3-DIMENSIONAL VIBRATIONS OF THICK, LINEARLY TAPERED, ANNULAR PLATES

The Ritz method is applied in a three-dimensional (3-D) analysis to ob tain accurate frequencies for thick, linearly tapered, annular plates. The method is formulated for annular plates having any combination of free or fixed boundaries at both inner and outer edges. Admissible fu nctions for the three displacement components are chosen as trigonomet ric functions in the circumferential co-ordinate, and algebraic polyno mials in the radial and thickness co-ordinates. Upper bound convergenc e of the non-dimensional frequencies to the exact values within at lea st four significant figures is demonstrated. Comparisons of results fo r annular plates with linearly varying thickness are made with ones ob tained by others using 2-D classical thin plate theory. Extensive and accurate (four significant figures) frequencies are presented for comp letely free, thick, linearly tapered annular plates having ratios of a verage plate thickness to difference between outer radius (a) and inne r radius (b) ratios (h(m)/L) of 0.1 and 0.2 for b/L = 0.2 and 0.5. All 3-D modes are included in the analyses; e.g., flexural, thickness-she ar, in-plane stretching, and torsional. Because frequency data given i s exact to at least four digits, it is benchmark data against which th e results from other methods (e.g., 2-D thick plate theory, finite ele ment methods) and may be compared. Throughout this work, Poisson's rat io v is fixed at 0.3 for numerical calculations.