Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation

• Autorzy: Njim E.K. , Bakhy S.H. , Al-Waily M.

Identyfikatory

DOI

10.5604/01.3001.0015.5805

• Języki publikacji: EN

Abstrakty

EN

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

Słowa kluczowe

EN

functionally graded materials; sandwich plate; porous metal; frequency analysis; finite element method (FEM)

PL

funkcjonalne materiały gradientowe; płyta warstwowa; metal porowaty; analiza częstotliwości; metoda elementów skończonych (FEM)

• Wydawca: International OCSCO World Press
• Czasopismo: Archives of Materials Science and Engineering
• Rocznik: 2021
• Tom: Vol. 111, nr 2
• Strony: 49--65
• Opis fizyczny: Bibliogr. 70 poz.

Twórcy

autor

Njim E.K.

• Mechanical Engineering Department, University of Technology, Baghdad, Iraq

autor

Bakhy S.H.

• Mechanical Engineering Department, University of Technology, Baghdad, Iraq

autor

Al-Waily M.

• Department of Mechanical Engineering, Faculty of Engineering, University of Kufa, Kufa, Iraq

• https://orcid.org/0000-0002-7630-1980

Bibliografia

• [1] E.K. Njim, M. Al-Waily, S. H. Bakhy, A Critical Review of Recent Research of Free Vibration and Stability of Functionally Graded Materials of Sandwich Plate, IOP Conference Series: Materials Science and Engineering 1094 (2021) 012081. DOI: https://doi.org/10.1088/1757-899X/1094/1/012081
• [2] B. Saleh, J. Jiang, R. Fathi, T. Al-hababi, Q. Xu, L. Wang, D. Song, A. Ma, 30 Years of functionally graded materials: An overview of manufacturing methods, Applications, and Future Challenges, Composites Part B: Engineering 201 (2020) 108376. DOI: https://doi.org/10.1016/j.compositesb.2020.108376
• [3] A. Garg, M.O. Belarbi, H.D. Chalak, A. Chakrabarti, A review of the analysis of sandwich FGM structures, Composite Structures 258 (2021) 113427. DOI: https://doi.org/10.1016/j.compstruct.2020.113427
• [4] E.K. Njim, S.H. Bakhy, M. Al-Waily, Analytical and numerical investigation of buckling load of functionally graded materials with porous metal of sandwich plate, Materials Today: Proceedings (2021) (available online). DOI: https://doi.org/10.1016/j.matpr.2021.03.557
• [5] Y.H. Dong, Y.H. Li, D. Chen, J. Yang, Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion, Composites Part B: Engineering 145 (2018) 1-13. DOI: https://doi.org/10.1016/j.compositesb.2018.03.009
• [6] A.M. Zenkour, A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities, Composite Structures 201 (2018) 38- 48. DOI: https://doi.org/10.1016/j.compstruct.2018.05.147
• [7] M. Arefi, F. Najafitabar, Buckling and free vibration analyses of a sandwich beam made of a soft core with FG-GNPs reinforced composite face-sheets using Ritz Method, Thin-Walled Structures 158 (2021) 107200. DOI: https://doi.org/10.1016/j.tws.2020.107200
• [8] M.D. Sciuva, M. Sorrenti, Bending, free vibration, and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended Refined Zigzag Theory, Composite Structures 227 (2019) 111324. DOI: https://doi.org/10.1016/j.compstruct.2019.111324
• [9] M. Amirpour, S. Bickerton, E. Calius, B.R. Mace, R. Das, Numerical and experimental study on free vibration of 3D-printed polymeric functionally graded plates, Composite Structures 189 (2018) 192-205. DOI: https://doi.org/10.1016/j.compstruct.2018.01.056
• [10] N. Wattanasakulpong, V. Ungbhakorn, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology 32/1 (2014) 111-120. DOI: https://doi.org/10.1016/j.ast.2013.12.002
• [11] N. Wattanasakulpong, A. Chaikittiratana, Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory, Chebyshev collocation method, Meccanica 50 (2015) 1331-1342. DOI: https://doi.org/10.1007/s11012-014-0094-8
