Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

• Autorzy: Bakhy S.H. , Al-Waily M. , Al-Shammari M.A.

Identyfikatory

DOI

10.5604/01.3001.0015.4314

• Języki publikacji: EN

Abstrakty

EN

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Słowa kluczowe

EN

FGMs; sandwich beam; classical beam theory; vibration; FEA; frequency; ANSYS

PL

FGMs; belka warstwowa; klasyczna teoria belek; wibracje; FEA; częstotliwość; ANSYS

• Wydawca: International OCSCO World Press
• Czasopismo: Archives of Materials Science and Engineering
• Rocznik: 2021
• Tom: Vol. 110, nr 2
• Strony: 72--85
• Opis fizyczny: Bibliogr. 64 poz.

Twórcy

autor

Bakhy S.H.

• Department of Mechanical Engineering, 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

autor

Al-Shammari M.A.

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

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] P.S. Ghatage, V.R. Kar, P.E. Sudhagar, On the numerical modelling and analysis of multi-directional functionally graded composite structures: A review, Composites Structure 236 (2020) 111837. DOI: https://doi.org/10.1016/j.compstruct.2019.111837
• [3] C.I. Le, N.A.T. Le, D.K. Nguyen, Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element, Composite Structures 261 (2021) 113309. DOI: https://doi.org/10.1016/j.compstruct.2020.113309
• [4] 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
• [5] A. Omidi Soroor, M. Asgari, H. Haddadpour, Effect of axially graded constraining layer on the free vibration properties of three layered sandwich beams with magnetorheological fluid core, Composite Structures 255 (2021) 112899. DOI: https://doi.org/10.1016/j.compstruct.2020.112899
• [6] D.K. Nguyen, T.T. Tran, V.N. Pham, N.A.T. Le, Dynamic analysis of an inclined sandwich beam with bidirectional functionally graded face sheets under a moving mass, European Journal of Mechanics ‒ A/Solids 88 (2021) 104276. DOI: https://doi.org/10.1016/j.euromechsol.2021.104276
• [7] A. Selmi, A.A. Mustafa, Dynamic analysis of bi-dimensional functionally graded beams, Materials Today: Proceedings 46/17 (2021) 8675-8680. DOI: https://doi.org/10.1016/j.matpr.2021.03.726
• [8] Y. Tang, H. Qing, Elastic buckling and free vibration analysis of functionally graded Timoshenko beam with nonlocal strain gradient integral model, Applied Mathematical Modelling 96 (2021) 657-677. DOI: https://doi.org/10.1016/j.apm.2021.03.040
• [9] D. Cao, Y. Gao, M. Yao, W. Zhang, Free vibration of axially functionally graded beams using the asymptotic development method, Engineering Structures 173 (2018) 442-448. DOI: https://doi.org/10.1016/j.engstruct.2018.06.111
• [10] H. Arvin, S.M.H. Hosseini, Y. Kiani, Free vibration analysis of pre/post buckled rotating functionally graded beams subjected to uniform temperature rise, Thin-Walled Structures 158 (2021) 107187. DOI: https://doi.org/10.1016/j.tws.2020.107187
• [11] S. Shahedi, M. Mohammadimehr, Vibration analysis of rotating fully-bonded and delaminated sandwich beam with CNTRC face sheets and AL-foam flexible core in thermal and moisture environments, Mechanics Based Design of Structures and Machines 48/5 (2020) 584- 614. DOI: https://doi.org/10.1080/15397734.2019.1646661
• [12] G.-d. Xu, T. Zeng, S. Cheng, X.-h. Wang, K. Zhang, Free vibration of composite sandwich beam with graded corrugated lattice core, Composite Structures, 229 (2019) 111466. DOI: https://doi.org/10.1016/j.compstruct.2019.111466
• [13] S. Rajasekaran, Buckling, and vibration of axially functionally graded non-uniform beams using differential transformation based dynamic stiffness approach, Meccanica 48 (2013) 1053-1070. DOI: https://doi.org/10.1007/s11012-012-9651-1
• [14] A. Karamanli, T.P. Vo, Size-dependent behaviour of functionally graded sandwich microbeams based on the modified strain gradient theory, Composite Structures 246 (2020) 112401. DOI: https://doi.org/10.1016/j.compstruct.2020.112401
• [15] M.S. Sari, E.A. Butcher, Free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries using the Chebyshev collocation method, International Journal of Mechanical Sciences 60/1 (2012) 1-11. DOI: https://doi.org/10.1016/j.ijmecsci.2012.03.008
• [16] A. Elmeiche, A. Megueni, A. Lousdad, Free Vibration Analysis of Functionally Graded Nanobeams Based on Different Order Beam Theories Using Ritz Method, Periodica Polytechnica Mechanical Engineering 60/4 (2016) 209-219. DOI: https://doi.org/10.3311/PPme.8707
• [17] O. Rahmani, O. Pedram, Analysis and modeling the size effect on vibration of functionally graded theory, International Journal of Engineering Science 77 (2014) 55-70. DOI: https://doi.org/10.1016/j.ijengsci.2013.12.003
• [18] M. Bouamama, K. Refassi, A. Elmeiche, A. Megueni, Dynamic behavior of sandwich FGM beams, Mechanics and Mechanical Engineering 22/4 (2018) 919-929.
• [19] N.J. Kanu, U. Vates, G.K. Singh, S. Chavan, Fracture problems, vibration, buckling, and bending analyses of functionally graded materials, A state-of-the-art review including smart FGMS, Particulate Science and Technology 37/5 (2019) 583-608. DOI: https://doi.org/10.1080/02726351.2017.1410265
• [20] C. Li, H.S. Shen, H. Wang, Nonlinear dynamic response of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core, The European Physical Journal Plus 134 (2019) 79. DOI: https://doi.org/10.1140/epjp/i2019-12572-7
• [21] S. Sepehri-Amin, R.T. Faal, R. Das, Analytical and numerical solutions for vibration of a functionally graded beam with multiple fractionally damped absorbers, Thin-Walled Structures 157 (2020) 106711. DOI: https://doi.org/10.1016/j.tws.2020.106711
