Abstract
The static response of an inhomogeneous fiber-reinforced viscoelastic sandwich plate is investigated by using the first-order shear deformation theory. Several types of sandwich plates are considered taking into account the symmetry of the plate and the thickness of each layer. In addition, two cases are considered depending on the viscoelastic material which are included in the core or the faces of the sandwich plates. The method of effective moduli and Illyushin’s approximation method are used to solve the equations governing the bending of simply supported inhomogeneous fiber-reinforced viscoelastic sandwich plates. Numerical computations were carried out to study the effect of the time parameter on deflections and stresses at different values of the aspect ratio, side-to-thickness ratio and constitutive parameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Plantema F.J.: Sandwich Construction. Wiley, New York (1966)
Reissner E.: On bending of elastic plates. Q. Appl. Math. 5, 55–68 (1947)
Hoff, N.J.: Bending and buckling of rectangular sandwich plates. NACA TN 2225 (1950)
Reissner E.: The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. Trans. ASME 12, 69–77 (1945)
Mindlin R.D.: Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech. 18, 31–38 (1951)
Yang P.C., Norris C.H., Stavsky Y.: Elastic wave propagation in heterogeneous plates. Int. J. Solids Struct. 2, 665–684 (1966)
Reissner E.: Reflection on the theory of elastic plates. Appl. Mech. Rev. 38, 1453–1464 (1985)
Noor A.K., Burton W.S.: Refinement of higher-order laminated plate theories. Appl. Mech. Rev. 42, 1–13 (1989)
Reddy J.N.: A review of refined theories of laminated composite plates. Shock Vib. Dig. 22, 3–17 (1990)
Whitney J.M., Sun C.T.: A higher-order theory for extensional motion of laminated composites. J. Sound Vib. 30, 85–97 (1973)
Yungian Q.I., Norman F.K.: A refined-first-order shear deformation theory and its justification by plane-strain bending problem of laminated plates. Int. J. Solids Struct. 33, 49–64 (1996)
Fares M.E., Zenkour A.M.: Mixed variational formula for the thermal bending of laminated plates. J. Thermal Stresses 22, 347–365 (1999)
Whitney J.M., Pagano N.J.: Shear deformation in heterogeneous anisotropic plates. J. Appl. Mech. Trans. ASME 37, 1031–1036 (1970)
Bert C.W.: Simplified analysis of elastic shear factors for beams of non-homogeneous cross-section. J. Compos. Mater. 7, 525–529 (1973)
Librescu L.: Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-type Structures. Noordhoff, Leiden (1975)
Reissner E.: A mixed variational equation for a twelfth-order theory of bending of nonhomogeneous transversely isotropic plates. Comput. Mech. 7, 255–260 (1991)
Reissner E.: On the equations of an eighth-order theory of nonhomogeneous transversely isotropic plates. Int. J. Solids Struct. 31, 89–96 (1994)
Fares M.E., Zenkour A.M.: Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories. Compos. Struct. 44, 279–287 (1999)
Douglas B.E., Yang J.C.S.: Transverse compressional damping in the vibratory response of elastic–viscoelastic beams. AIAA J. 16, 925–930 (1978)
Hashin Z.: Viscoelastic behavior of heterogeneous media. J. Appl. Mech. Trans. ASME 32, 630–636 (1965)
Wilson D.W., Vinson J.R.: Viscoelastic analysis of laminated plate buckling. AIAA J. 22, 982–988 (1984)
Kim C.G., Hong C.S.: Viscoelastic sandwich plates with cross-ply faces. J. Struct. Eng. 114, 150–164 (1988)
Huang N.N.: Viscoelastic buckling and post buckling of circular cylindrical laminated shells in hydrothermal environment. J. Marine Sci. Tech. 2, 9–16 (1994)
Pan H.: Vibrations of viscoelastic plates. J. Mécanique 5, 355–374 (1966)
Librescu L., Chandiramani N.K.: Dynamic stability of transversely isotropic viscoelastic plates. J. Sound Vib. 130, 467–486 (1989)
Zenkour A.M.: Buckling of fiber-reinforced viscoelastic composite plates using various plate theories. J. Eng. Math. 50, 75–93 (2004)
Zenkour A.M.: Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory. Acta Mech. 171, 171–187 (2004)
Illyushin, A., Pobedria, B.E.: Foundations of Mathematical Theory of Thermo Viscoelasticity. Nauka, Moscow (1970) [in Russian]
Pobedrya E.: Structural anisotropy in viscoelasticity. Polymer Mech. 12, 557–561 (1976)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Allam, M.N.M., Zenkour, A.M. & El-Mekawy, H.F. Bending response of inhomogeneous fiber-reinforced viscoelastic sandwich plates. Acta Mech 209, 231–248 (2010). https://doi.org/10.1007/s00707-009-0157-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-009-0157-4