Multiparametric shell eigenvalue problems

TL;DR

This paper investigates the eigenvalue problem for thin shells of revolution with uncertain material properties, focusing on the smallest eigenpairs and demonstrating stochastic algorithms' ability to resolve eigenclusters and mode crossings.

Contribution

It introduces stochastic subspace iteration algorithms capable of resolving eigenclusters in uncertain shell eigenproblems, and analyzes the impact of material models on eigenvalue asymptotics.

Findings

Algorithms resolve smallest eigenclusters effectively.

Eigenmodes can cross in stochastic parameter space.

Material model choice has negligible effect on asymptotics.

Abstract

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.