Three-dimensional vibrations of thick, linearly tapered, annular plates
Three-dimensional vibrations of thick, linearly tapered, annular plates
复制标题
厚线性锥形环形板的三维振动
DOI：
10.1006/jsvi.1998.1803
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发表时间：
1998
影响因子：
4.7
通讯作者：
A. Leissa
中科院分区：
文献类型：
--
作者：
J. Kang;A. Leissa
摘要 Ritz 方法应用于三维 (3-D) 分析，以获得厚线性锥形环形板的准确频率。该方法针对在内边缘和外边缘处具有自由或固定边界的任意组合的环形板而制定。三个位移分量的允许函数被选择为圆周坐标中的三角函数以及径向和厚度坐标中的代数多项式。证明了无量纲频率的上限收敛到至少四个有效数字内的精确值。将厚度线性变化的环形板的结果与其他人使用二维经典薄板理论得到的结果进行了比较。给出了完全自由、厚、线性锥形环形板的广泛且准确的（四个有效数字）频率，其平均板厚度与外半径（a）和内半径（b）之间的差值之比（hm/L）为0·1和0·2（对于b/L=0·2和0·5）。所有 3-D 模式均包含在分析中；例如，弯曲、厚度剪切、面内拉伸和扭转。由于给出的频率数据至少精确到四位数字，因此它是基准数据，可以与其他方法（例如二维厚板理论、有限元方法）的结果进行比较。在整个工作中，数值计算的泊松比固定为 0·3。
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 having 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 algebraic 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 plate theory. Extensive and accurate (four significant figures) frequencies are presented for completely free, thick, linearly tapered annular plates having ratios of average plate thickness to difference between outer radius (a) and inner radius (b) ratios (hm/L) of 0·1 and 0·2 forb/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 given is exact to at least four digits, it is benchmark data against which the results from other methods (e.g., 2-D thick plate theory, finite element methods) and may be compared. Throughout this work, Poisson's ratiovis fixed at 0·3 for numerical calculations.