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Original Articles

Transverse stretching vibration analysis of cross-ply composite and sandwich beams by means of an equivalent single-layer theory

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Pages 3303-3317 | Received 15 Feb 2022, Accepted 29 Apr 2022, Published online: 16 May 2022

References

  • A.K. Nayak, S.S.J. Moy, and R.A. Shenoi, Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory, Compos. Part B: Eng., vol. 33, no. 7, pp. 505–519, 2002. DOI: 10.1016/S1359-8368(02)00035-5.
  • M.A.A. Meziane, H.H. Abdelaziz, and A. Tounsi, An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions, J. Sandwich Struct. Mater., vol. 16, no. 3, pp. 293–318, 2014. DOI: 10.1177/1099636214526852.
  • P.V. Vinh, Analysis of bi-directional functionally graded sandwich plates via higher-order shear deformation theory and finite element method, J. Sandwich Struct. Mater., vol. 24, no. 2, pp. 860–899, 2022. DOI: 10.1177/10996362211025811.
  • H.T. Thai, T.K. Nguyen, T.P. Vo, and J. Lee, Analysis of functionally graded sandwich plates using a new first-order shear deformation theory, Eur. J. Mech. -A/Solids., vol. 45, pp. 211–225, 2014. DOI: 10.1016/j.euromechsol.2013.12.008.
  • T. Kant, and K. Swaminathan, Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory, Compos. Struct., vol. 53, no. 1, pp. 73–85, 2001. DOI: 10.1016/S0263-8223(00)00180-X.
  • S. Suganyadevi, and B.N. Singh, Assessment of composite and sandwich laminates using a new shear deformation theory, AIAA J., vol. 54, no. 2, pp. 789–792, 2016. DOI: 10.2514/1.J054443.
  • L. Iurlaro, M. Gherlone, and M. Di Sciuva, Bending and free vibration analysis of functionally graded sandwich plates using the refined zigzag theory, J. Sandwich Struct. Mater., vol. 16, no. 6, pp. 669–699, 2014. DOI: 10.1177/1099636214548618.
  • Z. Wu, et al., Experiment and analysis on free vibration of sandwich plates based on an alternative sinusoidal global-local theory, Compos. Struct., vol. 257, pp. 113145, 2021. DOI: 10.1016/j.compstruct.2020.113145.
  • M. Sahla, H. Saidi, K. Draiche, A.A. Bousahla, F. Bourada, and A. Tounsi, Free vibration analysis of angle-ply laminated composite and soft core sandwich plates, Steel Compos. Struct., vol. 33, no. 5, pp. 663–679, 2019.
  • V.N. Van Do, and C.H. Lee, Free vibration analysis of FGM plates with complex cutouts by using quasi-3D isogeometric approach, Int. J. Mech. Sci., vol. 159, pp. 213–233, 2019. DOI: 10.1016/j.ijmecsci.2019.05.034.
  • C. Hwu, H.W. Hsu, and Y.H. Lin, Free vibration of composite sandwich plates and cylindrical shells, Compos. Struct., vol. 171, pp. 528–537, 2017. DOI: 10.1016/j.compstruct.2017.03.042.
  • S. Pandey, and S. Pradyumna, Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory, Eur. J. Mech. -A/Solids., vol. 51, pp. 55–66, 2015. DOI: 10.1016/j.euromechsol.2014.12.001.
  • C.M.C. Roque, J.D. Rodrigues, and A.J.M. Ferreira, Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and a local radial basis functions-finite differences discretization, Mech. Adv. Mater. Struct., vol. 20, no. 8, pp. 666–678, 2013. DOI: 10.1080/15376494.2011.646053.
  • T.K. Nguyen, T.P. Vo, and H.T. Thai, Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., vol. 228, no. 12, pp. 2110–2131, 2014. DOI: 10.1177/0954406213516088.
  • E. Carrera, Layer-wise mixed models for accurate vibration analysis of multilayered plates, J. Appl. Mech., vol. 65, no. 4, pp. 820–828, 1998. DOI: 10.1115/1.2791917.
  • E. Carrera, An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates, Compos. Struct., vol. 50, no. 2, pp. 183–198, 2000. DOI: 10.1016/S0263-8223(00)00099-4.
