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FORCED VIBRATION ANALYSIS OF FUNCTIONALLY GRADED POROUS SANDWICH BEAMS

Yıl 2023, , 909 - 921, 03.12.2023

Ajmal Chopan Ahmad Reshad Noorı

https://doi.org/10.17780/ksujes.1320945

Öz

In this paper, the elastic and viscoelastic forced vibration behavior of sandwich beams made of functionally graded porous material is investigated theoretically. The bottom and top layers of the sandwich beam consisting of three layers are modeled as isotropic homogeneous and the core layer is modeled as porous material. ANSYS software is used to analyze the modeled beams by the finite element method. BEAM189 element which is based on the first-order shear deformation effect is used to generate the finite element models of the considered structural elements. The cross-sectional properties of the beam are assumed to be uniform. Three types of porosity functions are used in the analysis: symmetric, uniform, and monolithic. The modulus of elasticity and density are taken as variables along the section thickness and the poison ratio is taken as constant. The beams are modeled as clamped-clamped, clamped - pinned, pinned - pinned, and clamped - free. The effects of material variation coefficient, material functions, various boundary conditions, and damping coefficients on the dynamic analysis are investigated in detail. Based on the results obtained from this study, it has been seen that the material function and material distribution coefficients significantly affect the amplitude and period values of the results of dynamic analysis. In the viscoelastic case, it is observed that as the damping ratio increases, the amplitude values decrease more rapidly.

Anahtar Kelimeler

Sandwich Beam Forced Vibration Analysis Porous Material Viscoelastic Behavior Finite Element Method

