Influence of Porosity on the Free Vibration Response of Sandwich Functionally Graded Porous Beams

Yıl 2022, Cilt: 7 Sayı: 4, 291 - 301, 30.12.2022

Sura Kareem Al-ıtbı , Ahmad Reshad Noorı

https://doi.org/10.47481/jscmt.1165940

Cited By: 4

Öz

Functionally graded materials are composite materials used to build a variety of structures. These structures are used in ships industries, marine, automotive, high building structures, energy engineering applications, and many more. The porosity made in these materials may negatively affect some behavior aspects like stiffness, and strength, but it may provide superior performance in other fields like vibration reduction, thermal isolation, energy absorption, and others. In this paper, we will discuss the effect of porosity on the natural frequencies for functionally graded porous (FGP) sandwich beams. The mechanical properties of the FGP sandwich beams are changing with the porosity in the thickness direction. The free vibration of the beams is examined with the effect of porosity. The analysis is carried out for four different beam supporting types (hinged – hinged, fixed – fixed, fixed – free, fixed – hinged). Various porosity ratios are considered with a range from (0.1 – 0.9). Forty–four samples are analyzed for each type of core material distribution which is the symmetric material constitutive relationships (SMCR) and uniform core material. The results gained from the analysis show that the porosity constant has a significant effect on the natural frequencies of the FGP sandwich beams.

Anahtar Kelimeler

Dynamic analysis, Finite element method, FGM, Porous materials, Sandwich beam, Free vibration