  • E. Carrera, and S. Brischetto, Analysis of thickness locking in classical, refined and mixed multilayered plate theories, Compos. Struct., vol. 82, no. 4, pp. 549–562, 2008. DOI: 10.1016/j.compstruct.2007.02.002.
  • S. Brischetto, and E. Carrera, Importance of higher order modes and refined theories in free vibration analysis of composite plates, J. Appl. Mech., vol. 77, no. 1, pp. 011013, 2010. DOI: 10.1115/1.3173605.
  • E. Carrera, A. Büttner, J.P. Nalif, T. Wallmerperger, and B. Kröplin, A comparison of various two-dimensional assumptions in finite element analysis of multilayered plates, Int. J. Comput. Methods Eng. Sci. Mech., vol. 11, no. 6, pp. 313–327, 2010. DOI: 10.1080/15502287.2010.516790.
  • F.A. Fazzolari, and E. Carrera, Advanced variable kinematics Ritz and Galerkin formulations for accurate buckling and vibration analysis of anisotropic laminated composite plates, Compos. Struct., vol. 94, no. 1, pp. 50–67, 2011. DOI: 10.1016/j.compstruct.2011.07.018.
  • E. Carrera, F.A. Fazzolari, and L. Demasi, Vibration analysis of anisotropic simply supported plates by using variable kinematic and Rayleigh-Ritz method, J. Vibr. Acoust., vol. 133, no. 6, pp. 061017, 2011. DOI: 10.1115/1.4004680.
  • F.A. Fazzolari, and E. Carrera, Accurate free vibration analysis of thermo-mechanically pre/post-buckled anisotropic multilayered plates based on a refined hierarchical trigonometric Ritz formulation, Compos. Struct., vol. 95, pp. 381–402, 2013. DOI: 10.1016/j.compstruct.2012.07.036.
  • S. Kapuria, P.C. Dumir, and N.K. Jain, Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams, Compos. Struct., vol. 64, no. 3-4, pp. 317–327, 2004. DOI: 10.1016/j.compstruct.2003.08.013.
  • H.T. Thai, and T.P. Vo, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, Int. J. Mech. Sci., vol. 62, no. 1, pp. 57–66, 2012. DOI: 10.1016/j.ijmecsci.2012.05.014.
  • S. Kapuria, M. Bhattacharyya, and A.N. Kumar, Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation, Compos. Struct., vol. 82, no. 3, pp. 390–402, 2008. DOI: 10.1016/j.compstruct.2007.01.019.
  • M. Arefi, and 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 Struct., vol. 158, pp. 107200, 2021. DOI: 10.1016/j.tws.2020.107200.
  • T.P. Vo, H.T. Thai, T.K. Nguyen, A. Maheri, and J. Lee, Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory, Eng. Struct., vol. 64, pp. 12–22, 2014. DOI: 10.1016/j.engstruct.2014.01.029.
  • M.C. Amirani, S.M.R. Khalili, and N. Nemati, Free vibration analysis of sandwich beam with FG core using the element free Galerkin method, Compos. Struct., vol. 90, no. 3, pp. 373–379, 2009. DOI: 10.1016/j.compstruct.2009.03.023.
  • O. Rahmani, S.M.R. Khalili, K. Malekzadeh, and H. Hadavinia, Free vibration analysis of sandwich structures with a flexible functionally graded syntactic core, Compos. Struct., vol. 91, no. 2, pp. 229–235, 2009. DOI: 10.1016/j.compstruct.2009.05.007.
  • C.I. Le, N.A.T. Le, and D.K. Nguyen, Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element, Compos. Struct., vol. 261, pp. 113309, 2021. DOI: 10.1016/j.compstruct.2020.113309.
  • D.S. Mashat, E. Carrera, A.M. Zenkour, S.A. Al Khateeb, and M. Filippi, Free vibration of FGM layered beams by various theories and finite elements, Compos. Part B: Eng., vol. 59, pp. 269–278, 2014. DOI: 10.1016/j.compositesb.2013.12.008.