• [12] A. Muc, J. Flis, Flutter characteristics and free vibrations of rectangular functionally graded porous plates, Composite Structures 261 (2021) 113301. DOI: https://doi.org/10.1016/j.compstruct.2020.113301
• [13] K. Xie, Y. Wang, H. Niu, H. Chen, Large-amplitude nonlinear free vibrations of functionally graded plates with porous imperfection: A novel approach based on energy balance method, Composite Structures 246 (2020) 112367. DOI: https://doi.org/10.1016/j.compstruct.2020.112367
• [14] S. Hayat, S. Meriem, Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium, Fracture and Structural Integrity 13/50 (2019) 286-299. DOI: https://doi.org/10.3221/IGF-ESIS.50.24
• [15] X.Y. Zhang, G. Fang, S. Leeflang, A.A. Zadpoor, J. Zhou, Topological design, permeability, and mechanical behavior of additively manufactured functionally graded porous metallic biomaterials, Acta Biomaterialia 84 (2018) 437-452. DOI: https://doi.org/10.1016/j.actbio.2018.12.013
• [16] A.H. Mostefa, M. Slimane, Influence of porosity on the analysis of sandwich plates FGM using of high order shear deformation theory, Fracture and Structural Integrity 14/51 (2020) 199-214. DOI: https://doi.org/10.3221/IGF-ESIS.51.16
• [17] S.J. Singh, S.P. Harsha, Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’s method, Journal of Sandwich Structures and Materials 23/5 (2021) 1717-1760. DOI: https://doi.org/10.1177/1099636220904340
• [18] V. Kumar, S.J. Singh, V.H. Saran, S.P. Harsha, Vibration characteristics of porous FGM plate with variable thickness resting on Pasternak’s foundation, European Journal of Mechanics-A/Solids 85 (2021) 104124. DOI: https://doi.org/10.1016/j.euromechsol.2020.104124
• [19] T. Khan, O.A. Aydin, V. Acar, M.R. Aydin, B. Hülagü, H. Bayrakçeken, M.Ö. Seydibeyoğlu, H. Akbulut, Experimental investigation of mechanical and modal properties of Al2O3 nanoparticle reinforced polyurethane core sandwich structures, Materials Today Communications 24 (2020) 101233. DOI: https://doi.org/10.1016/j.mtcomm.2020.101233
• [20] M. Kaddari, A. Kaci, A.A. Bousahla, A. Tounsi, F. Bourada, A. Tounsi, E.A. Bedia, M.A. Al-Osta, A study on the structural behavior of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and free vibration analysis, Computers and Concrete 25/1 (2020) 37-57. DOI: https://doi.org/10.12989/cac.2020.25.1.037
• [21] Q. Li, D. Wu, X. Chen, L. Liu, Y. Yu, W. Gao, Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler– Pasternak elastic foundation, International Journal of Mechanical Sciences 148 (2018) 596-610. DOI: https://doi.org/10.1016/j.ijmecsci.2018.09.020
• [22] Y. Xue, G. Jin, X. Ma, H. Chen, T. Ye, M. Chen, Y. Zheng, Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach, International Journal of Mechanical Sciences 152 (2019) 346-362. DOI: https://doi.org/10.1016/j.ijmecsci.2019.01.004
• [23] M. Abderrahmane, K. Abdelhakim, A.B. Abdelmoumen, B. Fouad, T. Abdeldjebbar, H.B. Kouider, T. Abdelouahed, E.A. Adda Bedia, S.R. Mahmoud, A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions, Steel and Composite Structures 36/3 (2020) 355-367. DOI: https://doi.org/10.12989/scs.2020.36.3.355
• [24] C. Li, H.S. Shen, H. Wang, Z. Yu, Large amplitude vibration of sandwich plates with functionally graded auxetic 3D lattice core, International Journal of Mechanical Sciences 174 (2020) 105472. DOI: https://doi.org/10.1016/j.ijmecsci.2020.105472
• [25] S. Brischetto, Hygrothermoelastic analysis of multi-layered composite and sandwich shells, Journal of Sandwich Structures and Materials 15/2 (2013) 168- 202. DOI: https://doi.org/10.1177/1099636212471358
• [26] A. Garg, H.D. Chalak, A review on analysis of laminated composite and sandwich structures under hygrothermal conditions, Thin-Walled Structures 142 (2019) 205-226. DOI: https://doi.org/10.1016/j.tws.2019.05.005
