A double-superposition global-local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach. (English) Zbl 1271.74184

Summary: A higher-order global-local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.


74H45 Vibrations in dynamical problems in solid mechanics
74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics
74K20 Plates
74E30 Composite and mixture properties
Full Text: DOI


[1] Shariyat M.: Three energy-based multiaxial HCF criteria for fatigue life determination in components under random non-proportional stress fields. Fatigue Fract. Eng. Mater. Struct. 32, 785–808 (2009)
[2] Shariyat M., Djamshidi P.: Minimizing the engine-induced harshness based on the DOE method and sensitivity analysis of the full vehicle NVH model. Int. J. Automot. Tech. 10(6), 687–696 (2009)
[3] Drozdov A.: Viscoelastic Structures: Mechanics of Growth and Aging. Academic Press, London (1998) · Zbl 0990.74002
[4] Hal F., Brinson L.: Catherine Brinson, Polymer Engineering Science and Viscoelasticity: An Introduction. Springer, LLC, Berlin (2008)
[5] Shariyat M.: Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells, under combined axial compression and external pressure. Int. J. Solids Struct. 45, 25 (2008) · Zbl 1169.74438
[6] Shariyat M.: Dynamic buckling of suddenly loaded imperfect hybrid FGM cylindrical shells with temperature-dependent material properties under thermo-electro-mechanical loads. Int. J. Mech. Sci. 50, 1561–1571 (2008)
[7] Shariyat M.: Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material properties subjected to a thermo-electro-mechanical loading conditions. Compos. Struct. 88, 240–252 (2009)
[8] Shariyat M.: Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties. Compos. Struct. 88, 228–239 (2009)
[9] Matsunaga H.: Assessment of a global higher-order deformation theory for laminated composite and sandwich plates. Compos. Struct. 56, 279–291 (2002)
[10] Matsunaga H.: A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings. Compos. Struct. 64, 161–177 (2004)
[11] Robbins D.H., Reddy J.N.: Modelling of thick composites using a layerwise laminate theory. Int. J. Numer. Meth. Eng. 36, 665–677 (1993) · Zbl 0770.73089
[12] Shariyat M.: Thermal buckling analysis of rectangular composite plates with temperature-dependent properties based on a layerwise theory. Thin Wall. Struct. 45, 439–452 (2007)
[13] Plagianakos T.S., Saravanos D.A.: Higher-order layerwise laminate theory for the prediction of interlaminar shear stresses in thick composite and sandwich composite plates. Compos. Struct. 87(1), 23–35 (2009)
[14] Dafedar J.B., Desai Y.M.: Thermomechanical buckling of laminated composite plates using mixed, higher-order analytical formulation. J. Appl. Mech. 69, 790–799 (2002) · Zbl 1110.74403
[15] Rao M.K., Desai Y.M.: Analytical solutions for vibrations of laminated and sandwich plates using mixed theory. Comp. Struct. 63, 316–373 (2004)
[16] Plagianakos T.S., Saravanos D.A.: High-order layerwise finite element for the damped free-vibration response of thick composite and sandwich composite plates. Int. J. Numer. Meth. Eng. 77(11), 1593–1626 (2009) · Zbl 1158.74499
[17] Shariyat M., Eslami M.R.: On thermal dynamic buckling analysis of imperfect laminated cylindrical shells. ZAMM 80(3), 171–182 (2000) · Zbl 0996.74042
[18] Eslami M.R., Shariyat M., Shakeri M.: Layerwise theory for dynamic buckling and postbuckling of laminated composite cylindrical shells. AIAA J. 36(10), 1874–1882 (1998)
[19] Eslami M.R., Shariyat M.: A higher order theory for dynamic buckling and postbuckling analysis of laminated cylindrical shells. Trans. ASME J. Press. Ves. Tech. 121(1), 94–102 (1999)
[20] Oh J., Cho M.: A finite element based on cubic zig-zag plate theory for the prediction of thermo-electric-mechanical behaviors. Int. J. Solids Struct. 41(5–6), 1357–1375 (2004) · Zbl 1045.74606
[21] Demasi L.: Refined multilayered plate element based on Murakami zig-zag functions. Compos. Struct. 70, 308–316 (2005)
[22] Di Sciuva M., Gherlone M.: A global/local third-order Hermitian displacement field with damaged interfaces and transverse extensibility: analytical formulation. Compos. Struct. 59, 419–431 (2003)
[23] Kapuria S., Achary G.G.S.: An efficient higher-order zigzag theory for laminated plates subjected to thermal loading. Int. J. Solids Struct. 41, 4661–4684 (2004) · Zbl 1079.74573
[24] Ganapathi M., Patel B.P., Makhecha D.P.: Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory. Compos. B 35, 345–355 (2004)