  • A. Garg, and H.D. Chalak, Novel higher-order zigzag theory for analysis of laminated sandwich beams, Proc. Inst. Mech. Eng., Part L: J. Mate.: Des. Appl., vol. 235, no. 1, pp. 176–194, 2021. DOI: 10.1177/1464420720957045.
  • L.F. Qian, R.C. Batra, and L.M. Chen, Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov–Galerkin method, Compos. Part B: Eng., vol. 35, no. 6–8, pp. 685–697, 2004. DOI: 10.1016/j.compositesb.2004.02.004.
  • S. Chen, R. Geng, and W. Li, Vibration analysis of functionally graded beams using a higher-order shear deformable beam model with rational shear stress distribution, Compos. Struct., vol. 277, pp. 114586, 2021. DOI: 10.1016/j.compstruct.2021.114586.
  • T.K. Nguyen, T.T.P. Nguyen, T.P. Vo, and H.T. Thai, Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory, Compos. Part B: Eng., vol. 76, pp. 273–285, 2015. DOI: 10.1016/j.compositesb.2015.02.032.
  • G. Jin, C. Yang, and Z. Liu, Vibration and damping analysis of sandwich viscoelastic-core beam using Reddy’s higher-order theory, Compos. Struct., vol. 140, pp. 390–409, 2016. DOI: 10.1016/j.compstruct.2016.01.017.
  • A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, and O. Polit, Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations, Compos. Part B: Eng., vol. 42, no. 5, pp. 1276–1284, 2011. DOI: 10.1016/j.compositesb.2011.01.031.
  • E. Carrera, S. Brischetto, M. Cinefra, and M. Soave, Effects of thickness stretching in functionally graded plates and shells, Compos. Part B: Eng., vol. 42, no. 2, pp. 123–133, 2011. DOI: 10.1016/j.compositesb.2010.10.005.
  • A. Barut, E. Madenci, and A. Tessler, A refined zigzag theory for laminated composite and sandwich plates incorporating thickness stretch deformation, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 20th AIAA/ASME/AHS Adaptive Structures Conference 14th AIAA, 2012, p. 1705. DOI: 10.2514/6.2012-1705.
  • A. Bessaim, M.S.A. Houari, A. Tounsi, S.R. Mahmoud, and E.A.A. Bedia, A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets, J. Sandwich Struct. Mater., vol. 15, no. 6, pp. 671–703, 2013. DOI: 10.1177/1099636213498888.
  • D.A. Maturi, A.J.M. Ferreira, A.M. Zenkour, and D.S. Mashat, Analysis of sandwich plates with a new layerwise formulation, Compos. Part B: Eng., vol. 56, pp. 484–489, 2014. DOI: 10.1016/j.compositesb.2013.08.086.
  • S. Natarajan, M. Haboussi, and G. Manickam, Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets, Compos. Struct., vol. 113, pp. 197–207, 2014. DOI: 10.1016/j.compstruct.2014.03.007.
  • B. Han, K.K. Qin, Q.C. Zhang, Q. Zhang, T.J. Lu, and B.H. Lu, Free vibration and buckling of foam-filled composite corrugated sandwich plates under thermal loading, Compos. Struct., vol. 172, pp. 173–189, 2017. DOI: 10.1016/j.compstruct.2017.03.051.
  • A.S. Sayyad, and Y.M. Ghugal, Effect of thickness stretching on the static deformations, natural frequencies, and critical buckling loads of laminated composite and sandwich beams, J Braz. Soc. Mech. Sci. Eng., vol. 40, no. 6, pp. 1–16, 2018. DOI: 10.1007/s40430-018-1222-5.
  • B. Karami, and M. Janghorban, A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams, Thin-Walled Struct., vol. 143, pp. 106227, 2019. DOI: 10.1016/j.tws.2019.106227.
  • P.V. Katariya, and S.K. Panda, Numerical analysis of thermal post-buckling strength of laminated skew sandwich composite shell panel structure including stretching effect, Steel Compos. Struct., vol. 34, no. 2, pp. 279–288, 2020.
  • Y.X. Hao, M.X. Wang, W. Zhang, L.T. Liu, and S.W. Yang, Natural vibration of imperfect sandwich plates considering the effects of transverse stretching, J. Vibr. Control., p. 107754632110131, 2021. 10775463211013153. DOI: 10.1177/10775463211013153.
