Trommel screen. Shell of revolution generated by a profile function φ(x) = 1. Transverse deflection fields under angular excitation of wave number = 20. Effect of the deterministic parameters t (thickness) and f (frequency) is illustrated, (a) t = 1/100, f = 5, (b) t = 1/100, f = 40, (c) t = 1/1000, f = 5, (d) t = 1/1000, f = 40. Notice how, from (a) to (b), the maximal intensity moves from the area of the large perforations to the small ones, but from (c) to (d), the same effect does not take place. In (d), the solution is locally dominant and the energy is concentrated on the boundary layers.

Trommel screen. Shell of revolution generated by a profile function φ(x) = 1. Transverse deflection fields under angular excitation of wave number = 20. Effect of the deterministic parameters t (thickness) and f (frequency) is illustrated, (a) t = 1/100, f = 5, (b) t = 1/100, f = 40, (c) t = 1/1000, f = 5, (d) t = 1/1000, f = 40. Notice how, from (a) to (b), the maximal intensity moves from the area of the large perforations to the small ones, but from (c) to (d), the same effect does not take place. In (d), the solution is locally dominant and the energy is concentrated on the boundary layers.

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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 feature...

Contexts in source publication

Context 1
... screens are devices used in the grading of raw materials and solid waste classification. Consider a perforated cylinder as in Figure 1, but tilted so that the smaller holes are higher, and the whole cylinder rotating. As the raw materials are fed into the trommel from the top, the perforation structure separates objects of different sizes. ...
Context 2
... quantity of interest is the total energy of the response, since there are no guarantees for the convergence of local features such as pointwise displacement. In Figure 1, some of the effects of the deterministic parameters are illustrated. ...
Context 3
... the trommel screens with precisely these properties are considered. In Figure 1, an example of the axial effect (Figure 1a,b) and the saturation with high wave numbers in response (Figure 1d) are illustrated. Currently, even a case of two adjacent but different regular perforation grids is open in the sense that the asymptotics cannot be predicted. ...
Context 4
... the trommel screens with precisely these properties are considered. In Figure 1, an example of the axial effect (Figure 1a,b) and the saturation with high wave numbers in response (Figure 1d) are illustrated. Currently, even a case of two adjacent but different regular perforation grids is open in the sense that the asymptotics cannot be predicted. ...
Context 5
... the trommel screens with precisely these properties are considered. In Figure 1, an example of the axial effect (Figure 1a,b) and the saturation with high wave numbers in response (Figure 1d) are illustrated. Currently, even a case of two adjacent but different regular perforation grids is open in the sense that the asymptotics cannot be predicted. ...
Context 6
... Figures 8 and 10, both sets of asymptotics are shown. Let us first concentrate on the observed frequencies. ...
Context 7
... is explained with graphs in Figure 9. The energy asymptotics of Figure 10 tell a similar story. For K = 10, the sharpness of the transition leads to an almost monotone increase in the observed total energy. ...

Citations

... 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. ...
... 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. ...
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New applications introduced capsule designs with features that have not been fully analysed in the literature. In this study, thin shells of revolution are used to model drug delivery capsules both with closed and open designs including perforations. The effects of internal boundary layers and sensitivity on frequency response are discussed in the special case with symmetric concentrated load. The simulations are carried out using high-order finite element method and the frequency response is computed with a very accurate low-rank approximation. Due to the propagation of the singularities induced by the concentrated loads, the most energetic responses do not necessarily include a pinch-through at the point of action. In sensitive configurations, the presence of regions with elliptic curvature leads to strong oscillations at lower frequencies. The amplitudes of these oscillations decay as the frequencies increase. For efficient and reliable analysis of such structures, it is necessary to understand the intricate interplay of loading types and geometry, including the effects of the chosen shell models.