Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations. (English) Zbl 1397.74124

Summary: The investigation of bending response of a simply supported functionally graded (FG) viscoelastic sandwich beam with elastic core resting on Pasternak’s elastic foundations is presented. The faces of the sandwich beam are made of FG viscoelastic material while the core is still elastic. Material properties are graded from the elastic interfaces through the viscoelastic faces of the beam. The elastic parameters of the faces are considered to be varying according to a power-law distribution in terms of the volume fraction of the constituent. The interaction between the beam and the foundations is included in the formulation. Numerical results for deflections and stresses obtained using the refined sinusoidal shear deformation beam theory are compared with those obtained using the simple sinusoidal shear deformation beam theory, higher- and first-order shear deformation beam theories. The effects due to material distribution, span-to-thickness ratio, foundation stiffness and time parameter on the deflection and stresses are investigated.


74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74E30 Composite and mixture properties
74M15 Contact in solid mechanics
Full Text: DOI


[1] Shi Y., Sol H., Hua H.: Material parameter identification of sandwich beams by an inverse method. J. Sound Vib. 290, 1234–1255 (2006)
[2] Yim J.H., Cho S.Y., Seo Y.J., Jang B.Z.: A study on material damping of 0{\(\deg\)} laminated composite sandwich cantilever beams with a viscoelastic layer. Compos. Struct. 60, 367–374 (2003)
[3] Barbosa F.S., Farage M.C.R.: A finite element model for sandwich viscoelastic beams: Experimental and numerical assessment. J. Sound Vib. 317, 91–111 (2008)
[4] Bekuit J.-J.R.B., Oguamanam D.C.D., Damisa O.: A quasi-2D finite element formulation for the analysis of sandwich beams. Fin. Elem. Anal. Des. 43, 1099–1107 (2007)
[5] Nayfeh S.A.: Damping of flexural vibration in the plane of lamination of elastic-viscoelastic sandwich beams. J. Sound Vib. 276, 689–711 (2004)
[6] Lin C.Y., Chen L.W.: Dynamic stability of rotating composite beams with a viscoelastic core. Compos. Struct. 58, 185–194 (2002)
[7] Yan W., Chen W.Q., Wang B.S.: On time-dependent behavior of cross-ply laminated strips with viscoelastic interfaces. Appl. Math. Model. 31, 381–391 (2007) · Zbl 1136.74010
[8] Barkanov E., Rikards R., Holste C., Täger O.: Transient response of sandwich viscoelastic beams, plates, and shells under impulse loading. Mech. Compos. Mater. 36, 215–222 (2000)
[9] Galucio A.C., Deü J.-F., Ohayon R.: Finite element formulation of viscoelastic sandwich beams using fractional derivative operators. Comput. Mech. 33, 282–291 (2004) · Zbl 1067.74065
[10] Yen J.Y., Chen L.W., Wang C.C.: Dynamic stability of a sandwich beam with a constrained layer and electrorheological fluid core. Compos. Struct. 84, 209–219 (2008)
[11] Yan W., Ying J., Chen W.Q.: Response of laminated adaptive composite beams with viscoelastic interfaces. Compos. Struct. 74, 70–79 (2006)
[12] Teng T.L., Hu N.K.: Analysis of damping characteristics for viscoelastic laminated beams. Comput. Methods Appl. Mech. Engrg. 190, 3881–3892 (2001) · Zbl 1030.74024
[13] Beldica C.E., Hilton H.H.: Nonlinear viscoelastic beam bending with piezoelectric control–analytical and computational simulations. Compos. Struct. 51, 195–203 (2001)
[14] Zenkour A.M.: Benchmark trigonometric and 3-D elasticity solutions for an exponentiolly graded thick rectangular plate. Arch. Appl. Mech. 77, 197–214 (2007) · Zbl 1161.74436
[15] Zenkour A.M., Elsibai K.A., Mashat D.S.: Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders. Appl. Math. Mich. Engl. Ed. 29(12), 1601–1616 (2008) · Zbl 1165.74302
[16] Sankar B.V.: An elasticity solution for functionally graded beams. Compos. Sci. Tech. 61, 689–696 (2001)
[17] Zenkour A.M.: A comprehensive analysis of functionally graded sandwich plates: Part 1-deflection and stresses. Int. J. Solids Struct. 42, 5224–5242 (2005) · Zbl 1119.74471
[18] Zenkour A.M.: A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration. Int. J. Solids Struct. 42, 5243–5258 (2005) · Zbl 1119.74472
