Dynamic and static asymmetric response of a layered thick disk

AbstractTreated is the asymmetric static and dynamic response of a stack of layered thick disks from external load. Variables of the three-dimensional equations are separated assuming approximate simple supports along the cylindrical perimeter, yielding non-orthogonal eigenfunctions. This also couples the truncated set of radial wave numbers. Applying a radial transform to all variables eliminates radial dependence producing a diagonal eigenproblem in all coupled axial wave numbers. Comparing 3-D and 2-D asymmetric models of industrial glass disks reveals that the 3-D resonances are close to their 2-D counterparts adopting the Mindlin model. A Fourier analysis of a specific asymmetric line-load from pressure or thermal expansion produces a scale factor to static stress from a limited number of asymmetric solutions each with a different circumferential wave number