Kaynakça

  • Ai, Q., & Weaver, P. M. (2016). Simplified analytical model for tapered sandwich beams using variable stiffness materials. Journal of Sandwich Structures & Materials, 19(1), 3-25.‏ https://doi.org/10.1177/1099636215619775
  • 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, 71-84.‏ https://doi.org/10.1007/s10999-015-9318-x
  • Akbas Ş. D. (2015). Free vibration and bending of functionally graded beams resting on elastic foundation. Res. Eng. Struct. Mat., vol. 1, no. 1, pp. 25–37, 2015. http://dx.doi.org/10.17515/resm2015.03st0107
  • Akbaş, Ş. D. (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
  • Al Rjoub, Y.S., & Hamad, A.G(2017). Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE J. Civ. Eng. 21, 792–806. https://doi.org/10.1007/s12205-016-0149-6
  • Al-Itbı, S. K., & Noori, A. R. (2022). Influence of porosity on the free vibration response of sandwich functionally graded porous beams. Journal of Sustainable Construction Materials and Technologies, 7(4). https://doi.org/10.47481/jscmt.1165940
  • Alshorbagy E.A. , Eltaher A.M., & Mahmoud F. F. (2011) Free vibration characteristics of a functionally graded beam by finite element method, Appl. Math. Model, vol. 35, no. 1, pp. 412–425. https://doi.org/10.1016/j.apm.2010.07.006
  • Amirani, M. C., Khalili, S. M. R., & Nemati, N. (2009). Free vibration analysis of sandwich beam with FG core using the element free Galerkin method. Composite structures, 90(3), 373-379.‏ https://doi.org/10.1016/j.compstruct.2009.03.023
  • Aydogdu M. (2008). Semi-inverse method for vibration and buckling of axially functionally graded beams. J. Reinf. Plast.Compos., vol. 27, no. 7, pp. 683–691. https://doi.org/10.1177/0731684407081369
  • Aydogdu M., & Taskin V. (2007). Free vibration analysis of functionally graded beams with simply supported edges. Mater. Des., vol. 28, no. 5, pp. 1651–1656. https://doi.org/10.1016/j.matdes.2006.02.007
  • Aydogdu M., Maroti G., & Elishakoff I. (2013). A note on semiinverse method for buckling of axially functionally graded beams. J. Reinf. Plast.Compos., vol. 32, no. 7, pp. 511–512. https://doi.org/10.1177/0731684412474999
  • Bhangale R. K., & Ganesan N. (2006). Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core. J. Sound Vib., vol. 295, no. 1–2, pp. 294–316.
  • Celebi K., & Tutuncu N. (2014). Free vibration analysis of functionally graded beams using an exact plane elasticity approach. Proc. IMechE Part C: J. Mech. Eng. Sci., vol. 228, no. 14, pp. 2488–2494. https://doi.org/10.1177/0954406213519974
  • Chen D, Yang J, Kitipornchai S. (2019). Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method. Archives of Civil and Mechanical Engineering ;19(1):157-170. https://doi.org/10.1016/j.acme.2018.09.004
  • Chen, D., Kitipornchai, S., & Yang, J. (2016). Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures, 107, 39-48.‏ https://doi.org/10.1016/j.tws.2016.05.025
  • Chu P., X.F. Li, Wu J.X., & Lee K.Y. (2015). Two-dimensional elasticity solution of elastic strips and beams made of functionally graded materials under tension and bending, Acta Mech. vol. 226, no. 7, pp. 2235–2253. https://doi.org/10.1007/s00707-014-1294-y
  • Daikh, A.A., & Zenkour, A.M. (2019). Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory. Materials Research Express. 6(11):115707. https://doi.org/10.1088/2053-1591/ab48a9
  • Daouadji T. H., Henni A. H., Tounsi A., & El Abbes A. B. (2013). Elasticity solution of a cantilever functionally graded beam. Appl. Compos. Mater., vol. 20, no. 1, pp. 1–15. https://doi.org/10.1007/s10443-011-9243-6
  • Das, S., & Sarangi, S. K. (2016, September). Static analysis of functionally graded composite beams. In IOP Conference Series: Materials Science and Engineering (Vol. 149, No. 1, p. 012138). IOP Publishing. https://doi.org/10.1088/1757-899X/149/1/012138
  • Ding, D.H., Huang, D.J., & Chen, W.Q. (2007). Elasticity solutions for plane anisotropic functionally graded beams. Int. J. Solids Struct., vol. 44, no. 1, pp. 176–196. https://doi.org/10.1016/j.ijsolstr.2006.04.026
  • Ebrahimi, F., Ghasemi, F., & Salari, E. (2016). Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica 51, 223–249. https://doi.org/10.1007/s11012-015-0208-y
  • Fouaidi, M., Jamal, M., & Belouaggadia N. (2020). Nonlinear bending analysis of functionally graded porous beams using the multiquadric radial basis functions and a Taylor series-based continuation procedure. Composite Structures, 252:112593. https://doi.org/10.1016/j.compstruct.2020.112593
  • Gao, K., Li, R., & Yang, J. (2019). Dynamic characteristics of functionally graded porous beams with interval material properties. Eng. Struct. 197, 109441. https://doi.org/10.1016/j.engstruct.2019.109441
  • Huang D.J., Ding D.H., & Chen W.Q.. (2007). Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load. Appl. Math. Mech., vol. 28, no. 7, pp. 855– 860. https://doi.org/10.1016/j.ijsolstr.2006.04.026
  • Huang, D.J. Ding, D.H., & Chen. W.Q. (2009) . Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading. Sci. China Phys. Mech. Astron., vol. 52, no. 8, pp. 1244–1256. https://doi.org/10.1007/s11433-009-0152-8
  • Jabbari M., Mojahedin A., Khorshidvand A.R., & Eslami M.R. (2014). Buckling Analysis of a Functionally Graded Thin Circular Plate Made of Saturated Porous Materials. Journal of Engineering Mechanics,140(2):287-295. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000663
  • Jamshidi M, Arghavani J, & Maboudi G. (2019). Post-buckling optimization of two-dimensional functionally graded porous beams. International Journal of Mechanics and Materials in Design,15(4):801-815. https://doi.org/10.1007/s10999-019-09443-3
  • Kiani Y., & Eslami M. R. (2010). Thermal buckling analysis of functionally graded material beams. Int. J. Mech. Mater. Des., vol. 6, no. 3, pp. 229–238. https://doi.org/10.1007/s10999-010-9132-4
  • Kiani Y., & Eslami M. R. (2013). Thermomechanical buckling of temperature dependent FGM beams. Lat. Am. J. Solids Struct., vol. 10, no. 2, pp. 223–246. https://doi.org/10.1590/S1679-78252013000200001
  • Kim N., & Lee J. (2016). Theory of thin-walled functionally graded sandwich beams with single, and double-cell sections. Compos. Struct., vol. 157, pp. 141–154. https://doi.org/10.1016/j.compstruct.2016.07.024
  • Kim N., & Lee J. (2017). Flexural-torsional analysis of functionally graded sandwich I-beams considering shear effects. Compos. Part B-Eng., vol. 108, pp. 436–450. https://doi.org/10.1016/j.compositesb.2016.09.092
  • Liu Z., Yang C., Gao W., Wu D., & Li G. (2019). Nonlinear behaviour and stability of functionally graded porous arches with graphene platelets reinforcements. International Journal of Engineering Science, 137:37-56. https://doi.org/10.1016/j.ijengsci.2018.12.003
  • Mojahedin A., Jabbari M., Khorshidvand A.R., & Eslami M.R. (2016). Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory. Thin-Walled Structures; 99:83-90. https://doi.org/10.1016/j.tws.2015.11.008
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FONKSİYONEL DERECELENDİRİLMİŞ GÖZENEKLİ SANDVİÇ KİRİŞLERİN ZORLANMIŞ TİTREŞİM ANALİZİ