[19] Zenkour A.M.: Generalized shear deformation theory for bending analysis of functionally graded plates. Appl. Math. Model. 30, 67–84 (2006) · Zbl 1163.74529
[20] Zenkour A.M., Alghamdi N.A.: Thermoelastic bending analysis of functionally graded sandwich plates. J. Mater. Sci. 43, 2574–2589 (2008)
[21] Kadoli R., Akhtar K., Ganesan N.: Static analysis of functionally graded beams using higher order shear deformation theory. Appl. Math. Modell. 32, 2509–2525 (2008) · Zbl 1167.74584
[22] Reddy J.N.: Analysis of functionally graded plates. Int. J. Numer. Meth. Eng. 47, 663–684 (2000) · Zbl 0970.74041
[23] Reddy J.N., Chin C.D.: Thermomechanical analysis of functionally graded cylinders and plates. J. Thermal Stresses 21, 593–626 (1998)
[24] Reddy J.N., Cheng Z.Q.: Three-dimensional thermomechanical deformations of functionally graded rectangular plates. Eur. J. Mech. A Solids 20, 841–855 (2001) · Zbl 1002.74061
[25] Arciniega R.A., Reddy J.N.: Large deformation analysis of functionally graded shells. Int. J. Solids Struct. 44, 2036–2052 (2007) · Zbl 1108.74038
[26] Praveen G.N., Reddy J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates. Int. J. Solids Struct. 35, 4457–4476 (1998) · Zbl 0930.74037
[27] Chakraborty A., Gopalakrishnan S., Reddy J.N.: A new beam finite element for the analysis of functionally graded materials. Int. J. Mech. Sci. 45, 519–539 (2003) · Zbl 1035.74053
[28] Jin Z.H., Paulino G.H.: A viscoelastic functionally graded strip containing a crack subjected to in-plane loading. Eng. Fract. Mech. 69, 1769–1790 (2002)
[29] Ghosh M.K., Kanoria M.: Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on GreenûLindsay theory. Acta Mech. 207, 51–67 (2009) · Zbl 1172.74015
[30] Ueda S.: A cracked functionally graded piezoelectric material strip under transient thermal loading. Acta Mech. 199, 53–70 (2008) · Zbl 1148.74023
[31] Li X.Y., Ding H.J., Chen W.Q.: Axisymmetric elasticity solutions for a uniformly loaded annular plate of transversely isotropic functionally graded materials. Acta Mech. 196, 139–159 (2008) · Zbl 1142.74024
[32] Etemadi, E., Khatibi, A.A., Takaffoli, M.: 3D finite element simulation of sandwich panels with a functionally graded core subjected to low velocity impact. Compos. Struct (2009) (in press)
[33] Anderson T.A.: A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere. Compos. Struct. 60, 265–274 (2003)
[34] Ávila A.F.: Failure mode investigation of sandwich beams with functionally graded core. Compos. Struct. 81, 323–330 (2007)
[35] Bhangale R.K., Ganesan N.: Thermoelastic buckling and vibration behaior of functionally graded sandwich beam with constrained viscoelastic core. J. Sound Vib. 295, 294–316 (2006)
[36] Pradhan S.C., Murmu T.: Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method. J. Sound Vib. 321, 342–362 (2009)
[37] Ying J., Lü C.F., Chen W.Q.: Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations. Compos. Struct. 84, 209–219 (2008)
[38] Aköz A.Y., Kadioǧlu F.: The mixed finite element solution of circular beam on elastic foundation. Comput. Struct. 60(4), 643–651 (1996) · Zbl 0918.73208
[39] Chen W.Q., Lü C.F., Bian Z.G.: A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation. Appl. Math. Model. 28, 877–890 (2004) · Zbl 1147.74330
[40] Matsunaga H.: Vibration and buckling of deep beam-columns on two-parameter elastic foundations. J. Sound Vib. 228, 359–376 (1999)
[41] Sato M., Kanie S., Mikami T.: Mathematical analogy of a beam on elastic supports as a beam on elastic foundation. Appl. Math. Model. 32, 688–699 (2008) · Zbl 1130.74029
[42] Tsiatas, G.C.: Nonlinear analysis of non-uniform beams on nonlinear elastic foundation. Acta Mech. (2009) (in press) · Zbl 1381.74126
[43] Illyushin, A.A., Pobedrya, B.E.: Foundation of mathematical theory of thermo viscoelasticity. Moscow: Nauka (1970) (in Russian)
[44] Allam, M.N.M., Pobedrya, B.E.: On the solution of quasi-static problem in anisotropic viscoelasticity. ISV Acad Nauk Ar SSR, Mech. 31, 19–27 (1978) (in Russian) · Zbl 0449.73012
[45] Zenkour A.M.: Buckling of fiber-reinforced viscoelastic composite plates using various plate theories. J. Eng. Math. 50, 75–93 (2004) · Zbl 1073.74031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.