• [27] A. Garg, H.D. Chalak, Analysis of non-skew and skew laminated composite and sandwich plates under hygro-thermomechanical conditions including transverse stress variations, Journal of Sandwich Structures and Materials 23/8 (2021) 3471-3494. DOI: https://doi.org/10.1177/1099636220932782
• [28] H. Krishna, H.D. Chalak, Behaviour of laminated composite sandwiched structures under thermal conditions, IOP Conference Series: Materials Science and Engineering 872 (2020) 012148. DOI: https://doi.org/10.1088/1757-899X/872/1/012148
• [29] R. Kumar, A. Lal, B.M. Sutaria, Non-linear deflection and stress analysis of laminated composite sandwich plate with elliptical cutout under different transverse loadings in hygro-thermal environment, Curved and Layered Structures 7/1 (2020) 80-100. DOI: https://doi.org/10.1515/cls-2020-0008
• [30] A. Garg, H.D. Chalak, M.O. Belarbi, A. Chakrabarti, M.S.A. Houari, Finite Element-based Free Vibration Analysis of Power-Law, Exponential and Sigmoidal Functionally Graded Sandwich Beams, Journal of The Institution of Engineers (India): Series C 102 (2021) 1167-1201. DOI: https://doi.org/10.1007/s40032-021-00740-5
• [31] H. Hirane, M.O. Belarbi, M.S.A. Houari, A. Tounsi, On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates, Engineering with Computers (2021) (published online). DOI: https://doi.org/10.1007/s00366-020- 01250-1
• [32] P.V. Vinh, A. Tounsi, The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates. Engineering with Computers (2021) (published online). DOI: https://doi.org/10.1007/s00366-021-01475-8
• [33] P.V. Vinh, L.Q. Huy, Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory, Defence Technology (2021) (available online). DOI: https://doi.org/10.1016/j.dt.2021.03.006
• [34] P.V. Vinh, Analysis of bi-directional functionally graded sandwich plates via higher-order shear deformation theory and finite element method, Journal of Sandwich Structures & Materials (2021) (published online). DOI: https://doi.org/10.1177/10996362211025811
• [35] S.H. Chi, Y.L. Chung, Mechanical behavior of functionally graded material plates under transverse load Part I: Analysis, International Journal of Solids and Structures 43/13 (2006) 3657-3674. DOI: https://doi.org/10.1016/j.ijsolstr.2005.04.011
• [36] M. Latifi, F. Farhatnia, M. Kadkhodaei, Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion, Europe a Journal of Mechanics-A/Solids 41 (2013) 16-27. DOI: https://doi.org/10.1016/j.euromechsol.2013.01.008
• [37] M.A. Al-Shammari, M. Al-Waily, Theoretical and Numerical Vibration Investigation Study of Orthotropic Hyper Composite Plate Structure, International Journal of Mechanical and Mechatronics Engineering 14/6 (2014) 1-21.
• [38] M. Al-Waily, K.K. Resan, A.H. Al-Wazir, Z.A.A. Abud Ali, Influences of Glass and Carbon Powder Reinforcement on the Vibration Response and Characterization of an Isotropic Hyper Composite Materials Plate Structure, International Journal of Mechanical and Mechatronics Engineering 17/6 (2017) 74-85.
• [39] K.J. Jweeg, A.S. Hammood, M. Al-Waily, A Suggested Analytical Solution of Isotropic Composite Plate with Crack Effect, International Journal of Mechanical and Mechatronics Engineering 12/5 (2012) 44-58.
• [40] A.A. Alhumdany, M. Al-Waily, M.H.K. Al-Jabery, Theoretical and Experimental Investigation of Using Date Palm Nuts Powder into Mechanical Properties and Fundamental Natural Frequencies of Hyper Composite Plate, International Journal of Mechanical and Mechatronics Engineering 16/1 (2016) 70-80.
• [41] E.N. Abbas, M.J. Jweeg, M. Al-Waily, Analytical and Numerical Investigations for Dynamic Response of Composite Plates Under Various Dynamic Loading with the Influence of Carbon Multi-Wall Tube Nano Materials, International Journal of Mechanical and Mechatronics Engineering 18/6 (2018) 1-10.
