Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous Beams
A novel two-dimensional elasticity solution is presented in this paper, specifically designed for studying the vibration of functionally graded porous (FGP) beams. The kinetics of the beam are defined by two-dimensional elasticity theory, and Lagrange’s equations are used to derive the governing equ...
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Semnan University
2025-04-01
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| Series: | Mechanics of Advanced Composite Structures |
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| Online Access: | https://macs.semnan.ac.ir/article_8922_ca8ae39bdfcb6f36df8124d145b7b34c.pdf |
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| author | Quoc-Cuong Le Ba-Duy Nguyen |
| author_facet | Quoc-Cuong Le Ba-Duy Nguyen |
| author_sort | Quoc-Cuong Le |
| collection | DOAJ |
| description | A novel two-dimensional elasticity solution is presented in this paper, specifically designed for studying the vibration of functionally graded porous (FGP) beams. The kinetics of the beam are defined by two-dimensional elasticity theory, and Lagrange’s equations are used to derive the governing equations of motion. The Ritz method devises the expansion of displacement variables in polynomial and trigonometric series in the thickness and axial directions. Furthermore, microvoids can emerge as a result of technical issues during the manufacture of functionally graded materials (FGMs), leading to the development of porosities. The porosity distribution functions, one for three porosity distributions: uniform porosity (UP), non-uniform porosity-I (NUP-I), and non-uniform porosity-II (NUP-II), are considered in the problem. This study investigates the impact of the gradation exponents (p) in the z-direction, the slenderness ratio (L/h), the distribution of porosity, the porosity coefficient (e), and various boundary conditions on the natural frequencies. A comparison with the findings from higher-order shear deformation theory (HSDT) validated the accuracy and effectiveness of the proposed methodology. |
| format | Article |
| id | doaj-art-1120733b02914e0e96d7d18495595ac9 |
| institution | Kabale University |
| issn | 2423-4826 2423-7043 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Semnan University |
| record_format | Article |
| series | Mechanics of Advanced Composite Structures |
| spelling | doaj-art-1120733b02914e0e96d7d18495595ac92025-01-20T11:30:31ZengSemnan UniversityMechanics of Advanced Composite Structures2423-48262423-70432025-04-0112123524810.22075/macs.2024.32009.15948922Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous BeamsQuoc-Cuong Le0Ba-Duy Nguyen1Institute of Engineering and Technology, Thu Dau Mot University, Thu Dau Mot City, VietnamFaculty of Architecture, Thu Dau Mot University, Thu Dau Mot City, VietnamA novel two-dimensional elasticity solution is presented in this paper, specifically designed for studying the vibration of functionally graded porous (FGP) beams. The kinetics of the beam are defined by two-dimensional elasticity theory, and Lagrange’s equations are used to derive the governing equations of motion. The Ritz method devises the expansion of displacement variables in polynomial and trigonometric series in the thickness and axial directions. Furthermore, microvoids can emerge as a result of technical issues during the manufacture of functionally graded materials (FGMs), leading to the development of porosities. The porosity distribution functions, one for three porosity distributions: uniform porosity (UP), non-uniform porosity-I (NUP-I), and non-uniform porosity-II (NUP-II), are considered in the problem. This study investigates the impact of the gradation exponents (p) in the z-direction, the slenderness ratio (L/h), the distribution of porosity, the porosity coefficient (e), and various boundary conditions on the natural frequencies. A comparison with the findings from higher-order shear deformation theory (HSDT) validated the accuracy and effectiveness of the proposed methodology.https://macs.semnan.ac.ir/article_8922_ca8ae39bdfcb6f36df8124d145b7b34c.pdfvibrationfunctionally graded porous beamstwo-dimensional elasticityporosity distributions |
| spellingShingle | Quoc-Cuong Le Ba-Duy Nguyen Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous Beams Mechanics of Advanced Composite Structures vibration functionally graded porous beams two-dimensional elasticity porosity distributions |
| title | Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous Beams |
| title_full | Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous Beams |
| title_fullStr | Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous Beams |
| title_full_unstemmed | Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous Beams |
| title_short | Two-dimensional Elasticity Solutions For Analyzing Free Vibration Of Functionally Graded Porous Beams |
| title_sort | two dimensional elasticity solutions for analyzing free vibration of functionally graded porous beams |
| topic | vibration functionally graded porous beams two-dimensional elasticity porosity distributions |
| url | https://macs.semnan.ac.ir/article_8922_ca8ae39bdfcb6f36df8124d145b7b34c.pdf |
| work_keys_str_mv | AT quoccuongle twodimensionalelasticitysolutionsforanalyzingfreevibrationoffunctionallygradedporousbeams AT baduynguyen twodimensionalelasticitysolutionsforanalyzingfreevibrationoffunctionallygradedporousbeams |