  • M.L. Dehsaraji, M. Arefi, and A. Loghman, Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect, Defence Technol., vol. 17, no. 1, pp. 119–134, 2021. DOI: 10.1016/j.dt.2020.01.001.
  • F. Alijani, and M. Amabili, Non-linear static bending and forced vibrations of rectangular plates retaining non-linearities in rotations and thickness deformation, Int. J. Non-Linear Mech., vol. 67, pp. 394–404, 2014. DOI: 10.1016/j.ijnonlinmec.2014.10.003.
  • M. Amabili, Non-linearities in rotation and thickness deformation in a new third-order thickness deformation theory for static and dynamic analysis of isotropic and laminated doubly curved shells, Int. J. Non-Linear Mech., vol. 69, pp. 109–128, 2015. DOI: 10.1016/j.ijnonlinmec.2014.11.026.
  • F. Alijani, and M. Amabili, Effect of thickness deformation on large-amplitude vibrations of functionally graded rectangular plates, Compos. Struct., vol. 113, pp. 89–107, 2014. DOI: 10.1016/j.compstruct.2014.03.006.
  • M. Amabili, A non-linear higher-order thickness stretching and shear deformation theory for large-amplitude vibrations of laminated doubly curved shells, Int. J. Non-Linear Mech., vol. 58, pp. 57–75, 2014. DOI: 10.1016/j.ijnonlinmec.2013.08.006.
  • M. Amabili, and J.N. Reddy, The nonlinear, third-order thickness and shear deformation theory for statics and dynamics of laminated composite shells, Compos. Struct., vol. 244, pp. 112265, 2020. DOI: 10.1016/j.compstruct.2020.112265.
  • A. Yadav, M. Amabili, S.K. Panda, and T. Dey, Nonlinear analysis of cylindrical sandwich shells with porous core and CNT reinforced face-sheets by higher-order thickness and shear deformation theory, Eur. J. Mech. /A Solids, vol. 90, pp. 104366, 2021. DOI: 10.1016/j.euromechsol.2021.104366.
  • A. Yadav, M. Amabili, S.K. Panda, T. Dey, and R. Kumar, Forced nonlinear vibrations of circular cylindrical sandwich shells with cellular core using higher-order shear and thickness deformation theory, J. Sound Vibr., vol. 510, pp. 116283, 2021. DOI: 10.1016/j.jsv.2021.116283.
  • M. Amabili, and J.N. Reddy, Nonlinear mechanics of sandwich plates: Layerwise third-order thickness and shear deformation theory, Compos. Struct., vol. 278, pp. 114693, 2021. DOI: 10.1016/j.compstruct.2021.114693.
  • E. Carrera, and B. Kroplin, Zigzag and interlaminar equilibria effects in large-deflection and postbuckling analysis of multilayered plates, Mech. Adv. Mater. Struct., vol. 4, no. 1, pp. 69–94, 1997. DOI: 10.1080/10759419708945875.
  • E. Carrera, Transverse normal stress effects in multilayered plates, J. Appl. Mech., vol. 66, no. 4, pp. 1004–1012, 1999. DOI: 10.1115/1.2791769.
  • E. Carrera, Temperature profile influence on layered plates response considering classical and advanced theories, AIAA J., vol. 40, no. 9, pp. 1885–1896, 2002. DOI: 10.2514/2.1868.
  • A. Robaldo, E. Carrera, and A. Benjeddou, A unified formulation for finite element analysis of piezoelectric adaptive plates, Comput. Struct., vol. 84, no. 22–23, pp. 1494–1505, 2006. DOI: 10.1016/j.compstruc.2006.01.029.
  • E. Carrera, M. Boscolo, and A. Robaldo, Hierarchic multilayered plate elements for coupled multifield problems of piezoelectric adaptive structures: formulation and numerical assessment, Arch. Comput. Methods Eng., vol. 14, no. 4, pp. 383–430, 2007. DOI: 10.1007/s11831-007-9012-8.