• [42] M.J. Jweeg, M. Al-Waily, A.A. Deli, Theoretical and Numerical Investigation of Buckling of Orthotropic Hyper Composite Plates, International Journal of Mechanical and Mechatronics Engineering 15/4 (2015) 1-12.
• [43] J.S. Chiad, M. Al-Waily, M.A. Al-Shammari, Buckling Investigation of Isotropic Composite Plate Reinforced by Different Types of Powders, International Journal of Mechanical Engineering and Technology 9/9 (2018) 305-317.
• [44] M. Al-Waily, M.A. Al-Shammari, M.J. Jweeg, An Analytical Investigation of Thermal Buckling Behavior of Composite Plates Reinforced by Carbon Nano Particles, Engineering Journal 24/3 (2020) 11-21. DOI: https://doi.org/10.4186/ej.2020.24.3.11
• [45] E.K. Njim, M. Al-Waily, S.H. Bakhy, A Review of the Recent Research on the Experimental Tests of Functionally Graded Sandwich Panels, Journal of Mechanical Engineering Research and Developments 44/3 (2021) 420-441.
• [46] M. Al-Waily, A.A. Deli, A.D. Al-Mawash, Z.A.A. Abud Ali, Effect of Natural Sisal Fiber Reinforcement on the Composite Plate Buckling Behavior, International Journal of Mechanical and Mechatronics Engineering 17/1 (2017) 30-37.
• [47] V.N. Burlayenko, T. Sadowski, Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements, Meccanica 55 (2020) 815-832. DOI: https://doi.org/10.1007/s11012-019-01001-7
• [48] S.E. Sadiq, M.J. Jweeg, S.H. Bakhy, The Effects of Honeycomb Parameters on Transient Response of an Aircraft Sandwich Panel Structure, IOP Conference Series: Materials Science and Engineering 928 (2020) 022126. DOI: https://doi.org/10.1088/1757-899X/928/2/022126
• [49] Z.A.A. Abud Ali, A.A. Kadhim, R.H. Al-Khayat, M. Al-Waily, Review Influence of Loads upon Delamination Buckling in Composite Structures, Journal of Mechanical Engineering Research and Developments 44/3 (2021) 392-406.
• [50] M. Al-Waily, Z.A.A. Abud Ali, A Suggested Analytical Solution of Powder Reinforcement Effect on Buckling Load for Isotropic Mat and Short Hyper Composite Materials Plate, International Journal of Mechanical and Mechatronics Engineering 15/4 (2015) 80-95.
• [51] M.R. Ismail, Z.A.A. Abud Ali, M. Al-Waily, Delamination Damage Effect on Buckling Behavior of Woven Reinforcement Composite Materials Plate, International Journal of Mechanical and Mechatronics Engineering 18/5 (2018) 83-93.
• [52] E.K. Njim, S.H. Bakhy, M. Al-Waily, Optimization design of vibration characterizations for functionally graded porous metal sandwich plate structure, Materials Today: Proceedings (2021) (available online). DOI: https://doi.org/10.1016/j.matpr.2021.03.235
• [53] K.F. Arndt, M.D. Lechner, Polymer Solids and Polymer Melts–Mechanical and Thermomechanical Properties of Polymers, 1st Edition, Springer-Verlag Berlin Heidelberg, 2014. DOI: https://doi.org/10.1007/978-3-642-55166-6
• [54] L. Zheng, X.S. Huo, Y. Yuan, Experimental investigation on dynamic properties of rubberized concrete, Construction and Building Materials 22/5 (2008) 939-947. DOI: https://doi.org/10.1016/j.conbuildmat.2007.03.005
• [55] M.A. Al-Shammari, M. Al-Waily, Analytical Investigation of Buckling Behavior of Honeycombs Sandwich Combined Plate Structure, International Journal of Mechanical and Production Engineering Research and Development 8/4 (2018) 771-786. [56] S.M. Abbas, K.K. Resan, A.K. Muhammad, M. Al- Waily, Mechanical and Fatigue Behaviors of Prosthetic for Partial Foot Amputation with Various Composite Materials Types Effect, International Journal of Me-chanical Engineering and Technology 9/9 (2018) 1-8.
