The bending analysis of homogenous and non-homogenous sandwich plates is investigated using classical thin plate theory. Two types of homogenous and non-homogenous sandwich plates are considered. The case of the first type is made of viscoelastic material while the faces have elastic properties and vice versa for the second type. Young’s modulus is assumed to be a function of the thickness while Poisson’s ratio is assumed to be a constant. The method of effective moduli and Illyushin’s approximation method are used to solve the governing equations for bending of simply supported viscoelastic sandwich plates. Numerical computations were carried out and the results show how the stresses change with time: Comparison between the behavior of stresses with various parameters for homogenous and non-homogenous viscoelastic sandwich plates are presented.
References
[1]
Plantema, F.J. (1966) Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates and Shells, John Wiley & Sons.
[2]
Reissner, E. (1947) On Bending of Elastic Plates. QuarterlyofAppliedMathematics, 5, 55-68. https://doi.org/10.1090/qam/20440
[3]
Hoff, N.J. (1950) Bending and Buckling of Rectangular Sandwich Plates, NACA TN 2225. https://ntrs.nasa.gov/api/citations/19930082873/downloads/19930082873.pdf
[4]
Yu, Y. (1959) A New Theory of Elastic Sandwich Plates—One-Dimensional Case. JournalofAppliedMechanics, 26, 415-421. https://doi.org/10.1115/1.4012054
[5]
Ganowicz, R. (1967) Singular Solutions in the General Theory of Three-Layer Plates. MechanikaTeoretycznaiStosowana, 3, 293-307.
[6]
Pagano, N.J. (1970) Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates. JournalofCompositeMaterials, 4, 20-34. https://doi.org/10.1177/002199837000400102
[7]
Noor, A.K., Burton, W.S. and Bert, C.W. (1996) Computational Models for Sandwich Panels and Shells. AppliedMechanicsReviews, 49, 155-199. https://doi.org/10.1115/1.3101923
[8]
Reddy, J.N. (1997) Mechanics of Laminated Composite Plates: Theory and Analysis. 2nd Edition, CRC Press.
[9]
Vinson, J.R. (1999) The Behavior of Sandwich Structures of Isotropic and Composite Materials. Routledge. https://doi.org/10.1201/9780203737101
[10]
Zenkour, A.M. (1999) Transverse Shear and Normal Deformation Theory for Bending Analysis of Laminated and Sandwich Elastic Beams. MechanicsofAdvancedMaterialsandStructures, 6, 267-283. https://doi.org/10.1080/107594199305566
[11]
Zenkour, A.M. (2005) A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 1—Deflection and Stresses. InternationalJournalofSolidsandStructures, 42, 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
[12]
Zenkour, A.M. (2005) A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 2—Buckling and Free Vibration. InternationalJournalofSolidsandStructures, 42, 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
[13]
DiTaranto, R.A. (1965) Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite-Length Beams. JournalofAppliedMechanics, 32, 881-886. https://doi.org/10.1115/1.3627330
[14]
Mead, D.J. and Markus, S. (1969) The Forced Vibration of a Three-Layer, Damped Sandwich Beam with Arbitrary Boundary Conditions. JournalofSoundandVibration, 10, 163-175. https://doi.org/10.1016/0022-460x(69)90193-x
[15]
Douglas, B.E. and Yang, J.C.S. (1978) Transverse Compressional Damping in the Vibratory Response of Elastic-Viscoelastic-Elastic Beams. AIAAJournal, 16, 925-930. https://doi.org/10.2514/3.7595
[16]
Hashin, Z. (1965) Viscoelastic Behavior of Heterogeneous Media. JournalofAppliedMechanics, 32, 630-636. https://doi.org/10.1115/1.3627270
[17]
Ahmed, S. and Jones, F.R. (1990) A Review of Particulate Reinforcement Theories for Polymer Composites. JournalofMaterialsScience, 25, 4933-4942. https://doi.org/10.1007/bf00580110
[18]
Wilson, D.W. and Vinson, J.R. (1984) Viscoelastic Analysis of Laminated Plate Buckling. AIAAJournal, 22, 982-988. https://doi.org/10.2514/3.8718
[19]
Kim, C. and Hong, C. (1988) Viscoelastic Sandwich Plates with Crossply Faces. JournalofStructuralEngineering, 114, 150-164. https://doi.org/10.1061/(asce)0733-9445(1988)114:1(150)
[20]
Huang, N.N. (1994) Viscoelastic Buckling and Postbuckling of Circular Cylindrical Laminated Shells in Hygrothermal Environment. JournalofMarineScienceandTechnology, 2, Article 2. https://doi.org/10.51400/2709-6998.2483
[21]
Pan, H. (1966) Vibrations of Viscoelastic Plates. JournaldeMécanique, 5, 355-374.
