A Spectral-Tchebychev Solution for Tapered Axially Functionally Graded Straight and Curved Beams with Multiple Attached Masses

This paper conducts free vibration analysis of AFG straight and curved beams with multiple attached masses based on the spectral-Tchebychev method. The mass matrix and stiffness matrix of the AFG beam element with tip mass have been derived in detail. All the presented results were compared with existing research or the commercial software ANSYS to verify validity and accuracy of the proposed method, and it turned out that the spectral-Tchebychev method can deal with both AFG straight and curved beams with multiple attached masses and non-uniform cross-sections under different boundary conditions. And the attached masses were found to have a significant impact on the vibration forms of high-order modes of curved beams. Furthermore, the spectral-Tchebychev method can achieve high accuracy with much fewer degrees of freedom compared to finite element method and other methods used in existing literature, and the computing efficiency is much higher than that of ANSYS.