• [57] H.J. Abbas, M.J. Jweeg, M. Al-Waily, A.A. Diwan, Experimental Testing and Theoretical Prediction of Fiber Optical Cable for Fault Detection and Identification, Journal of Engineering and Applied Sciences 14/2 (2019) 430-438. DOI: http://dx.doi.org/10.36478/jeasci.2019.430.438
• [58] E.N. Abbas, M. Al-Waily, T.M. Hammza, M.J. Jweeg, An Investigation to the Effects of Impact Strength on Laminated Notched Composites used in Prosthetic Sockets Manufacturing, IOP Conference Series: Materials Science and Engineering 928 (2020) 022081. DOI: https://doi.org/10.1088/1757-899X/928/2/022081
• [59] S.G. Hussein, M.A. Al-Shammari, A.M. Takhakh, M. Al-Waily, Effect of Heat Treatment on Mechanical and Vibration Properties for 6061 and 2024 Aluminum Alloys, Journal of Mechanical Engineering Research and Developments 43/1 (2020) 48-66.
• [60] A.A. Kadhim, E.A. Abbod, A.K. Muhammad, K.K. Resan, M. Al-Waily, Manufacturing and Analyzing of a New Prosthetic Shank with Adapters by 3D Printer, Journal of Mechanical Engineering Research and Developments 44/3 (2021) 383-391.
• [61] Q.H. Jebur, M.J. Jweeg, M. Al-Waily, H.Y. Ahmad, K.K. Resan, Hyperelastic models for the description and simulation of rubber subjected to large tensile loading, Archives of Materials Science and Engineering 108/2 (2021) 75-85. DOI: https://doi.org/10.5604/01.3001.0015.0256
• [62] E.K. Njim, S.H. Bakhy, M. Al-Waily, Analytical and Numerical Investigation of Buckling Behavior of Functionally Graded Sandwich Plate with Porous Core, Journal of Applied Science and Engineering 25/2 (2022) 339-347. DOI: https://doi.org/10.6180/jase.202204_25(2).0010
• [63] M.J. Jweeg, A.S. Hammood, M. Al-Waily, Experimental and Theoretical Studies of Mechanical Properties for Reinforcement Fiber Types of Composite Materials, International Journal of Mechanical and Mechatronics Engineering 12/4 (2012) 62-75.
• [64] A.A. Kadhim, M. Al-Waily, Z.A.A. Abud Ali, M.J. Jweeg, K.K. Resan, Improvement Fatigue Life and Strength of Isotropic Hyper Composite Materials by Reinforcement with Different Powder Materials, International Journal of Mechanical and Mechatronics Engineering 18/2 (2018) 77-86.
• [65] M.J. Jweeg, M. Al-Waily, A.K. Muhammad, K.K. Resan, Effects of Temperature on the Characterisation of a New Design for a Non-Articulated Prosthetic Foot, IOP Conference Series: Materials Science and Engineering 433 (2018) 012064. DOI: https://doi.org/10.1088/1757-899X/433/1/012064
• [66] E.N. Abbas, M.J. Jweeg, M. Al-Waily, Fatigue Characterization of Laminated Composites used in Prosthetic Sockets Manufacturing, Journal of Mechanical Engineering Research and Developments 43/5 (2020) 384-399.
• [67] M. Al-Waily, M.H. Tolephih, M.J. Jweeg, Fatigue Characterization for Composite Materials used in Artificial Socket Prostheses with the Adding of Nanoparticles, IOP Conference Series: Materials Science and Engineering 928 (2020) 022107. DOI: https://doi.org/10.1088/1757-899X/928/2/022107
• [68] E.K. Njim, S.H. Bakhy, M. Al-Waily, Analytical and Numerical Investigation of Free Vibration Behavior for Sandwich Plate with Functionally Graded Porous Metal Core, Pertanika Journal of Science and Technology 29/3 (2021) 1655-1682. DOI: https://doi.org/10.47836/pjst.29.3.39
• [69] N.D. Fahad, A.A. Kadhim, R.H. Al-Khayat, M. Al- Waily, Effect of SiO2 and Al2O3 hybrid nano materials on fatigue behavior for laminated composite materials used to manufacture artificial socket prostheses, Materials Science Forum 1039 (2021) 493-509. DOI: https://doi.org/10.4028/www.scientific.net/MSF.1039.493
• [70] Q.H. Jebur, M.J. Jweeg, M. Al-Waily, Ogden model for characterising and simulation of PPHR Rubber under different strain rates, Australian Journal of Mechanical Engineering (2021) (published online). DOI: https://doi.org/10.1080/14484846.2021.1918375