Yıl 2023, , 909 - 921, 03.12.2023

Ajmal Chopan Ahmad Reshad Noorı

https://doi.org/10.17780/ksujes.1320945

Öz

Bu çalışmada, fonksiyonel derecelendirilmiş gözenekli malzemeden yapılmış sandviç kirişlerin elastik ve viskoelastik zorlanmış titreşim davranışı teorik olarak incelenmiştir. Üç tabakadan oluşan sandviç kirişin alt ve üst katmanı izotropik homojen ve çekirdek tabakası ise gözenekli malzemeli olarak modellenmiştir. Modellenen kirişlerin sonlu elemanlar metodu ile analiz edilebilmesi için ANSYS programı kullanılmıştır. Ele alınan yapı elemanlarının sonlu eleman modellerinin kurulması için birinci mertebeden kayma deformasyon etkisine dayalı BEAM189 elemanı kullanılmıştır. Kirişin kesit özelliklerinin üniform olduğu varsayılmıştır. Analizlerde simetrik, üniform ve monolitik olmak üzere üç çeşit gözenek fonksiyonundan faydalanmıştır. Kesit kalınlığı boyunca elastiste modülü ve yoğunluk değişken olarak, Poison oranı ise sabit olarak alınmıştır. Kirişler ankastre – ankastre, ankastre – sabit, sabit – sabit ve ankastre – serbest olarak modellenmiştir. Malzeme değişim katsayısının, malzeme değişim fonksiyonun, çeşitli sınır koşullarının ve sönüm katsayılarının dinamik analiz üzerindeki etkileri detaylı bir şekilde araştırılmıştır. Bu çalışmadan elde edilen sonuçlara göre malzeme gözenek fonksiyonu ve malzeme değişim katsayıları dinamik analizin sonuçlarından genlik ve periyot değerlerini önemli ölçüde etkilediği görülmüştür. Viskoelastik durumunda sönüm oranı arttıkça genlik değerlerinin daha hızlı bir şekilde küçüldüğü gözlemlenmiştir.

Anahtar Kelimeler

Sandviç kiriş Zorlanmış Titreşim Analizi Gözenekli Malzeme Viskoelastik Davranış Sonlu Elemanlar Yöntemi

