Yıl: 2022 Cilt: 5 Sayı: 4 Sayfa Aralığı: 277 - 288 Metin Dili: İngilizce DOI: 10.31462/jseam.2022.04277288 İndeks Tarihi: 13-01-2023

Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory

Öz:
This study considers free vibration analysis of a porous functionally graded (FG) beam using a higher-order shear deformation theory (HSDT). The change in the material properties is described by a power law. The porosity distribution functions, one for even cases and two for uneven cases, are considered in the problem. The governing equations are derived utilizing Lagrange’s principle. The solution to the problem is carried out using FEM with a three-node and 12-DOF element. Dimensionless natural frequencies obtained in the present study are compared to those reported in four studies from the literature for validation purposes. The effect of material properties, porosity, and boundary conditions on the dimensionless neutral frequencies and mode shapes are investigated with the help of a parametric study.
Anahtar Kelime: FGM HSDT Finite element method

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Karama M, Afaq KS, Mistou S (2003) Mechanical behaviour of laminated composite beam by the new multi- layered laminated composite structures model with transverse shear stress continuity. International Journal of Solids and Structures 40(6):1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  • [2] Sayyad AS, Ghugal YM (2019) Modeling and analysis of functionally graded sandwich beams: a review. Mechanics of Advanced Materials and Structures 26(21):1776-1795. https://doi.org/10.1080/ 15376494.2018.1447178
  • [3] Hadji L, Zouatnia N, Bernard F (2019) An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models. Structural Engineering and Mechanics 69(2):231-241. https://doi.org/0.12989/sem.2019.69.2.231
  • [4] Kahya V, Turan M (2017) Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory. Composites Part B: Engineering 109:108-115. https://doi.org/10.1016/ j.compositesb.2016.10.039
  • [5] Nguyen T-K, Truong-Phong Nguyen T, Vo TP, Thai H-T (2015) Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory. Composites Part B: Engineering 76:273- 285. https://doi.org/10.1016/j.compositesb.2015.02.032
  • [6] Vo TP, Thai H-T, Nguyen T-K, Maheri A, Lee J (2014) Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Engineering Structures 64:12- 22. https://doi.org/10.1016/j.engstruct.2014.01.029
  • [7] Chen D, Yang J, Kitipornchai S (2015) Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures 133:54-61. https://doi.org/10.1016/j.compstruct.2015.07.052
  • [8] Wattanasakulpong N, Chaikittiratana A (2015) Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica 50(5):1331-1342. https://doi.org/ 10.1007/s11012-014-0094-8
  • [9] Ebrahimi F, Ghasemi F, Salari E (2016) Investigating thermal effects on vibration behavior of temperature- dependent compositionally graded Euler beams with porosities. Meccanica 51(1):223-249. https://doi.org/ 10.1007/s11012-015-0208-y
  • [10] Ait Atmane H, Tounsi A, Bernard F (2017) Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations. International Journal of Mechanics and Materials in Design 13(1):71-84. https://doi.org/10.1007/s10999-015-9318-x
  • [11] Al Rjoub YS, Hamad AG (2017) Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE Journal of Civil Engineering 21(3):792-806. https://doi.org/10.1007/s12205-016-0149-6
  • [12] Kitipornchai S, Chen D, Yang J (2017) Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Materials & Design 116:656-665. https://doi.org/10.1016/j.matdes.2016.12.061
  • [13] Thi B-P, Minh Tu T, Hoang T-P, Long N (2019) Bending analysis of functionally graded beam with porosities resting on elastic foundation based on neutral surface position. Journal of Science and Technology in Civil Engineering (STCE) - NUCE 13:33-45. https://doi.org/10.31814/stce.nuce2019-13(1)-04
  • [14] Tang H, Li L, Hu Y (2019) Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams. Applied Mathematical Modelling 66:527-547. https://doi.org/ 10.1016/j.apm.2018.09.027
  • [15] Demirhan VT, Pınar A (2020) Free vibration analysis of functionally graded porous beam. 8(1):49-60 (in Turkish). https://doi.org/10.20290/estubtdb.538586
  • [16] Derikvand M, Farhatnia F, Hodges DH (2021) Functionally graded thick sandwich beams with porous core: Buckling analysis via differential transform method. Mechanics Based Design of Structures and Machines. https://doi.org/10.1080/15397734.2021.1931309
