Natural frequencies of elliptical cylindrical shells

✍ Scribed by G. Yamada; T. Irie; S. Notoya

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 301 KB
• Volume: 101
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(85)80049-3

✦ Synopsis

NATURAL FREQUENCIES OF ELLIPTICAL CYLINDRICAL SHELLS

The natural frequencies (the eigenvalues of vibration) are tabulated for elliptical cylindrical shells under six practical combinations of boundary conditions. Though the free vibration of the shells has been studied by several researchers [1-5], sufficient engineering data have not been presented for all combinations of boundary conditions.

The numerical calculations have been carried out by use of the Ritz method which assures an accuracy sufficient for practical purposes. A brief explanation of the method and the symbols used here are necessary in order for the results presented to be easily understood. With the axial length denoted by L, the radius of curvature by R, and the wall thickness by H, the cylindrical co-ordinates (x, 0, z) are taken in the middle surface of an elliptical cylindrical shell. The maximum kinetic energy of the shell is written as

in terms of the maximum deflection displacements u, o and w in the axial, circumferential and normal directions, respectively, where p is the mass density and to is the frequency in radians/second. Based upon the Sanders theory, the maximum strain energy is written as