Kaynakça

• [1] Prasad, M. S., Reddy, P. S., Manoj, M., & Murthy, N. G. (2014). Analysis of sandwich beam. International Journal of Science Engineering and Advance Technology, 2(12), 901–908.
• [2] Wu, H., Yang, J., & Kitipornchai, S. (2020). Mechanical analysis of functionally graded porous structures: A review. International Journal of Structural Stability and Dynamics, 20(13), Article 2041015. [CrossRef]
• [3] Noori, A. R., Aslan, T. A., & Temel, B. (2021). dynamic analysis of functionally graded porous beams using complementary functions method in the Laplace domain. Composite Structures, 256, Article 113094. [CrossRef]
• [4] Zhao, J., Wang, Q., Deng, X., Choe, K., Xie, F., & Shuai, C. (2018). 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. [CrossRef]
• [5] Akbaş, Ş. D. (2017). Forced vibration analysis of functionally graded porous deep beams. Composite Structures, 186, 293–302. [CrossRef]
• [6] Rao, S. S. (2007). Vibration of continuous systems. John Wiely & Sons.
• [7] Wang, Q., & Quek, S. T. (2000). Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator. Smart Materials and Structures, 9(1), Article 103. [CrossRef]
• [8] Chen, D., Kitipornchai, S., & Yang, J. (2016). Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. ThinWalled Structures, 107, 39–48. [CrossRef]
• [9] Yang, Y., Lam, C. C., Kou, K. P., & Iu, V. P. (2014). Free vibration analysis of the functionally graded sandwich beams by a mesh free boundary-domain integral equation method. Composite Structures, 117, 32–39. [CrossRef]
• [10] Wattanasakulpong, N., & Ungbhakorn, V. (2014). Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology, 32(1), 111– 120. [CrossRef]
• [11] Mechab, I., Mechab, B., Benaissa, S., Serier, B., & Bouiadjra, B. B. (2016). Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(8), 2193–2211. [CrossRef]
• [12] Chen, D., Yang, J., & Kitipornchai, S. (2015). Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures, 33, 54–61. [CrossRef]
• [13] Şimşek, M., & Aydın, M. (2016). Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory. Composite Structures, 160, 408–421. [CrossRef]
• [14] Ebrahimi, F., & Jafari, A. (2016). A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities. Journal of Engineering, 2016, Article 9561504. [CrossRef]
• [15] Ait Atmane, H., Tounsi, A., & Bernard, F. (2015). Effect of thickness stretching and porosity on mechcal response of a functionally graded beams resting on elastic foundations. International Journal of Mechanics and Materials in Design, 13(1), 71–84. [CrossRef]
• [16] Chen, D., Yang, J., & Kitipornchai, S. (2016). Free and forced vibrations of shear deformable functionally graded porous beams. International Journal of Mechanical Sciences, 108, 14–22. [CrossRef]
• [17] Dilbas, H. (2021). Application of finite element method on recycled aggregate concrete and reinforced recycled aggregate concrete: A review. Journal of Sustainable Construction Materials and Technologies, 4(6), 173–191. [CrossRef]
• [18] Doori, S., & Noori, A. R. (2021). Finite element approach for the bending analysis of castellated steel beams with various web openings. ALKU Journal of Science, 2(3), 38–49. [CrossRef]
• [19] Noori, A. R., Aslan, T. A., & Temel, B. (2019). Dairesel plakların sonlu elemanlar yöntemi ile laplace uzayında dinamik analizi. Omer Halisdemir University Journal of Engineering Sciences, 8(1), 193–205. [CrossRef]
• [20] Aslan, T. A., & Temel, B. (2022). Finite element analysis of the seepage problem in the dam body and foundation based on the Galerkin's approach. European Mechanical Science, 6(2), 143–151. [CrossRef]
• [21] Yildirim, S. (2021). Free vibration of axially or transversely graded beams using finite-element and artificial intelligence. Alexandria Engineering Journal, 6, 2220–2229. [CrossRef]
• [22] Temel, B., & Şahan, M. F. (2013). Transient analysis of orthotropic, viscoelastic thick plates in the Laplace domain. European Journal of Mechanics A/ Solids, 37, 96–105. [CrossRef]
• [23] Aribas, U. N., Ermis, M., Eratli, N., & Omurtag, M. H. (2019). The static and dynamic analyses of warping included composite exact conical helix by mixed FEM. Composites Part B, 160, 285–297. [CrossRef]
• [24] Chen, J., Shou, Y., & Zhou, X. (2022). Implementation of the novel perfectly matched layer element for elastodynamic problems in time-domain finite element method. Soil Dynamics and Earthquake Engineering, 152, Article 107054. [CrossRef]
• [25] Hobiny, A. D., & Abbas, I. (2022). The impacts of variable thermal conductivity in a semiconducting medium using finite element method. Case Studies in Thermal Engineering, 31, Article 101773. [CrossRef]
• [26] Chai, Y., Li, W., & Liu, Z. (2022). Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions. Applied Mathematics and Computation, 412, Article 126564. [CrossRef]
• [27] Wu, N., Liang, Z., Zhang, Z., Li, S., & Lang, Y. (2022). Development and verification of three-dimensional equivalent discrete fracture network modelling based on the finite element method. Engineering Geology, 306, Article 106759. [CrossRef]
• [28] Zhou, L., Wang, J., Liu, M., Li, M., & Chai, Y. (2022). Evaluation of the transient performance of magneto-electro-elastic based structures with the enriched finite element method. Composite Structures, 280, Article 114888. [CrossRef]
• [29] Noori, A. R., & Temel, B. (2020). On the vibration analysis of laminated composite parabolic arches with variable cross-section of various ply stacking sequences. Mechanics of Advanced Materials and Structures, 27(19), 1658–1672. [CrossRef]
• [30] Van Vinh, P. (2022). Nonlocal free vibration characteristics of power-law and sigmoid functionally graded nanoplates considering variable nonlocal parameter. Physica E: Low-dimensional Systems and Nanostructures, 135, Article 114951. [CrossRef]
• [31] Akbari, H., Azadi, M., & Fahham, H. (2022). Free vibration analysis of thick sandwich cylindrical panels with saturated FG-porous core. Mechanics Based Design of Structures and Machines, 50(4), 1268– 1286. [CrossRef]
• [32] Liu, X., Zhao, Y., Zhou, W., & Banerjee, J. R. (2022). Dynamic stiffness method for exact longitudinal free vibration of rods and trusses using simple and advanced theories. Applied Mathematical Modelling, 104, 401–420. [CrossRef]
