Two simple cases are used to show in detail how this developed method can obtain an exact analytical solution to the forced torsional vibration of shaft and the results are compared with Eigenfunction Expansion Method and Finite Element Method (FEM) to demonstrate the accuracy and effectiveness of the developed method. Two more complex cases are investigated to further show the superiority of the developed method over FEM in highly efficient and accurate. Finally, using the developed method, the effects of parameters on forced torsional vibration response of shaft are discussed, including the stiffness, the location of elastic supports and the time interval of impact loading. The developed method can provide a reliable theoretical base not only for analysis and fault diagnosis of a shaft system in engineering signal testing projects but also for the verification of other numerical and analytical methods.