Low-Rank Approximation of Frequency Response Analysis of Perforated Cylinders under Uncertainty

Abstract

Frequency response analysis under uncertainty is computationally expensive. Low-rank approximation techniques can significantly reduce the solution times. Thin perforated cylinders, as with all shells, have specific features affecting the approximation error. There exists a rich thickness-dependent boundary layer structure, leading to local features becoming dominant as the thickness tends to zero. Related to boundary layers, there is also a connection between eigenmodes and the perforation patterns. The Krylov subspace approach for proportionally damped systems with uncertain Young’s modulus is compared with the full system, and via numerical experiments, it is shown that the relative accuracy of the low-rank approximation of perforated shells measured in energy depends on the dimensionless thickness. In the context of frequency response analysis, it then becomes possible that, at some critical thicknesses, the most energetic response within the observed frequency range is not identified correctly. The reference structure used in the experiments is a trommel screen with a non-regular perforation pattern with two different perforation zones. The low-rank approximation scheme is shown to be feasible in computational asymptotic analysis of trommel designs when the proportional damping model is used.

Effects of Internal Boundary Layers and Sensitivity on Frequency Response of Shells of Revolution

“…In all cases, the material parameters are the same: E = 2.069 × 10 11 MPa, ν = 1/3, and ρ = 7868 kg m −3 , unless otherwise specified. For damping, the selected weights are simply α = β = 1/2, and ζ = 1/2000 (see also [8,9]). The loading is a symmetric concentrated load (in N), (19) where point (x 0 , y 0 ) is where the load acts, i.e., is concentrated, and C is a scaling parameter.…”

“…This choice is based on calibration with full analysis. In [9], where only constant coefficient cases were considered, r = 4 was sufficient.…”

“…Frequency response analysis of perforated shells has been studied by this author previously; see [8,9]. There, the focus was on material uncertainty and stochastic finite element method when the dimensionless thickness tended to zero.…”