Vibration analysis of a torus–cylinder shell assembly

Differential equations based on the Sanders–Budiansky theory are expressed in a general form for the linear vibration analysis of thin isotropic shells. The general equations are applied to toroidal and cylindrical shells and to a torus–cylinder shell assembly (pipe bend). Solutions to the equations are set up using the differential quadrature method. Sample results obtained for the cylindrical shell are compared with results given in the literature. Further results are given for some standard-size 90° pipe bends, and these results are compared with finite element results. The paper ends with an appropriate set of conclusions.