Multiparametric shell eigenvalue problems
For engineers analyzing thin shell structures, this work provides numerical methods to handle eigenvalue problems with uncertain material parameters, though the results are incremental.
The paper presents stochastic subspace iteration algorithms for solving the smallest eigenpairs of thin shells of revolution under material parameter uncertainty, demonstrating eigenmode crossing in stochastic parameter space and showing that the material model choice has negligible effect on asymptotics.
The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs depend on a deterministic parameter, the dimensionless thickness. The stochastic subspace iteration algorithms presented here are capable of resolving the smallest eigenclusters. In the case of random material parameters, it is possible that the eigenmodes cross in the stochastic parameter space. This interesting phenomenon is demonstrated via numerical experiments. Finally, the effect of the chosen material model on the asymptotics in relation to the deterministic parameter is shown to be negligible.