FONKSİYONEL DERECELENDİRİLMİŞ GÖZENEKLİ KİRİŞLERİN SERBEST TİTREŞİM ANALİZİ
Yıl 2020,
Cilt: 8 Sayı: 1, 49 - 60, 28.02.2020
Vedat Taşkın
,
Pınar Aydan Demirhan
Öz
Malzeme
özelliklerinde kesit boyunca sürekliliği sağlayan fonksiyonel derecelendirilmiş
malzemeler tabakalı kompozitlerin yerini almaya başlamıştır. Fonksiyonel
derecelendirilmiş malzemelerin üretimi esnasında malzeme içinde bir miktar
gözeneğin hapsolduğu görülmektedir. Bu çalışmada gözenekli fonksiyonel
derecelendirilmiş kirişlerin serbest titreşim analizi gerçekleştirilmiştir.
Malzeme özelliklerinin kesit boyunca değişimi karışımlar kuralı yoluyla tanımlanırken,
gözeneklilik oranı bir katsayı ile ilave edilmiştir. Gözenekli fonksiyonel
derecelendirilmiş kiriş denklemi Hamilton prensibi ile elde edilmiş, basit
destekli kiriş için Navier yaklaşımı kullanılarak çözüm elde edilmiştir. Doğal
frekans değerlerinin kiriş kalınlığı, hacimsel değişim üsteli, gözeneklilik
dağılımı ve oranı ile değişimi incelenmiştir. Elde edilen değerlerin
literatürle uyumlu olduğu görülmüştür.
Kaynakça
- [1] Chen L, Goto T. Handbook Of Advanced Ceramics. Chapter 16: Functionally Graded Materials. 445-464, 2003.
- [2] Jones RM. Mechanics of Composite Materials. Taylor and Francis, 1999.
- [3] Reddy JN. Analysis of functionally graded plates. Int J Numer Meth Engng 2000; 47: 663-684.
- [4] Demirhan PA. Fonksiyonel Derecelendirilmiş Sandviç Kiriş ve Plakların Dört Değişkenli Kayma Deformasyon Teorisi ile Eğilme ve Titreşim Analizi. Doktora Tezi, Trakya Üniversitesi Fen Bilimleri Enstitüsü, Edirne, Türkiye, 2016.
- [5] Shimpi RP. Refined Plate Theory and Its Variants. AIAA Journal. 2002; 40:1.
- [6] Shimpi RP, Patel HG. A two variable refined plate theory for orthotropic plate analysis. Int J Solids Struct. 2006; 43: 6783–6799.
- [7] S.E. Kim, H.T. Thai, J. Lee, A two variable refined plate theory for laminated composite plates, Compos Struc. 89, 197–205, 2009
- [8] Mechab I, Atmane HA, Tounsi A, Belhadj HA, Bedia EAA. A two variable refined plate theory for the bending analysis of functionally graded plates. Acta Mech Sin. 2010; 26: 941–949.
- [9] Demirhan PA, Taskin V. Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory. Compos Struct 2017; 177: 80–95.
- [10] Demirhan PA, Taskin V. Static analysis of simply supported functionally graded sandwich plates by using four variable plate theory. Teknik Dergi. 2019; 8987-9007.
- [11] Demirhan PA, Taskin V. Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach. Compos B Eng. 2019; 160:661-676.
- [12] Thai HT, Vo TP. Bending and free vibration of functionally graded beams using various higher- order shear deformation beam theories. Int J Mech Sci. 2012; 62:57–66.
- [13] Rezaei AS, Saidi AR, Abrishamdari M, Pour Mohammadi MH. Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: An analytical approach. Thin-Walled Struct. 2017; 120:366–77.
- [14] Ebrahimi F, Jafari A. A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities. Mechanics of Mech Adv Mater Struct. 2018; 25:212-224.
- [15] Zenkour AM. Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory. J Sandw Struct Mater 2013; 1–28.
- [16] Thai CH, Zenkour AM, Wahab MA, Nguyen-Xuan H. A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis, Compos Struc. 2016; 139: 77–95.
- [17] Thai HT, Kim SE. A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates. Compos Struc. 2013; 96: 165–173.
- [18] Zhu J, Lai Z, Yin Z, Jeon J, Lee S. Fabrication of ZrO2–NiCr functionally graded material by powder metallurgy. Mater Chem Phys 2001; 68: 130–5.
- [19] Chen D, Kitipornchai S, Yang J. Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Struct 2016; 107: 39–48.
- [20] Hadji L, Zouatnia N, Bernard F. An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models. Struct Eng Mech. 2019; 69: 231-241.
- [21] Tang H, Li L, Hu Y. Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams. Appl. Math. Model. 2019; 66: 527–547.
- [22] Kitipornchai S, Chen D, Yang J. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater Des. 2017; 116: 656-665.
