Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory
Functionally graded material (FGM) is an in-homogeneous composite, constructed from various phases of material elements, often ceramic and metal. This work aims to examine the behavior of free vibration in porous Functionally Graded Beams (FGBs) in 2 directions (2D) by using nth-order shear deformat...
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Semnan University
2023-04-01
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| Series: | Mechanics of Advanced Composite Structures |
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| Online Access: | https://macs.semnan.ac.ir/article_7040_2295525d13aa0be2f8cd055d378ba1b3.pdf |
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| author | G. Reddy Nathi Kumar |
| author_facet | G. Reddy Nathi Kumar |
| author_sort | G. Reddy |
| collection | DOAJ |
| description | Functionally graded material (FGM) is an in-homogeneous composite, constructed from various phases of material elements, often ceramic and metal. This work aims to examine the behavior of free vibration in porous Functionally Graded Beams (FGBs) in 2 directions (2D) by using nth-order shear deformation theory. With the help of Hamilton's principle and Reddy's beam theory, equilibrium equations for free vibration were derived. Boundary conditions such as Simply Supported – Simply Supported (SS), Clamped – Clamped (CC) and Clamped-Free (CF) were employed. A unique shear shape function was derived and nth-order theory was adapted to take into account the effect of transverse shear deformation to get zero shear stress conditions at the top and bottom surfaces of the beam. Based on power law, FGB properties were changed in length and thickness directions. The displacement functions in axial directions were articulated in algebraic polynomials, including admissible functions which were used to fulfill different boundary conditions. Convergence and verification were performed on computed results with findings of previous studies. It was found that the results obtained using the nth-order theory were in agreement and allows for better vibration analysis in a porous material. |
| format | Article |
| id | doaj-art-e64446f21ed2437c9d40ce70d6f2fad5 |
| institution | Kabale University |
| issn | 2423-4826 2423-7043 |
| language | English |
| publishDate | 2023-04-01 |
| publisher | Semnan University |
| record_format | Article |
| series | Mechanics of Advanced Composite Structures |
| spelling | doaj-art-e64446f21ed2437c9d40ce70d6f2fad52024-12-16T21:03:40ZengSemnan UniversityMechanics of Advanced Composite Structures2423-48262423-70432023-04-01101698410.22075/macs.2022.28118.14287040Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order TheoryG. Reddy0Nathi Kumar1Research Scholar, Department of Mechanical Engineering, School of Technology, GITAM, Hyderabad, 502329, India.Professor, Department of Mechanical Engineering, School of Technology, GITAM, Hyderabad, India.Functionally graded material (FGM) is an in-homogeneous composite, constructed from various phases of material elements, often ceramic and metal. This work aims to examine the behavior of free vibration in porous Functionally Graded Beams (FGBs) in 2 directions (2D) by using nth-order shear deformation theory. With the help of Hamilton's principle and Reddy's beam theory, equilibrium equations for free vibration were derived. Boundary conditions such as Simply Supported – Simply Supported (SS), Clamped – Clamped (CC) and Clamped-Free (CF) were employed. A unique shear shape function was derived and nth-order theory was adapted to take into account the effect of transverse shear deformation to get zero shear stress conditions at the top and bottom surfaces of the beam. Based on power law, FGB properties were changed in length and thickness directions. The displacement functions in axial directions were articulated in algebraic polynomials, including admissible functions which were used to fulfill different boundary conditions. Convergence and verification were performed on computed results with findings of previous studies. It was found that the results obtained using the nth-order theory were in agreement and allows for better vibration analysis in a porous material.https://macs.semnan.ac.ir/article_7040_2295525d13aa0be2f8cd055d378ba1b3.pdffree vibration behaviournth order shear deformation theorylagrange’ s equations2d fgb |
| spellingShingle | G. Reddy Nathi Kumar Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory Mechanics of Advanced Composite Structures free vibration behaviour nth order shear deformation theory lagrange’ s equations 2d fgb |
| title | Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory |
| title_full | Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory |
| title_fullStr | Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory |
| title_full_unstemmed | Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory |
| title_short | Free Vibration Analysis of 2D Functionally Graded Porous Beams Using Novel Higher-Order Theory |
| title_sort | free vibration analysis of 2d functionally graded porous beams using novel higher order theory |
| topic | free vibration behaviour nth order shear deformation theory lagrange’ s equations 2d fgb |
| url | https://macs.semnan.ac.ir/article_7040_2295525d13aa0be2f8cd055d378ba1b3.pdf |
| work_keys_str_mv | AT greddy freevibrationanalysisof2dfunctionallygradedporousbeamsusingnovelhigherordertheory AT nathikumar freevibrationanalysisof2dfunctionallygradedporousbeamsusingnovelhigherordertheory |