  • [17] Nguyen N-D, Nguyen T-N, Nguyen T-K, Vo TP (2022) A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams. Composite Structures 282:115095. https://doi.org/10.1016/j.compstruct.2021.115095
  • [18] Fouda N, El-midany T, Sadoun AM (2017) Bending, buckling and vibration of a functionally graded porous beam using finite elements. Journal of Applied and Computational Mechanics 3(4):274-282. https://doi.org/ 10.22055/jacm.2017.21924.1121
  • [19] Akbaş ŞD (2018) Forced vibration analysis of functionally graded porous deep beams. Composite Structures 186:293-302. https://doi.org/10.1016/j.compstruct.2017.12.013
  • [20] Wu D, Liu A, Huang Y, Huang Y, Pi Y, Gao W (2018) Dynamic analysis of functionally graded porous structures through finite element analysis. Engineering Structures 165:287-301. https://doi.org/10.1016/ j.engstruct.2018.03.023
  • [21] Wu D, Liu A, Huang Y, Huang Y, Pi Y, Gao W (2018) Mathematical programming approach for uncertain linear elastic analysis of functionally graded porous structures with interval parameters. Composites Part B: Engineering 152:282-291. https://doi.org/10.1016/j.compositesb.2018.06.032
  • [22] Hamed MA, Sadoun AM, Eltaher MA (2019) Effects of porosity models on static behavior of size dependent functionally graded beam. Structural Engineering and Mechanics 71(1):89-98. https://doi.org/10.12989 /sem.2019.71.1.089
  • [23] Karamanli A, Vo TP (2021) A quasi-3D theory for functionally graded porous microbeams based on the modified strain gradient theory. Composite Structures 257:113066. https://doi.org/10.1016/j.compstruct.2020.113066
  • [24] Zghal S, Ataoui D, Dammak F (2022) Static bending analysis of beams made of functionally graded porous materials. Mechanics Based Design of Structures and Machines 50(3):1012-1029. https://doi.org/10.1080/ 15397734.2020.1748053
  • [25] Alnujaie A, Akbas SD, Eltaher MA, Assie AE (2021) Damped forced vibration analysis of layered functionally graded thick beams with porosity. Smart Structures and Systems 27(4):679-689. https://doi.org/10.12989/ sss.2021.27.4.679
APA ADIYAMAN G (2022). Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. , 277 - 288. 10.31462/jseam.2022.04277288
Chicago ADIYAMAN GOKHAN Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. (2022): 277 - 288. 10.31462/jseam.2022.04277288
MLA ADIYAMAN GOKHAN Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. , 2022, ss.277 - 288. 10.31462/jseam.2022.04277288
AMA ADIYAMAN G Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. . 2022; 277 - 288. 10.31462/jseam.2022.04277288
Vancouver ADIYAMAN G Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. . 2022; 277 - 288. 10.31462/jseam.2022.04277288
IEEE ADIYAMAN G "Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory." , ss.277 - 288, 2022. 10.31462/jseam.2022.04277288
ISNAD ADIYAMAN, GOKHAN. "Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory". (2022), 277-288. https://doi.org/10.31462/jseam.2022.04277288
APA ADIYAMAN G (2022). Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. Journal of Structural Engineering & Applied Mechanics (Online), 5(4), 277 - 288. 10.31462/jseam.2022.04277288
Chicago ADIYAMAN GOKHAN Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. Journal of Structural Engineering & Applied Mechanics (Online) 5, no.4 (2022): 277 - 288. 10.31462/jseam.2022.04277288
MLA ADIYAMAN GOKHAN Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. Journal of Structural Engineering & Applied Mechanics (Online), vol.5, no.4, 2022, ss.277 - 288. 10.31462/jseam.2022.04277288
AMA ADIYAMAN G Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. Journal of Structural Engineering & Applied Mechanics (Online). 2022; 5(4): 277 - 288. 10.31462/jseam.2022.04277288
Vancouver ADIYAMAN G Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory. Journal of Structural Engineering & Applied Mechanics (Online). 2022; 5(4): 277 - 288. 10.31462/jseam.2022.04277288
IEEE ADIYAMAN G "Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory." Journal of Structural Engineering & Applied Mechanics (Online), 5, ss.277 - 288, 2022. 10.31462/jseam.2022.04277288
ISNAD ADIYAMAN, GOKHAN. "Free vibration analysis of a porous functionally graded beam using higher-order shear deformation theory". Journal of Structural Engineering & Applied Mechanics (Online) 5/4 (2022), 277-288. https://doi.org/10.31462/jseam.2022.04277288