A linearly tapered beam finite element incorporating shear deformation and rotary inertia for vibration analysis

✍ Scribed by C.W.S. To

• Book ID: 104154143
• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 431 KB
• Volume: 78
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(81)80118-6

✦ Synopsis

Explicit expressions for the element mass and stillness matrices of a linearly tapered beam finite element including shear deformation and rotary inertia are given in this paper. The element cross section rotation is assumed to be a sum of the slope of the transverse displacement and the shear. The cross-sectional dimensions vary linearly along the length of the element. Two series of eigenvalue solutions have been carried out. One was performed with various taper ratios in order to provide a comparison with classical cases. The other was used to determine the aspect ratio effect on the eigenvalues of thin-walled tapered cantilever beam structures. The approach presented is straightforward, and allows comparisons to be made with other explicit solutions without recourse to numerical examples.