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    Determination of natural frequencies of non-uniform aluminum beams coated with functionally graded materialModalanalyse von ungleichmäßigen Aluminiumträgern, die mit funktional abgestuftem Material beschichtet sind
    (Wiley-V C H Verlag Gmbh, 2024) Pekel, H.; Erdurcan, E. F.
    The present study comprises a numerical analysis used to find the dimensionless natural frequencies of non-uniform aluminum beams coated with functionally graded material. The beams have variable width, and their variation is described by exponential and linear functions. While the coating material properties vary with a polynomial function, the lamination theory is used to calculate the overall properties of the functionally graded material coating. The beam is modeled as a modified Timoshenko beam and the gradual transition of the coating material properties as 25 layers of homogeneous isotropic material. In order to find the natural frequencies of the beam, finite element analysis was used, and the numerical results were processed with MATLAB, which were in good agreement with literature values. A parametric study is performed to study the effects of slenderness (L/H), coating thickness (h/H), skewness rate (S) and taper ratio (w2/w1) on the dimensionless natural frequencies. The study showed that tapering and skewing had a limited effect on the natural frequencies in general, however there exists a critical slenderness for every taper ratio and skewness rate where shape variation has a significant effect on the natural frequencies and should be considered. In der vorliegenden Studie wird eine numerische Analyse durchgefuhrt, um die dimensionslosen Eigenfrequenzen von ungleichmassigen Aluminiumtragern, die mit funktional abgestuftem Material beschichtet sind, zu ermitteln. Die Trager haben eine variable Breite und ihre Variation wird durch Exponential- und Linearfunktionen beschrieben. Weil die Eigenschaften des Beschichtungswerkstoffs mit einer Polynomfunktion variieren, wird die Laminierungstheorie verwendet, um die Gesamteigenschaften der funktional abgestuften Material-Beschichtung zu berechnen. Der Trager wird als modifizierter Timoshenko-Balken modelliert, und der allmahliche ubergang der Beschichtungsmaterialeigenschaften wird als 25 Schichten aus homogenem isotropem Material modelliert. Um die Eigenfrequenzen des Tragers zu ermitteln, wurde die Finite-Elemente-Analyse verwendet. Die von MATLAB gefundenen numerischen Ergebnisse stimmen mit Literaturwerten uberein. Eine Parameterstudie wurde durchgefuhrt, um die Auswirkungen von Schlankheit (L/H), Beschichtungsdicke (h/H), Schieferate (S) und Verjungungsverhaltnis (w2/w1) auf die dimensionslosen Eigenfrequenzen zu untersuchen. Die Studie zeigte, dass Verjungung und Schragstellung im Allgemeinen einen begrenzten Einfluss auf die Eigenfrequenzen haben, jedoch gibt es eine kritische Schlankheit fur jedes Verjungungsverhaltnis und jede Schieferate, bei der Formvariationen einen grossen Einfluss auf die Eigenfrequenzen haben und berucksichtigt werden sollten. The current paper elucidates the factors which should be considered when designing a metal structural element with non-uniform shape coated with functionally graded material. As a result, the effects of both material and shape parameters on the dimensionless natural frequencies are presented individually. image
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    Free vibration analysis of an aluminum beam coated with imperfect and damaged functionally graded material
    (Springer, 2021) Erdurcan, E. F.; Cunedioglu, Y.
    In this paper, the free vibration of an aluminum beam coated with imperfect and damaged functionally graded material is investigated. The imperfections consist of porosities, while 4 evenly distributed cracks represent the damage profile. A polynomial function is used to vary the density and elasticity through the thickness of the coating, while the effective elastic modulus and density are found with classical lamination theory. To achieve a truthful modeling, the gradually changing mechanical properties of the coating are modeled with 25 layers of material. The individual layers are isotropic and homogeneous. Numerical solutions are found with the finite element method using Timoshenko beam elements. MATLAB is used to write a finite element code, and the beam natural frequencies are found. To show the influences of porosity, crack depth, coating thickness and the polynomial function index (n) on the natural beam frequencies, a parametric study is conducted. It was found that the natural frequency values were significantly affected by the studied parameters.
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    Modal analysis of an aluminum beam coated with damaged and porous functionally graded material
    (Wiley-V C H Verlag Gmbh, 2021) Erdurcan, E. F.; Cunedioglu, Y.
    In this paper modal analysis is performed on a symmetric aluminum beam which is coated with functionally graded material containing porosities. A polynomial function is used to vary the density and elasticity through the thickness of the coating, while the effective elastic modulus and density are found with classical lamination theory. To achieve a truthful modeling the gradually changing mechanical properties of the coating are modeled as 25 layers of material, while each individual layer is isotropic and homogeneous. MATLAB is used to write a finite element code and Timoshenko beam elements are used to include shear deformation effects. To show the influences of crack location, crack depth, porosity and the polynomial function index on the natural beam frequencies a parametric study is conducted. Multiple boundary conditions were also considered and it was found that the natural frequency values were significantly affected by the studied parameters.