[22]
Librescu, L. and Chandiramani, N.K. (1989) Dynamic Stability of Transversely Isotropic Viscoelastic Plates. JournalofSoundandVibration, 130, 467-486. https://doi.org/10.1016/0022-460x(89)90070-9
[23]
Zenkour, A.M. (2004) Buckling of Fiber-Reinforced Viscoelastic Composite Plates Using Various Plate Theories. JournalofEngineeringMathematics, 50, 75-93. https://doi.org/10.1023/b:engi.0000042123.94111.35
[24]
Zenkour, A.M. (2004) Thermal Effects on the Bending Response of Fiber-Reinforced Viscoelastic Composite Plates Using a Sinusoidal Shear Deformation Theory. ActaMechanica, 171, 171-187. https://doi.org/10.1007/s00707-004-0145-7
[25]
Allam, M.N.M., Zenkour, A.M. and El-Mekawy, H.F. (2009) Bending Response of Inhomogeneous Fiber-Reinforced Viscoelastic Sandwich Plates. ActaMechanica, 209, 231-248. https://doi.org/10.1007/s00707-009-0157-4
[26]
Zenkour, A.M. (2012) Viscoelastic Analysis of an Exponentially Graded Sandwich Plate. JournalofMechanicalScienceandTechnology, 26, 889-898. https://doi.org/10.1007/s12206-011-1244-8
[27]
Zenkour, A.M., and El-Mekawy H.F. (2014) Bending of Inhomogeneous Sandwich Plates with Viscoelastic Cores. JournalofVibroengineering, 16, 3260-3272. https://www.extrica.com/article/15273
[28]
Zenkour, A.M. and El-Mekawy, H.F. (2018) Stresses in Inhomogeneous Elastic-Viscoelastic-Elastic Sandwich Plates via Hyperbolic Shear Deformation Theory. JournaloftheBrazilianSocietyofMechanicalSciencesandEngineering, 40, Article No. 363. https://doi.org/10.1007/s40430-018-1284-4
[29]
Tekili, S., Khadri, Y. and Karmi, Y. (2020) Dynamic Analysis of Sandwich Beam with Viscoelastic Core under Moving Loads. Mechanics, 26, 325-330. https://doi.org/10.5755/j01.mech.26.4.23956
[30]
Huang, Z., Pan, J., Yang, Z., Wang, X. and Chu, F. (2021) Transverse Vibration of Viscoelastic Sandwich Structures: Finite Element Modeling and Experimental Study. Materials, 14, Article 7751. https://doi.org/10.3390/ma14247751
[31]
Permoon, M.R. and Farsadi, T. (2021) Free Vibration of Three-Layer Sandwich Plate with Viscoelastic Core Modelled with Fractional Theory. MechanicsResearchCommunications, 116, Article 103766. https://doi.org/10.1016/j.mechrescom.2021.103766
[32]
Baro, D.K., and Mahto, S. (2022) Dynamics of Viscoelastic Material Sandwich Beam Using FEM. Advances in Materials and Processing Technologies, 8, 2350-2366. https://doi.org/10.1080/2374068X.2022.2038842
[33]
Zenkour, A.M. and El-Shahrany, H.D. (2021) Hygrothermal Vibration of a Cross-Ply Composite Plate with Magnetostrictive Layers, Viscoelastic Faces, and a Homogeneous Core. EngineeringwithComputers, 38, 4437-4456. https://doi.org/10.1007/s00366-021-01482-9
[34]
Zenkour, A.M. and El-Shahrany, H.D. (2021) Active Control of a Sandwich Plate with Reinforced Magnetostrictive Faces and Viscoelastic Core, Resting on Elastic Foundation. JournalofIntelligentMaterialSystemsandStructures, 33, 1321-1337. https://doi.org/10.1177/1045389x211053047
[35]
Tantawy, R.M., Zenkour, A.M. (2023) Bending Response of a Rotating Viscoelastic Functionally Graded Porous Disk with Variable Thickness. JournalofComputationalAppliedMechanics, 54, 482-500. https://doi.org/10.22059/jcamech.2023.366194.885
[36]
Bennedjadi, M., Aldosari, S.M., Chikh, A., Kaci, A., Bousahla, A.A. and Bourada, F. (2023) Visco-Elastic Foundation Effect on Buckling Response of Exponentially Graded Sandwich Plates under Various Boundary Conditions. GeomechanicsandEngineering, 32, 159-177. https://doi.org/10.12989/gae.2023.32.2.159
[37]
Messaoud, B. and Amrane, M.N. (2024) Vibration Analysis of Damaged Viscoelastic Composite Sandwich Plate. PeriodicaPolytechnicaMechanicalEngineering, 68, 85-96. https://doi.org/10.3311/ppme.19466
[38]
Illyushin, A. and Pobedria, B.E. (1970) Foundations of Mathematical Theory of Thermo-Viscoelasticity. Nauka.
[39]
Pobedrya, B.E. (1977) Structural Anisotropy in Viscoelasticity. PolymerMechanics, 12, 557-561. https://doi.org/10.1007/bf00857005