Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Frequencies and Mode Shapes of Annular Plates tilth Variable Thickness by the Ritz Method in Three-Dimensional Analysis

변두께를 갖는 두꺼운 환형판의 삼차원적 리츠방법에 의한 진동수와 모드형상

  • Published : 2001.08.01
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Abstract

The Ritz method Is applied In a three-dimensional (3-D) analysis to obtain accurate frequencies for thick. linearly tapered. annular plates. The method is formulated for annular plates haying any combination of free or fixed boundaries at both Inner and outer edges. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate. and a1gebraic polynomials in the radial and thickness co-ordinates. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant figures is demonstrated. Comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2-D classical thin place theory. Extensive and accurate ( four significant figures ) frequencies are presented 7or completely free. thick, linearly tapered annular plates haying ratios of average place thickness to difference between outer radius (a) and inner radius (b) radios (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-shear. In-plane stretching, and torsional. Because frequency data liven is exact 7o a\ulcorner least four digits. It is benchmark data against which the results from other methods (e.g.. 2-D 7hick plate theory, finite element methods. finite difference methods) and may be compared. Throughout this work, Poisson\`s ratio $\upsilon$ is fixed at 0.3 for numerical calculations.s.

Keywords

References

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