Kaynakça

  • Ai, Q., & Weaver, P. M. (2016). Simplified analytical model for tapered sandwich beams using variable stiffness materials. Journal of Sandwich Structures & Materials, 19(1), 3-25.‏ https://doi.org/10.1177/1099636215619775
  • 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, 71-84.‏ https://doi.org/10.1007/s10999-015-9318-x
  • Akbas Ş. D. (2015). Free vibration and bending of functionally graded beams resting on elastic foundation. Res. Eng. Struct. Mat., vol. 1, no. 1, pp. 25–37, 2015. http://dx.doi.org/10.17515/resm2015.03st0107
  • Akbaş, Ş. D. (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
  • Al Rjoub, Y.S., & Hamad, A.G(2017). Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method. KSCE J. Civ. Eng. 21, 792–806. https://doi.org/10.1007/s12205-016-0149-6
  • Al-Itbı, S. K., & Noori, A. R. (2022). Influence of porosity on the free vibration response of sandwich functionally graded porous beams. Journal of Sustainable Construction Materials and Technologies, 7(4). https://doi.org/10.47481/jscmt.1165940
  • Alshorbagy E.A. , Eltaher A.M., & Mahmoud F. F. (2011) Free vibration characteristics of a functionally graded beam by finite element method, Appl. Math. Model, vol. 35, no. 1, pp. 412–425. https://doi.org/10.1016/j.apm.2010.07.006
  • Amirani, M. C., Khalili, S. M. R., & Nemati, N. (2009). Free vibration analysis of sandwich beam with FG core using the element free Galerkin method. Composite structures, 90(3), 373-379.‏ https://doi.org/10.1016/j.compstruct.2009.03.023
  • Aydogdu M. (2008). Semi-inverse method for vibration and buckling of axially functionally graded beams. J. Reinf. Plast.Compos., vol. 27, no. 7, pp. 683–691. https://doi.org/10.1177/0731684407081369
  • Aydogdu M., & Taskin V. (2007). Free vibration analysis of functionally graded beams with simply supported edges. Mater. Des., vol. 28, no. 5, pp. 1651–1656. https://doi.org/10.1016/j.matdes.2006.02.007
  • Aydogdu M., Maroti G., & Elishakoff I. (2013). A note on semiinverse method for buckling of axially functionally graded beams. J. Reinf. Plast.Compos., vol. 32, no. 7, pp. 511–512. https://doi.org/10.1177/0731684412474999
  • Bhangale R. K., & Ganesan N. (2006). Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core. J. Sound Vib., vol. 295, no. 1–2, pp. 294–316.
  • Celebi K., & Tutuncu N. (2014). Free vibration analysis of functionally graded beams using an exact plane elasticity approach. Proc. IMechE Part C: J. Mech. Eng. Sci., vol. 228, no. 14, pp. 2488–2494. https://doi.org/10.1177/0954406213519974
  • Chen D, Yang J, Kitipornchai S. (2019). Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method. Archives of Civil and Mechanical Engineering ;19(1):157-170. https://doi.org/10.1016/j.acme.2018.09.004
  • Chen, D., Kitipornchai, S., & Yang, J. (2016). Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures, 107, 39-48.‏ https://doi.org/10.1016/j.tws.2016.05.025
  • Chu P., X.F. Li, Wu J.X., & Lee K.Y. (2015). Two-dimensional elasticity solution of elastic strips and beams made of functionally graded materials under tension and bending, Acta Mech. vol. 226, no. 7, pp. 2235–2253. https://doi.org/10.1007/s00707-014-1294-y
  • Daikh, A.A., & Zenkour, A.M. (2019). Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory. Materials Research Express. 6(11):115707. https://doi.org/10.1088/2053-1591/ab48a9
  • Daouadji T. H., Henni A. H., Tounsi A., & El Abbes A. B. (2013). Elasticity solution of a cantilever functionally graded beam. Appl. Compos. Mater., vol. 20, no. 1, pp. 1–15. https://doi.org/10.1007/s10443-011-9243-6
  • Das, S., & Sarangi, S. K. (2016, September). Static analysis of functionally graded composite beams. In IOP Conference Series: Materials Science and Engineering (Vol. 149, No. 1, p. 012138). IOP Publishing. https://doi.org/10.1088/1757-899X/149/1/012138
  • Ding, D.H., Huang, D.J., & Chen, W.Q. (2007). Elasticity solutions for plane anisotropic functionally graded beams. Int. J. Solids Struct., vol. 44, no. 1, pp. 176–196. https://doi.org/10.1016/j.ijsolstr.2006.04.026
  • Ebrahimi, F., Ghasemi, F., & Salari, E. (2016). Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica 51, 223–249. https://doi.org/10.1007/s11012-015-0208-y