• [33] Daikh, A. A., Bachiri, A., Houari, M. S. A., & Tounsi, A. (2022). Size dependent free vibration and buckling of multilayered carbon nanotubes reinforced composite nanoplates in thermal environment. Mechanics Based Design of Structures and Machines, 50(4), 1371–1399. [CrossRef]
• [34] Chen, W., Luo, W. M., Chen, S. Y., & Peng, L. X. (2022). A FSDT meshfree method for free vibration analysis of arbitrary laminated composite shells and spatial structures. Composite Structures, 279, Article 114763. [CrossRef]
• [35] Garg, A., Chalak, H. D., Zenkour, A. M., Belarbi, M. O., & Sahoo, R. (2022). Bending and free vibration analysis of symmetric and unsymmetric functionally graded CNT reinforced sandwich beams containing softcore. Thin-Walled Structures, 170, Article 108626. [CrossRef]
• [36] Rachid, A., Ouinas, D., Lousdad, A., Zaoui, F. Z., Achour, B., Gasmi, H., Butt T.A. & Tounsi, A. (2022). Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs. Thin-Walled Structures, 172, Article 108783. [CrossRef]
• [37] Bozyigit, B., & Acikgoz, S. (2022). Determination of free vibration properties of masonry arch bridges using the dynamic stiffness method. Engineering Structures, 250, Article 113417. [CrossRef]
• [38] Babuscu Yesil, U., & Yahnioglu, N. (2022). Free vibration of simply supported piezoelectric plates containing a cylindrical cavity. Archive of Applied Mechanics, 92, 2665–2678. [CrossRef]
• [39] Jin, H., Sui, S., Zhu, C., & Li, C. (2022). Axial free vibration of rotating fg piezoelectric nano rods accounting for nonlocal and strain gradient effects. Journal of Vibration Engineering & Technologies, 1–13. [CrossRef]
• [40] Zamani, H. A. (2021). Free vibration of functionally graded viscoelastic foam plates using shearand normal-deformation theories. Mechanics of Time-Dependent Materials, 1–22. [CrossRef]
• [41] Yildirim, S. (2020). An efficient method for the plane vibration analysis of composite sandwich beam with an orthotropic core. Cumhuriyet Science Journal, 41(2), 521–526. [CrossRef]
• [42] Temel, B. (2004). Transient analysis of viscoelastic helical rods subject to time-dependent loads. International Journal of Solids and Structures, 41(5–6), 1605–1624. [CrossRef]
• [43] Calim, F. F. (2016). Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation. Composites Part B, 103, 98–112. [CrossRef]
• [44] Noori, A. R. , Rasooli, H. , Aslan, T. A. & Temel, B. (2020). Static analysis of functionally graded sandwich beams by the complementary functions method. Çukurova University Journal of the Faculty of Engineering and Architecture, 35(4), 1091–1102.
• [45] Rasooli, H., Noori, A. R., & Temel, B. (2021). On the static analysis of laminated composite frames having variable cross section. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, Article 258. [CrossRef]
• [46] Humaish, H., Ruet, B., Marmoret, L., & Beji, H. (2016). Assessment of long time approximation equation to determine thermal conductivity of high porous materials with NSS probe. Journal of Sustainable Construction Materials and Technologies, 1(1), 1–15. [CrossRef]
• [47] Pham, Q. H., Tran, T. T., Tran, V. K., Nguyen, P. C., & Nguyen-Thoi, T. (2022). Free vibration of functionally graded porous non-uniform thickness annular-nanoplates resting on elastic foundation using ES-MITC3 element. Alexandria Engineering Journal, 61, 1788–1802. [CrossRef]
• [48] 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. [CrossRef]
• [49] Chen, D., Rezaei, S., Rosendahl, P. L., Xu, B. X., & Schneider, J. (2022). Multiscale modelling of functionally graded porous beams: Buckling and vibration analyses. Engineering Structures, 266, Article 114568. [CrossRef]
• [50] Najibi, A., & Shojaeefard, M. H. (2022). Fourier and time-phase-lag heat conduction analysis of the functionally graded porosity media. International Communications in Heat and Mass Transfer, 136, Article 106183. [CrossRef]
• [51] Ramteke, P. M., Panda, S. K., & Patel, B. (2022). Nonlinear eigenfrequency characteristics of multi-directional functionally graded porous panels. Composite Structures, 279, Article 114707. [CrossRef]
• [52] Liu, Y., Qin, Z., & Chu, F. (2022). Analytical study of the impact response of shear deformable sandwich cylindrical shell with a functionally graded porous core. Mechanics of Advanced Materials and Structures, 29(9), 1338–1347. [CrossRef]
• [53] Surmeneva, M. A., Khrapov, D., Prosolov, K., Kozadayeva, M., Koptyug, A., Volkova, A., Paveleva, A. & Surmenev, R. A (2022). The influence of chemical etching on porous structure and mechanical properties of the Ti6AL4V Functionally Graded Porous Scaffolds fabricated by EBM. Materials Chemistry and Physics, 275, Article 125217. [CrossRef]
• [54] Ansari, R., Oskouie, M. F., & Zargar, M. (2022). Hygrothermally induced vibration analysis of bidirectional functionally graded porous beams. Transport in Porous Media, 142, 41–62. [CrossRef]
• [55] Teng, M. W., & Wang, Y. Q. (2021). Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets. Thin-Walled Structures, 164, Article 107799. [CrossRef]
• [56] Pham, Q. H., Tran, T. T., Tran, V. K., Nguyen, P. C., Nguyen-Thoi, T., & Zenkour, A. M. (2021). Bending and hygro-thermo-mechanical vibration analysis of a functionally graded porous sandwich nanoshell resting on elastic foundation. Mechanics of Advanced Materials and Structures, 1–21. [CrossRef]
• [57] Su, J., Qu, Y., Zhang, K., Zhang, Q., & Tian, Y. (2021). Vibration analysis of functionally graded porous piezoelectric deep curved beams resting on discrete elastic supports. Thin-Walled Structures, 164, Article 107838. [CrossRef]
• [58] 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, [Epub ahead of print] doi: 10.1142/ S0219455423500396 [CrossRef]
• [59] ANSYS Mechanical APDL Element Reference. Mechanical APDL element reference. Pennsylvania: ANSYS Inc; 2013.
• [60] ANSYS Inc. (Oct 10, 2022). Gain greater engineering and product life cycle perspectives 2022 product releases & updates. Release Ansys 2022 R2, Canonsburg, PA, 2022. Available at: https://www.ansys. com/products/release-highlights.