Free vibration and buckling of functionally graded porous beams using analytical, finite element, and artificial neural network methods

In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artifici...

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Vydáno v:	Archive of applied mechanics (1991) Ročník 93; číslo 4; s. 1351 - 1372
Hlavní autoři:	Turan, Muhittin, Uzun Yaylacı, Ecren, Yaylacı, Murat
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023 Springer Nature B.V
Témata:	Artificial neural networks Boundary conditions Buckling Civil engineering Classical Mechanics Composite materials Engineering Equations of motion Exact solutions Finite element method Free vibration Functionally gradient materials Mathematical analysis Methods Neural networks Numerical analysis Original Polynomials Porosity Power law Resonant frequencies Shear deformation Shear strain Theoretical and Applied Mechanics Vibration analysis Finite element method Artificial neural network Free vibration Buckling Ritz-based analytical solution Functionally graded porous beam
ISSN:	0939-1533, 1432-0681
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Abstract	In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index ( k ), slenderness ( L/h ), porosity coefficient ( e ), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other.
AbstractList	In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index ( k ), slenderness ( L/h ), porosity coefficient ( e ), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other. In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index (k), slenderness (L/h), porosity coefficient (e), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other.
Author	Turan, Muhittin Yaylacı, Murat Uzun Yaylacı, Ecren
Author_xml	– sequence: 1 givenname: Muhittin orcidid: 0000-0002-5703-0580 surname: Turan fullname: Turan, Muhittin organization: Department of Civil Engineering, Bayburt University – sequence: 2 givenname: Ecren orcidid: 0000-0002-2558-2487 surname: Uzun Yaylacı fullname: Uzun Yaylacı, Ecren organization: Surmene Faculty of Marine Science, Karadeniz Technical University – sequence: 3 givenname: Murat orcidid: 0000-0003-0407-1685 surname: Yaylacı fullname: Yaylacı, Murat email: murat.yaylaci@erdogan.edu.tr organization: Department of Civil Engineering, Recep Tayyip Erdogan University
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Snippet	In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally...
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SubjectTerms	Artificial neural networks Boundary conditions Buckling Civil engineering Classical Mechanics Composite materials Engineering Equations of motion Exact solutions Finite element method Free vibration Functionally gradient materials Mathematical analysis Methods Neural networks Numerical analysis Original Polynomials Porosity Power law Resonant frequencies Shear deformation Shear strain Theoretical and Applied Mechanics Vibration analysis
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Title	Free vibration and buckling of functionally graded porous beams using analytical, finite element, and artificial neural network methods
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