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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Bibliographic Details
Published in:Archive of applied mechanics (1991) Vol. 93; no. 4; pp. 1351 - 1372
Main Authors: Turan, Muhittin, Uzun Yaylacı, Ecren, Yaylacı, Murat
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-022-02332-w