  • Fouaidi, M., Jamal, M., & Belouaggadia N. (2020). Nonlinear bending analysis of functionally graded porous beams using the multiquadric radial basis functions and a Taylor series-based continuation procedure. Composite Structures, 252:112593. https://doi.org/10.1016/j.compstruct.2020.112593
  • Gao, K., Li, R., & Yang, J. (2019). Dynamic characteristics of functionally graded porous beams with interval material properties. Eng. Struct. 197, 109441. https://doi.org/10.1016/j.engstruct.2019.109441
  • Huang D.J., Ding D.H., & Chen W.Q.. (2007). Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load. Appl. Math. Mech., vol. 28, no. 7, pp. 855– 860. https://doi.org/10.1016/j.ijsolstr.2006.04.026
  • Huang, D.J. Ding, D.H., & Chen. W.Q. (2009) . Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading. Sci. China Phys. Mech. Astron., vol. 52, no. 8, pp. 1244–1256. https://doi.org/10.1007/s11433-009-0152-8
  • Jabbari M., Mojahedin A., Khorshidvand A.R., & Eslami M.R. (2014). Buckling Analysis of a Functionally Graded Thin Circular Plate Made of Saturated Porous Materials. Journal of Engineering Mechanics,140(2):287-295. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000663
  • Jamshidi M, Arghavani J, & Maboudi G. (2019). Post-buckling optimization of two-dimensional functionally graded porous beams. International Journal of Mechanics and Materials in Design,15(4):801-815. https://doi.org/10.1007/s10999-019-09443-3
  • Kiani Y., & Eslami M. R. (2010). Thermal buckling analysis of functionally graded material beams. Int. J. Mech. Mater. Des., vol. 6, no. 3, pp. 229–238. https://doi.org/10.1007/s10999-010-9132-4
  • Kiani Y., & Eslami M. R. (2013). Thermomechanical buckling of temperature dependent FGM beams. Lat. Am. J. Solids Struct., vol. 10, no. 2, pp. 223–246. https://doi.org/10.1590/S1679-78252013000200001
  • Kim N., & Lee J. (2016). Theory of thin-walled functionally graded sandwich beams with single, and double-cell sections. Compos. Struct., vol. 157, pp. 141–154. https://doi.org/10.1016/j.compstruct.2016.07.024
  • Kim N., & Lee J. (2017). Flexural-torsional analysis of functionally graded sandwich I-beams considering shear effects. Compos. Part B-Eng., vol. 108, pp. 436–450. https://doi.org/10.1016/j.compositesb.2016.09.092
  • Liu Z., Yang C., Gao W., Wu D., & Li G. (2019). Nonlinear behaviour and stability of functionally graded porous arches with graphene platelets reinforcements. International Journal of Engineering Science, 137:37-56. https://doi.org/10.1016/j.ijengsci.2018.12.003
  • Mojahedin A., Jabbari M., Khorshidvand A.R., & Eslami M.R. (2016). Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory. Thin-Walled Structures; 99:83-90. https://doi.org/10.1016/j.tws.2015.11.008
  • Naderi A., & Saidi. A.R. (2013). Bending–stretching analysis of moderately thick functionally graded anisotropic wide beams. Arch. Appl. Mech., vol. 83, no. 9, pp. 1359–1370. https://doi.org/10.1007/s00419-013-0751-8
  • Njim, E. K., Bakhi, S. H., & Al-Waily, M. (2022). Experimental and numerical flexural properties of sandwich structure with functionally graded porous materials. Engineering and Technology Journal, 40(01), 137-147.‏ https://doi.org/10.30684/etj.v40i1.2184
  • Noori, A. R., Aslan, T. A., & Temel, B. (2018). Damped transient response of in-plane and out-of-plane loaded stepped curved rods. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 1-25. https://doi.org/10.1007/s40430-017-0949-8
  • Noori A. R., Rasooli H., Aslan T. A., & Temel B. (2020). Fonksiyonel derecelenmiş sandviç kirişlerin tamamlayıcı fonksiyonlar yöntemi ile statik analizi. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 35(4), 1091-1102.‏ https://doi.org/10.21605/cukurovaummfd.869180
  • Noori, A. R., Aslan, T. A., & Temel, B. (2020). Static analysis of FG beams via complementary functions method. European Mechanical Science, 4(1), 1-6.‏ https://doi.org/10.26701/ems.590864
  • Rezaiee-Pajand, M., Masoodi, A. R., & Mokhtari, M. (2018). Static analysis of functionally graded non-prismatic sandwich beams. Adv. Comput. Des, 3(2), 165-190.‏ https://doi.org/10.12989/acd.2018.3.2.165
