THREE-DIMENSIONAL VIBRATIONS OF THICK CIRCULAR AND ANNULAR PLATES

✍ Scribed by J. So; A.W. Leissa

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 238 KB
• Volume: 209
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1997.1228

✦ Synopsis

The Ritz method is applied in a three-dimensional (3-D) analysis to obtain accurate frequencies for thick circular and annular plates. The method is formulated in a manner which allows one to have any combination of free or fixed plate boundaries. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate, and algebraic polynomials in the radial and axial co-ordinates. Upper bound convergence of the non-dimensional frequencies to at least four significant figures is demonstrated. Comparisons of results are made with ones obtained by others using 2-D Mindlin thick plate theory, and with other 3-D solutions. Extensive and accurate (four significant figure) frequencies are presented for completely free circular plates having thickness-to-diameter ratios of 0•2, 0•3, 0•4 and 0•5 for Poisson's ratios n = 0, 0•3 and 0•499. Frequencies are also given for thick annular plates having a thickness-to-outer-diameter of 0•2, inside-to-outside-diameter ratios of 0•1, 0•5 and 0•9, and n = 0•3. All 3-D modes are included in the analyses; e.g., flexural thickness-shear, inplane stretching, and torsional. The circular and annular plate frequency data given is exact to at least four digits, thus being benchmark data against which results from 2-D thick plate theories or other approximate methods (e.g., finite elements) may be compared.