Abstract
In the present research, free vibration of circular and annular sandwich plates with auxetic (negative Poisson’s ratio) cores and isotropic/orthotropic face sheets is investigated for different combinations of the boundary conditions. To ensure that the results are accurate and reliable, a global–local layerwise plate theory is employed instead of the traditional equivalent single-layer theories. The governing equations are derived based on Hamilton’s principle and solved using a Taylor transform whose center is located at the outer radius of the plate. Due to this hint, the resulting semi-analytical solution can be employed for both circular and annular sandwich plates. After investigation of vibration behavior of a single-layer annular auxetic plate, a comprehensive parametric study including evaluation of effects of the auxeticity for sandwich plates with isotropic and orthotropic face sheets, symmetric and asymmetric layups, different core to sheet thickness, radius to thickness, and inner to outer radius ratios, and various boundary conditions, is carried out. Results show that unlike the single-layer auxetic plates that exhibit a transition state, the auxeticity may considerably increase the natural frequencies and rigidities of the circular/annular sandwich plates, especially when the boundary conditions induce higher rigidity in the plate or when the fibers are along the radial direction. Accuracy of results of the employed layerwise theory and the proposed semi-analytical solution is verified by comparing the results with those of the three-dimensional theory of elasticity extracted from the ABAQUS software.
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Alipour, M.M., Shariyat, M.: Stress analysis of two-directional FGM moderately thick constrained circular plates with non-uniform load and substrate stiffness distributions. J. Solid Mech. 2, 316–331 (2010)
Alipour, M.M., Shariyat, M.: Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations. Mech. Res. Commun. 38, 594–601 (2011)
Alipour, M.M., Shariyat, M.: An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution. Eur. J. Mech. A. Solids 34, 78–101 (2012)
Alipour, M.M., Shariyat, M.: Analytical zigzag-elasticity transient and forced dynamic stress and displacement response prediction of the annular FGM sandwich plates. Compos. Struct. 106, 426–445 (2013a)
Alipour, M.M., Shariyat, M.: Semianalytical solution for buckling analysis of variable thickness two-directional functionally graded circular plates with nonuniform elastic foundations. ASCE J. Eng. Mech. 139, 664–676 (2013b)
Alipour, M.M., Shariyat, M.: Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a zigzag-elasticity plate theory. Aerosp. Sci. Technol. 32, 235–259 (2014a)
Alipour, M.M., Shariyat, M.: An analytical global–local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by nonuniform elastic foundations. Arch. Civ. Mech. Eng. 14, 6–24 (2014b)
Alipour, M.M., Shariyat, M.: Analytical zigzag formulation with 3D elasticity corrections for bending and stress analysis of circular/annular composite sandwich plates with auxetic cores. Compos. Struct. 132, 175–197 (2015)
Alipour, M.M., Shariyat, M., Shaban, M.: A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations. Int. J. Mech. Mater. Des. 6, 293–304 (2010)
Azoti, W.L., Koutsawa, Y., Bonfoh, N., Lipinski, P., Belouettar, S.: Analytical modeling of multilayered dynamic sandwich composites embedded with auxetic layers. Eng. Struct. 57, 248–253 (2013)
Carrera, E., Brischetto, S.: A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates. Appl. Mech. Rev. 62, 010803 (2009)
Carrera, E., Brischetto, S., Nali, P.: Plates and Shells for Smart Structures. Wiley, Chichester (2011)
Di Sciuva, M., Gherlone, M., Iurlaro, L., Tessler, A.: A class of higher-order C0 composite and sandwich beam elements based on the Refined Zigzag Theory. Compos. Struct. 132, 784–803 (2015)
Di Sciuva, M., Gherlone, M., Tessler, A.: A robust and consistent first-order zigzag theory for multilayered beams. Adv. Math. Model Exp. Methods Mater. Struct. 168, 255–268 (2009)
Di Sciuva, M., Icardi, U., Librescu, L.: Effects of interfacial damage on the global and local static response of cross-ply laminates. Int. J. Fract. 96, 17–35 (1999)
Dong, C.Y.: Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev–Ritz method. Mater. Des. 29, 1518–1525 (2008)
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)