- [23] Al Rjoub YS, Hamad AG. Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE J Civ Eng. 2017; 21: 792.
- [24] Ebrahimi F, Ghasemi F, Salari E. Investigating thermal effects on vibration behavior of temperature dependent compositionally graded Euler beams with porosities. Meccanica. 2016: 51; 223.
- [25] Akbaş ŞD. Forced vibration analysis of functionally graded porous deep beams. Compos Struct 2018; 186: 293–302.
- [26] Ebrahimi F, Jafari A. Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory. Struct Eng Mech. 2016: 59; 343-371.
- [27] Touratier M. An efficient standard plate theory. Int J Eng Sci. 1991; 29: 901–16.
FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED POROUS BEAM
Yıl 2020,
Cilt: 8 Sayı: 1, 49 - 60, 28.02.2020
Vedat Taşkın
,
Pınar Aydan Demirhan
Kaynakça
- [1] Chen L, Goto T. Handbook Of Advanced Ceramics. Chapter 16: Functionally Graded Materials. 445-464, 2003.
- [2] Jones RM. Mechanics of Composite Materials. Taylor and Francis, 1999.
- [3] Reddy JN. Analysis of functionally graded plates. Int J Numer Meth Engng 2000; 47: 663-684.
- [4] Demirhan PA. Fonksiyonel Derecelendirilmiş Sandviç Kiriş ve Plakların Dört Değişkenli Kayma Deformasyon Teorisi ile Eğilme ve Titreşim Analizi. Doktora Tezi, Trakya Üniversitesi Fen Bilimleri Enstitüsü, Edirne, Türkiye, 2016.
- [5] Shimpi RP. Refined Plate Theory and Its Variants. AIAA Journal. 2002; 40:1.
- [6] Shimpi RP, Patel HG. A two variable refined plate theory for orthotropic plate analysis. Int J Solids Struct. 2006; 43: 6783–6799.
- [7] S.E. Kim, H.T. Thai, J. Lee, A two variable refined plate theory for laminated composite plates, Compos Struc. 89, 197–205, 2009
- [8] Mechab I, Atmane HA, Tounsi A, Belhadj HA, Bedia EAA. A two variable refined plate theory for the bending analysis of functionally graded plates. Acta Mech Sin. 2010; 26: 941–949.
- [9] Demirhan PA, Taskin V. Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory. Compos Struct 2017; 177: 80–95.
- [10] Demirhan PA, Taskin V. Static analysis of simply supported functionally graded sandwich plates by using four variable plate theory. Teknik Dergi. 2019; 8987-9007.
- [11] Demirhan PA, Taskin V. Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach. Compos B Eng. 2019; 160:661-676.
- [12] Thai HT, Vo TP. Bending and free vibration of functionally graded beams using various higher- order shear deformation beam theories. Int J Mech Sci. 2012; 62:57–66.
- [13] Rezaei AS, Saidi AR, Abrishamdari M, Pour Mohammadi MH. Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: An analytical approach. Thin-Walled Struct. 2017; 120:366–77.
- [14] Ebrahimi F, Jafari A. A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities. Mechanics of Mech Adv Mater Struct. 2018; 25:212-224.
- [15] Zenkour AM. Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory. J Sandw Struct Mater 2013; 1–28.
- [16] Thai CH, Zenkour AM, Wahab MA, Nguyen-Xuan H. A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis, Compos Struc. 2016; 139: 77–95.
- [17] Thai HT, Kim SE. A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates. Compos Struc. 2013; 96: 165–173.
- [18] Zhu J, Lai Z, Yin Z, Jeon J, Lee S. Fabrication of ZrO2–NiCr functionally graded material by powder metallurgy. Mater Chem Phys 2001; 68: 130–5.
- [19] Chen D, Kitipornchai S, Yang J. Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Struct 2016; 107: 39–48.
- [20] Hadji L, Zouatnia N, Bernard F. An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models. Struct Eng Mech. 2019; 69: 231-241.
- [21] Tang H, Li L, Hu Y. Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams. Appl. Math. Model. 2019; 66: 527–547.
- [22] Kitipornchai S, Chen D, Yang J. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater Des. 2017; 116: 656-665.
- [23] Al Rjoub YS, Hamad AG. Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE J Civ Eng. 2017; 21: 792.
- [24] Ebrahimi F, Ghasemi F, Salari E. Investigating thermal effects on vibration behavior of temperature dependent compositionally graded Euler beams with porosities. Meccanica. 2016: 51; 223.
- [25] Akbaş ŞD. Forced vibration analysis of functionally graded porous deep beams. Compos Struct 2018; 186: 293–302.
- [26] Ebrahimi F, Jafari A. Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory. Struct Eng Mech. 2016: 59; 343-371.
- [27] Touratier M. An efficient standard plate theory. Int J Eng Sci. 1991; 29: 901–16.