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In this paper, we give an overview of the issues one must consider when designing methods for vibration based health monitoring systems for perforated thin shells especially in relation to frequency response analysis. In particular, we allow either the material parameters or the structure or both to be random. The numerical experiments are computed...
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... 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. ...
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.
... From the point of view of the analysis, no changes are necessary even if the perforation patterns were randomly perturbed as well. Many of these issues have been addressed in a previous study [8]. Modern stochastic analysis of multiparametric problems leads to a large number of simulations. ...
... This section introduces both the shell eigenproblems and the collocation scheme, which is used to compute the frequency responses in the cases where the material parameters, e.g., Young's modulus, are random. The discussion below follows closely that in [8]. ...
... Material constants adopted for all simulations are: 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, which is as in earlier work [8]. The deterministic parameter ranges of t ∈ [1/100, 1/1000] (the so-called practical range), and frequency f ∈ [5, 240] Hz (chosen experimentally) with angular frequency ω = 2π f , are covered. ...
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.
... Hou et al. [2] used the FEM to analyse the stiffness of the grid in a crossed helical gear. The method was also used to locate mechanical damage [3] as well as damage to perforated materials [4]. It was also used to analyse the fracture of elements of machines [5], [6] as well as in tests on contacts between such elements [7]. ...
Small organic farms still use potato lifters for harvesting. This harvesting technology involves a lot of work because potatoes need to be picked manually. The aim of this study was to design an innovative organic farming potato harvester aggregated with a 38 kW tractor and to analyse its strength with the finite element method (FEM). The research assumption was to fit the innovative construction with a potato basket in order to minimise the labour consumption of organic potato cultivation. The project involved analytical calculations of the strength, which were followed by the design of a CAD model and a detailed strength analysis with the FEM. Autodesk Inventor and Femap were the programs used to aid the design of the machine. The designed model had no nodes where stresses would be greater than 32% of the maximum allowable stress in the material structure and 43% of the maximum allowable stress in the structure of welds. The innovative design of the potato harvester developed in this study can be used with all tractors (farm and orchard tractors) equipped with a three-point linkage.
... We can't apply an analytical solution of the equations regarding plates and the freeform holes. It would be appropriate to use here the finite-element model to calculate the natural frequencies of these details [7][8][9][10]. ...
During this research, the analytical and numerical oscillation models have been deduced of cooling grills of terminal devices for voice communication control systems used by air traffic controllers. The adequacy of obtained models was verified by a full-scale experiment. Vibration stability of telecommunication terminal cases has high importance for the high-quality reproduction of voice information. Obtained results make it possible to solve two problems at once – problem of reducing heat pressure and of increasing vibration stability of audio reproduction device cases.
... Hou et al. [6] used the FEM method to analyze the stiffness of the mesh of a helical gear. It can also be used to locate mechanical damages [7] or damages to perforated materials [8]. FEM was also used for crack analysis of machine elements [9,10] and for tests related to mutual contacts of machine elements [11]. ...
Most of the front loaders are compact structures that do not allow loading at greater heights. On the Polish and foreign market, there was a need to develop a front loader design that would allow to increase the loading height. As a result, the front loader was designed a front loader with the possibility of extending the arms for the Kubota M5 agricultural tractor. The system enables unloading and loading of cubes, straw and hay bales on higher piles. Before starting the design process, the available front loader solutions were analyzed and on this basis, three concepts of design solutions were proposed. These concepts were scored on the basis of the adopted criteria and the one with the highest number of points was selected. For the selected concept, strength analytical calculations and verification calculations using the FEM method were performed. The developed loader is innovative compared to other available designs and has a good chance of implementation.
... For the application of vibration analysis to system identification, direct methods analyzing responses from external loads are preferred. Frequency response analysis for vibration prediction of perforated shells was performed for application to statistical modeling techniques and to be used for damage detection [2]. Damage detection using modal rotational mode shapes was proposed [3]. ...
Structural health monitoring by vibration requires the understanding of multidisciplinary fields of engineering sciences [...]
... Allahkarami et al. [13] studied the dynamic buckling behavior of higher-order shear deformable FGM porous cylindrical shells with even and uneven porosity distribution types. Hakula and Laaksonen [14] discussed the frequency responses of perforated shells with uncertain materials and damage by using the higher-order finite element method. ...
The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.