[25] Li X., Liu D.: A laminate theory based on global–local superposition. Commun. Numer. Meth. Eng. 11, 633–641 (1995) · Zbl 0870.73043
[26] Li X., Liu D.: Generalized laminate theories based on double superposition hypothesis. Int. J. Numer. Meth. Eng. 40, 1197–1212 (1997) · Zbl 0905.73040
[27] Wu Z., Chen W.: Free vibration of laminated composite and sandwich plates using global–local higher-order theory. J. Sound Vib. 298, 333–349 (2006)
[28] Wu Z., Chen W.: A study of global–local higher-order theories for laminated composite plates. Compos. Struct. 79, 44–54 (2007)
[29] Wu Z., Cheung Y.K., Lo S.H., Chen W.: Effects of higher-order global–local shear deformations on bending, vibration and buckling of multilayered plates. Compos. Struct. 82, 277–289 (2008)
[30] Shariyat M.: A generalized high-order global-local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads. Compos. Struct. 92, 130–143 (2010)
[31] Shariyat M.: Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global-local plate theory. Compos. Struct. 92, 72–85 (2010)
[32] Shariyat M.: A generalized global-local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads. Int. J. Mech. Sci. 52, 495–514 (2010)
[33] Chandra R., Singh S.P., Gupta K.: Damping studies in fiber-reinforced composites–a review. J Compos. Struct. 46(1), 41–51 (1999)
[34] Malekzadeh K., Khalili M.R., Mittal R.K.: Local and global damped vibrations of plates with a viscoelastic soft flexible core: an improved high-order approach. J. Sandw. Struct. Mater. 7, 431–456 (2005)
[35] Ganapathi M., Patel B.P., Touratier M.: Influence of amplitude of vibrations on loss factors of laminated composite beams and plates. J. Sound Vib. 219, 730–738 (1999)
[36] Hu Y.-C., Haung S.-C.: The frequency response and damping effect of three-layer thin shell with viscoelastic core. Comput. Struct. 76, 577–591 (2000)
[37] Meunier M., Shenoi R.A.: Dynamic analysis of composite plates with damping model using high-order shear deformation theory. J. Compos. Struct. 54, 243–254 (2001)
[38] Nayak A.K., Shenoi R.A., Moy S.S.J.: Analysis of damped composite sandwich plates using plate bending elements with substitute shear strain fields based on Reddy’s higher order theory. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 216(5), 591–606 (2002)
[39] Makhecha D.P., Ganapathi M., Patel B.P.: Vibration and damping analysis of laminated/sandwich composite plates using higher-order theory. J. Reinf. Plas. Comp. 21(6), 559–575 (2002)
[40] Lee D.G., Kosmatka J.B.: Damping analysis of composite sandwich plates with zig-zag triangular elements. AIAA J. 40(6), 1211–1219 (2002)
[41] Moreira R.A.S., Rodrigues J.D.: A layerwise model for thin soft core sandwich plates. Comput. Struct. 84, 1256–1263 (2006)
[42] Pradeep V., Ganesan N.: Thermal buckling and vibration behavior of multi-layer rectangular viscoelastic sandwich plates. J. Sound Vib. 310, 169–183 (2008)
[43] Araújo A.L., Mota Soares C.M., Mota Soares C.A., Herskovits J.: Optimal design and parameter estimation of frequency dependent viscoelastic laminated sandwich composite plates. Compos. Struct. 92(9), 2321–2327 (2010)
[44] Touati D., Cederbaum G.: Influence of large deflections on the dynamic stability of nonlinear viscoelastic plates. Acta Mech. 113, 215–231 (1995) · Zbl 0857.73040
[45] Touati D., Cederbaum G.: Postbuckling of non-linear viscoelastic imperfect laminated llates part II: structural analysis. Compos. Struct. 42, 43–51 (1998)
[46] Batra R.C., Wei Z.: Dynamic buckling of a thin thermoviscoplastic rectangular plate. Thin-Walled Struct. 43, 273–290 (2005)
[47] Pradeep V., Ganesan N.: Thermal buckling and vibration behavior of multi-layer rectangular viscoelastic sandwich plates. J. Sound Vib. 310, 169–183 (2008)
[48] Lakes R.S.: Viscoelastic Materials. 1st edn. Cambridge University Press, Cambridge (2009) · Zbl 1049.74012
[49] Shariyat, M.: Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global–local theory inherently suitable for non-linear analyses. Int. J. Non Linear Mech. (2010). doi: 10.1016/j.ijnonlinmec.2010.09.006
[50] Araújo, A.L., Mota Soares, C.M., Mota Soares, C.A.: Finite element model for Hybrid active_passive damping analysis of anisotropic laminated sandwich structures. J. Sandwich Struct. Mater. (2009). doi: 10.1177/1099636209104534
[51] Duigou L., Daya E.M., Potier-Ferry M.: Iterative algorithms for non-linear eigenvalue problems: application to vibrations of vscoelastic shells. Comput. Meth. Appl. Mech. Eng. 192, 1323–1335 (2003) · Zbl 1031.74029
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.