EXPLICIT FREQUENCY EQUATION AND MODE SHAPES OF A CANTILEVER BEAM COUPLED IN BENDING AND TORSION

✍ Scribed by J.R. BANERJEE

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 160 KB
• Volume: 224
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2194

✦ Synopsis

Exact explicit analytical expressions which give the natural frequencies and mode shapes of a bending}torsion coupled beam with cantilever end condition are derived by rigorous application of the symbolic computing package REDUCE. The expressions are surprisingly concise and very simple to use. By way of illustration in this paper, they are used to determine the natural frequencies and mode shapes of a cantilever wing with substantial coupling between the bending and torsional modes of deformation. The results are compared with exact published results to con"rm the correctness and accuracy of the expressions. The derived expressions can be used to solve bench-mark free vibration problems as an aid in validating the "nite element and other approximate methods. They are also intended for future applications in aeroelastic and/or optimization studies. Computer implementation and a comparison of solution times show that there is more than a four-fold advantage in c.p.u. time when using the explicit expressions as opposed to the alternative numerical method involving determinant evaluation and matrix manipulation.