• [22] A. Garg, H.D. Chalak, A. Chakrabarti, Comparative study on the bending of sandwich FGM beams made up of different material variation laws using refined layerwise theory, Mechanics of Materials 151 (2020) 103634. DOI: https://doi.org/10.1016/j.mechmat.2020.103634
• [23] A. Karamanli, Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory, Composite Structures 189 (2018) 127-136. DOI: https://doi.org/10.1016/j.compstruct.2018.01.060
• [24] M. Simsek, T. Kocaturk, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Composite Structures 90/4 (2009) 465-473. DOI: https://doi.org/10.1016/j.compstruct.2009.04.024
• [25] D.K. Nguyen, Q.H. Nguyen, T.T. Tran, V.T. Bui, Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load, Acta Mechanica 228 (2017) 141-155. DOI: https://doi.org/10.1007/s00707-016-1705-3
• [26] Y. Huang, L.E. Yang, Q.Z. Luo, Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section, Composites Part B: Engineering 45/1 (2013) 1493-1498. DOI: https://doi.org/10.1016/j.compositesb.2012.09.015
• [27] A.E. Alshorbagy, M.A. Eltaher, F.F. Mahmoud, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling 35/1 (2011) 412-425. DOI: https://doi.org/10.1016/j.apm.2010.07.006
• [28] K.K. Pradhan, S. Chakraverty, Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method, Composites Part B: Engineering 51 (2013) 175-184. DOI: https://doi.org/10.1016/j.compositesb.2013.02.027
• [29] N.-D. Nguyen, T.-K Nguyen, T.P. Vo, T.-N. Nguyen, S. Lee, Vibration and buckling behaviours of thin-walled composite and functionally graded sandwich I-beams, Composites Part B: Engineering 166 (2019) 414-427. DOI: https://doi.org/10.1016/j.compositesb.2019.02.033
• [30] W.R. Chen, H. Chang, Closed-Form Solutions for Free Vibration Frequencies of Functionally Graded Euler- Bernoulli Beams, Mechanics of Composite Materials 53/1 (2017) 79-98. DOI: https://doi.org/10.1007/s11029-017-9642-3
• [31] A. Shahba, S. Rajasekaran, Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials, Applied Mathematical Modelling 36/7 (2012) 3094-3111. DOI: https://doi.org/10.1016/j.apm.2011.09.073
• [32] D.S. Mashat, E. Carrera, A.M. Zenkour, S.A. Al- Khateeb, M. Filippi, Free vibration of FGM layered beams by various theories and finite elements, Composites Part B: Engineering 59 (2014) 269-278. DOI: https://doi.org/10.1016/j.compositesb.2013.12.008
• [33] T.K. Nguyen, T.P. Vo, H.T. Thai, Static and free vibration analysis of axially loaded functionally graded beams based on the first-order shear deformation theory, Composites Part B: Engineering 55 (2013) 147-157. DOI: https://doi.org/10.1016/j.compositesb.2013.06.011
• [34] C.M. Wang, J.N. Reddy, K.H. Lee, Shear deformable beams and plates. Relationships with Classical Solutions, Elsevier Science, 2000. DOI: https://doi.org/10.1016/B978-0-08-043784-2.X5000-X
• [35] H.J. Xiang, J. Yang, Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction, Composites Part B: Engineering 39/2 (2008) 292-303. DOI: https://doi.org/10.1016/j.compositesb.2007.01.005
• [36] 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) (in press). DOI: https://doi.org/10.1016/j.matpr.2021.03.557
• [37] S.S. Rao, Vibration of Continuous Systems, First Edition, John Wiley & Sons, 2006. DOI: https://doi.org/10.1002/9780470117866
• [38] 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
• [39] 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
• [40] 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.
• [41] 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.
• [42] 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.
• [43] S.M. Abbas, A.M. Takhakh, M.A. Al-Shammari, M. Al-Waily, Manufacturing and Analysis of Ankle Disarticulation Prosthetic Socket (SYMES), International Journal of Mechanical Engineering and Technology 9/7 (2018) 560-569.
• [44] 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.
• [45] 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.
• [46] 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
• [47] 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) (in press). DOI: https://doi.org/10.1016/j.matpr.2021.03.235
• [48] M.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.
• [49] 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.
• [50] M. Al-Waily, K.K. Resan, A.H. Al-Wazir, Z.A.A. Abud Ali, Influences of glass and carbon powder rein-forcement on the vibration response and characteri-zation of an isotropic hyper composite materials plate structure, International Journal of Mechanical and Mechatronics Engineering 17/6 (2017) 74-85.
• [51] 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. DOI: https://doi.org/10.24247/ijmperdaug201883
• [52] 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.
• [53] 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
• [54] 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.
• [55] 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.
• [56] 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.
• [57] 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.
• [58] 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.
• [59] 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 Mechan-ical Engineering and Technology 9/9 (2018) 383-394.
• [60] 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
• [61] M.A. Al-Shammari, Q.H. Bader, M. Al-Waily, A.M. Hasson, Fatigue Behavior of Steel Beam Coated with Nanoparticles under High Temperature, Journal of Mechanical Engineering Research and Developments 43/4 (2020) 287-298.
• [62] 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
• [63] 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.
• [64] 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.