  • E. Carrera, F. Miglioretti, and M. Petrolo, Accuracy of refined finite elements for laminated plate analysis, Compos. Struct., vol. 93, no. 5, pp. 1311–1327, 2011. DOI: 10.1016/j.compstruct.2010.11.007.
  • E. Carrera, M. Petrolo, and E. Zappino, Performance of CUF approach to analyze the structural behavior of slender bodies, J. Struct. Eng., vol. 138, no. 2, pp. 285–297, 2012. DOI: 10.1061/(ASCE)ST.1943-541X.0000402.
  • S.M.R. Khalili, M.B. Dehkordi, E. Carrera, and M. Shariyat, Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory, Compos. Struct., vol. 96, pp. 243–255, 2013. DOI: 10.1016/j.compstruct.2012.08.020.
  • E. Carrera, M. Filippi, and E. Zappino, Free vibration analysis of rotating composite blades via Carrera Unified Formulation, Compos. Struct., vol. 106, pp. 317–325, 2013. DOI: 10.1016/j.compstruct.2013.05.055.
  • E. Carrera, A. Pagani, and M. Petrolo, Classical, refined, and component-wise analysis of reinforced-shell wing structures, AIAA J., vol. 51, no. 5, pp. 1255–1268, 2013. DOI: 10.2514/1.J052331.
  • A. Pagani, E. Carrera, M. Boscolo, and J.R. Banerjee, Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions, Compos. Struct., vol. 110, pp. 305–316, 2014. DOI: 10.1016/j.compstruct.2013.12.010.
  • F.A. Fazzolari, and E. Carrera, Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions, J. Therm. Stress., vol. 37, no. 12, pp. 1449–1481, 2014. DOI: 10.1080/01495739.2014.937251.
  • A. Pagani, A.G. de Miguel, M. Petrolo, and E. Carrera, Analysis of laminated beams via Unified Formulation and Legendre polynomial expansions, Compos. Struct., vol. 156, pp. 78–92, 2016. DOI: 10.1016/j.compstruct.2016.01.095.
  • E. Carrera, A study of transverse normal stress effect on vibration of multilayered plates and shells, J. Sound Vibr., vol. 225, no. 5, pp. 803–829, 1999. DOI: 10.1006/jsvi.1999.2271.
  • T. Kant, and K. Swaminathan, Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory, Compos. Struct., vol. 56, no. 4, pp. 329–344, 2002. DOI: 10.1016/S0263-8223(02)00017-X.
  • M. Cho, and R.R. Parmerter, An efficient higher-order plate theory for laminated composites, Compos. Struct., vol. 20, no. 2, pp. 113–123, 1992. DOI: 10.1016/0263-8223(92)90067-M.
  • X.Y. Li, and D. Liu, Generalized laminate theories based on double superposition hypothesis, Int. J. Numer. Methods Eng., vol. 40, no. 7, pp. 1197–1212, 1997. DOI: 10.1002/(SICI)1097-0207(19970415)40:7<1197::AID-NME109>3.0.CO;2-B.
  • R. Kumar, A. Lal, B.N. Singh, and J. Singh, New transverse shear deformation theory for bending analysis of FGM plate under patch load, Compos. Struct., vol. 208, pp. 91–100, 2019. DOI: 10.1016/j.compstruct.2018.10.014.
  • R.T. Babu, V. Surendra, B.N. Singh, and D.K. Maiti, Dynamic analysis of folded laminated composite plate using nonpolynomial shear deformation theory, Aerospace Sci. Technol., vol. 106, pp. 106083, 2020. DOI: 10.1016/j.ast.2020.106083.
  • M. Cho, and J. Oh, Higher order zig-zag theory for fully coupled thermo- electric-mechanical smart composite plates, Int. J. Solids Struct., vol. 41, no. 5–6, pp. 1331–1356, 2004. DOI: 10.1016/j.ijsolstr.2003.10.020.
  • J.B. Dafedar, Y.M. Desai, and A.A. Mufti, Stability of sandwich plates by mixed, higher-order analytical formulation, Int. J. Solids Struct., vol. 40, no. 17, pp. 4501–4517, 2003. DOI: 10.1016/S0020-7683(03)00283-X.

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