Hosseini Hashemi, S.H., Rokni Damavandi Taher, H., Omidi, M.: 3-D free vibration analysis of annular plates on Pasternak elastic foundation via p-Ritz method. J. Sound Vib. 311, 1114–1140 (2008)
Hutchinson, J.R.: Vibrations of thick free circular plates, exact versus approximate solutions. ASME J. Appl. Mech. 51, 581–585 (1984)
Iurlaro, L., Gherlone, M., Di Sciuva, M., Tessler, A.: Refined Zigzag Theory for laminated composite and sandwich plates derived from Reissner’s Mixed Variational Theorem. Compos. Struct. 133(2015), 809–817 (2015)
Khalili, S.M.R., Shariyat, M., Rajabi, I.: A finite element based global–local theory for static analysis of rectangular sandwich and laminated composite plates. Compos. Struct. 107, 177–189 (2014)
Lal, R., Ahlawat, N.: Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method. Eur. J. Mech. A. Solids 52, 85–94 (2015)
Lee, D., Waas, A.M., Karnopp, B.H.: Analysis of a rotating multi-layer annular plate modeled via layerwise zig-zag theory: free vibration and transient analysis. Comput. Struct. 66, 313–335 (1998)
Liew, K.M., Yang, B.: Elasticity solutions for free vibrations of annular plates from three-dimensional analysis. J. Sound Vib. 37, 7689–7702 (2000)
Lim, T.-C.: Buckling and vibration of circular auxetic plates. J. Eng. Mater. Technol. 136, 021007-1-6 (2014)
Malekzadeh, P., Afsari, A., Zahedinejad, P., Bahadori, R.: Three-dimensional layerwise-finite element free vibration analysis of thick laminated annular plates on elastic foundation. Appl. Math. Model. 34, 776–790 (2010a)
Malekzadeh, P., Shahpari, S.A., Ziaee, H.R.: Three-dimensional free vibration of thick functionally graded annular plates in thermal environment. J. Sound Vib. 329, 425–442 (2010b)
Maturi, D.A., Ferreira, A.J.M., Zenkour, A.M., Mashat, D.S.: Analysis of sandwich plates with a new layerwise formulation. Compos. B 56, 484–489 (2014)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)
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(1), 130–143 (2010)
Shariyat, M., Alipour, M.M.: Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations. Arch. Appl. Mech. 81, 1289–1306 (2011)
Shariyat, M., Alipour, M.M.: A zigzag theory with local shear correction factors for semi-analytical bending modal analysis of functionally graded viscoelastic circular sandwich plates. J. Solid Mech. 4, 84–105 (2012)
Shariyat, M., Alipour, M.M.: Semi-analytical consistent zigzag-elasticity formulations with implicit layerwise shear correction factors for dynamic stress analysis of sandwich circular plates with FGM layers. Compos. B 49, 43–64 (2013)
Shariyat, M., Alipour, M.M.: A novel shear correction factor for stress and modal analyses of annular FGM plates with non-uniform inclined tractions and non-uniform elastic foundations. Int. J. Mech. Sci. 87, 60–71 (2014)
Shariyat, M., Alipour, M.M.: Novel layerwise shear correction factors for zigzag theories of circular sandwich plates with functionally graded layers. Lat. Am. J. Solids Struct. 12, 1362–1396 (2015)
Shariyat, M., Eslami, M.R.: Dynamic buckling and postbuckling of imperfect orthotropic cylindrical shells under mechanical and thermal loads, based on the three dimensional theory of elasticity. ASME J. Appl. Mech. 66(2), 476–484 (1999)
Shariyat, M., Khalili, S.M.R., Rajabi, I.: A global–local theory with stress recovery and a new post-processing technique for stress analysis of asymmetric orthotropic sandwich plates with single/dual cores. Comput. Methods Appl. Mech. Eng. 286, 192–215 (2015)
So, J., Leissa, A.W.: Three dimensional vibrations of thick circular and annular plates. J. Sound Vib. 209, 15–41 (1998)
Tajeddini, V., Ohadi, A., Sadighi, M.: Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation. Int. J. Mech. Sci. 53, 300–308 (2011)
Tornabene, F., Viola, E., Inman, D.J.: 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures. J. Sound Vib. 328, 259–290 (2009)
Washizu, K.: Variational Methods in Elasticity and Plasticity, 2nd edn. Pergamon Press, New York (1975)
Zhou, D., Au, F.T.K., Cheung, Y.K., Lo, S.H.: Three-dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method. Int. J. Solids Struct. 40, 3089–3105 (2003)
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Alipour, M.M., Shariyat, M. Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores. Int J Mech Mater Des 13, 125–157 (2017). https://doi.org/10.1007/s10999-015-9321-2
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DOI: https://doi.org/10.1007/s10999-015-9321-2