  • Sankar, B. V. (2001). An elasticity solution for functionally graded beams. Compos. Sci. Technol., vol. 61, no. 5, pp. 689–696. https://doi.org/10.1016/S0266-3538(01)00007-0
  • Srikarun, B., Songsuwan, W., & Wattanasakulpong, N. (2021). Linear and nonlinear static bending of sandwich beams with functionally graded porous core under different distributed loads. Composite Structures, 276, 114538. https://doi.org/10.1016/j.compstruct.2021.114538
  • Su J., Xiang Y., Ke L-L., & Wang Y-S. (2019). Surface effect on static bending of functionally graded porous nanobeams based on Reddy’s Beam Theory. International Journal of Structural Stability and Dynamics. 19(06):1950062 https://doi.org/10.1142/S0219455419500627
  • Şimşek M., & Al-Shujairi M. (2017) Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads. Compos. Part B-Eng., vol. 108, pp. 18–34, 2017. https://doi.org/10.1016/j.compositesb.2016.09.098
  • Turan, M. (2022). Fonksiyonel derecelendirilmiş gözenekli kirişlerin sonlu elemanlar yöntemiyle statik analizi. Mühendislik Bilimleri ve Tasarım Dergisi, 10(4), 1362-1374. https://doi.org/10.21923/jesd.1134356
  • Turan, M., & Adiyaman, G. (2023). Free vibration and buckling analysis of porous two-directional functionally graded beams using a higher-order finite element model. Journal of Vibration Engineering & Technologies, 1-20. https://doi.org/10.1007/s42417-023-00898-5
  • Turan M., & Kahya V. (2021). Free vibration and buckling analysis of functionally graded sandwich beams by Navier’s method. J. Fac. Eng. Archit. Gazi Univ. 36, 743–75. https://doi.org/10.17341/gazimmfd.599928
  • Turan, M., Uzun Yaylacı, E., & Yaylacı, M. (2023). Free vibration and buckling of functionally graded porous beams using analytical, finite element, and artificial neural network methods. Archive of Applied Mechanics, 93(4), 1351-1372. https://doi.org/10.1007/s00419-022-02332-w
  • Venkataraman S., & Sankar B.V. (2003). Elasticity solution for stresses in a sandwich beam with functionally graded core, AIAA J., vol. 41, no. 12, pp. 2501–2505. https://doi.org/10.2514/2.6853
  • Vo T. P., Thai H. T., Nguyen T. K. & Inam F. (2014). Static and vibration analysis of functionally graded beams using refined shear deformation theory. Meccanica, 49, 155-168.‏ https://doi.org/10.1007/s11012-013-9780-1
  • Wattanasakulpong N., & Chaikittiratana A. (2015). Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method. Meccanica 50, 1331–1342. https://doi.org/10.1007/s11012-014-0094-8
  • Wattanasakulpong, N., & Eiadtrong, S. (2022). Transient Responses of Sandwich Plates with a Functionally Graded Porous Core: Jacobi–Ritz Method. International Journal of Structural Stability and Dynamics, 2350039. https://doi.org/10.1142/S0219455423500396
  • Xu Y., Yu T., & Zhou D., Two-dimensional elasticity solution for bending of functionally graded beams with variable thickness. Meccanica, vol. 49, no. 10, pp. 2479–2489, 2014. https://doi.org/10.1007/s11012-014-9958-1
  • Ying J., Lu C.F., & Chen W.Q.. (2008). Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations. Compos. Struct., vol. 84, no. 3, pp. 209–219. https://doi.org/10.1016/j.compstruct.2007.07.004
  • Zhao, J., Wang, Q., Deng, X., Choe, K., Xie, F., & Shuai, C. (2019). A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams. Composites Part B: Engineering, 165, 155-166.‏ https://doi.org/10.1016/j.compositesb.2018.11.080
  • Zhong Z., & Yu T. (2007). Analytical solution of a cantilever functionally graded beam. Compos. Sci. Technol., vol. 67, no. 3–4, pp. 481–488, 2007. https://doi.org/10.1016/j.compscitech.2006.08.023
Toplam 55 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular İnşaat Mühendisliğinde Sayısal Modelleme, Yapı Dinamiği
Bölüm İnşaat Mühendisliği
Yazarlar

Ajmal Chopan 0009-0000-8718-4321

Ahmad Reshad Noorı 0000-0001-6232-6303

Yayımlanma Tarihi 3 Aralık 2023
Gönderilme Tarihi 29 Haziran 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Chopan, A., & Noorı, A. R. (2023). FONKSİYONEL DERECELENDİRİLMİŞ GÖZENEKLİ SANDVİÇ KİRİŞLERİN ZORLANMIŞ TİTREŞİM ANALİZİ. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 26(4), 909-921. https://doi.org/10.17780/ksujes.1320945