Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method
Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) a...
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MDPI AG
2024-01-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/29/1/10 |
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| author | Lidiya Kurpa Francesco Pellicano Tetyana Shmatko Antonio Zippo |
| author_facet | Lidiya Kurpa Francesco Pellicano Tetyana Shmatko Antonio Zippo |
| author_sort | Lidiya Kurpa |
| collection | DOAJ |
| description | Free vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz’s method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied. |
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| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-07T22:22:57Z |
| publishDate | 2024-01-01 |
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| series | Mathematical and Computational Applications |
| spelling | doaj.art-8d01ce7c9c204e3aae50d3ee139a44642024-02-23T15:26:21ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472024-01-012911010.3390/mca29010010Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions MethodLidiya Kurpa0Francesco Pellicano1Tetyana Shmatko2Antonio Zippo3Department of Applied Mathematics, National Technical University “KhPI”, Kyrpychova Str. 2, 61002 Kharkiv, UkraineDepartment of Engineering “Enzo Ferrari”, Centre InterMech MoRe, University of Modena and Reggio Emilia, Via P. Vivarelli 10, 41124 Modena, ItalyDepartment of Higher Mathematics, National Technical University “KhPI”, Kyrpychova Str. 2, 61002 Kharkiv, UkraineDepartment of Engineering “Enzo Ferrari”, Centre InterMech MoRe, University of Modena and Reggio Emilia, Via P. Vivarelli 10, 41124 Modena, ItalyFree vibrations of porous functionally graded material (FGM) plates with complex shapes are analyzed by using the R-functions method. The thickness of the plate is variable in the direction of one of the axes. Two types of porosity distributions through the thickness are considered: uniform (even) and non-uniform (uneven). The elastic foundation is defined by two parameters (Winkler and Pasternak). To obtain the mathematical model of the problem, the first-order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction are modeled by means of a power law. Variational Ritz’s method joined with the R-functions theory is used for obtaining a semi-analytical solution of the problem. The approach is applied to a number of case studies and validated by means of comparative analyses carried out on rectangular plates with a traditional finite element approach. The proof of the efficiency of the approach and its capability to handle actual engineering problems is fulfilled for FGM plates having complex shapes and various boundary conditions. The effect of different parameters, such as porosity distribution, volume fraction index, elastic foundation, FGM types, and boundary conditions, on the vibrations is studied.https://www.mdpi.com/2297-8747/29/1/10functionally graded materialR-function methodelastic foundation |
| spellingShingle | Lidiya Kurpa Francesco Pellicano Tetyana Shmatko Antonio Zippo Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method Mathematical and Computational Applications functionally graded material R-function method elastic foundation |
| title | Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method |
| title_full | Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method |
| title_fullStr | Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method |
| title_full_unstemmed | Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method |
| title_short | Free Vibration Analysis of Porous Functionally Graded Material Plates with Variable Thickness on an Elastic Foundation Using the R-Functions Method |
| title_sort | free vibration analysis of porous functionally graded material plates with variable thickness on an elastic foundation using the r functions method |
| topic | functionally graded material R-function method elastic foundation |
| url | https://www.mdpi.com/2297-8747/29/1/10 |
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