A fully numerical and consistent method using the three-dimensional theory of elasticity is presented in this paper to study the free vibrations of an axially symmetric solid. The solid is defined in the cylindrical coordinates (r,θ,z) by a quadrilateral cross section in the r-z plane bounded by four straight and/or curved edges. The cross section is then mapped using the natural coordinates (ξ,η) to simplify the mathematics of the problem. The displacement fields are expressed in terms of the product of two simple algebraic polynomials in ξ and η, respectively. Boundary conditions are enforced in the later part of the solution by simply controlling coefficients of the polynomials. The procedure setup in this paper is such that it was possible to investigate the free axisymmetric and asymmetric vibrations of a wide range of problems, namely; circular disks, cylinders, cones, and spheres with considerable success. The numerical cases include circular disks of uniform as well as varying thickness, conical/cylindrical shells and finally a spherical shell of uniform thickness. Convergence study is also done to examine the accuracy of the results rendered by the present method. The results are compared with the finite element method using the eight-node isoparametric element for the solids of revolution and published data by other researchers.
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机译:万向节密封件-具有细长的球形密封表面,该表面可滑入较厚的外表面,以提供防尘密封等。AB DE4036616A两根轴(1、2)通过万向节连接,一根轴(2)装有一个球面联轴器(3)在第二轴的外球面内移动。第二根轴具有细长的球形密封表面(8),该表面在较厚的外表面内滑动。相互交叉的球形密封表面提供了有限的灰尘等进入的密封。密封唇(8a,9)密封了壳体的作用。优势-改进了对万向接头的保护,将砂砾损坏的风险降至最低。 AN 91194459 TI用于转速测量的脉冲环-倾斜的计数器部分沿环的外围压出,与传感器单元相互作用以确定速度和方向