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Transient forced vibration response analysis of heterogeneous sandwich circular plates under viscoelastic boundary support

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Abstract

For the first time the transient bending analysis of a sandwich plate with viscoelastic boundary support is investigated in this study. Viscoelastic support consists of two sets of translational springs and dashpots connected in parallel along the in-plane and transverse directions. The sandwich plate is fabricated from heterogeneous face sheets where the material properties of each face sheets are assumed to be varied continuously in the radial direction according to a power-law function. Variations of the material properties of each face sheets are monitored by eight distinct inhomogeneity parameters. Therefore, the solution procedure may be used for a wide range of the practical problems. In order to investigate the effects of viscoelastic edge supports on the transient response of sandwich plate a wide range of the stiffness and damping coefficients of the edge supports in the in-plane and transverse directions are applied. Results of sandwich plates with the classical edge conditions as some special cases of the elastic/viscoelastic supports are compared with those extracted from the ABAQUS software based on the 3D theory of elasticity. The comparisons show that even for relatively complicated cases, there is a good agreement between the results.

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References

  1. H.S. Shen, J. Yang, L. Zhang, Dynamic response of Reisner– Mindlin plates under thermomechanical loading and resting on elastic foundation, Journal of Sound and Vibration 232 (2) (2000) 309–329.

    Article  Google Scholar 

  2. O. Civalek, Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods, Applied Mathematical Modelling 31 (2007) 606–624.

    Article  MATH  Google Scholar 

  3. P. Ribeiro, Non-linear forced vibrations of thin/thick beams and plates by the finite element and shooting methods, Computers & Structures 82 (2004) 1413–1423.

    Article  Google Scholar 

  4. P. Ribeiro, Forced periodic vibrations of laminated composite plates by a p-version, first order shear deformation, finite element, Composites Science and Technology 66 (2006) 1844– 1856.

    Article  Google Scholar 

  5. W.L.A. Pereira, V.J. Karam, J.A.M. Carrer, W.J. Mansur, A dynamic formulation for the analysis of thick elastic plates by the boundary element method, Engineering Analysis with Boundary Elements 36 (2012) 1138–1150.

    Article  MathSciNet  MATH  Google Scholar 

  6. H.M. Sedighi, F. Daneshmand, J. Zare, The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect, Archives of Civil and Mechanical Engineering 14 (2014) 766–775.

    Article  Google Scholar 

  7. B. Khalfi, A. Ross, Transient and harmonic response of a sandwich with partial constrained layer damping: a parametric study, Composites Part B: Engineering 91 (2016) 44–55.

    Article  Google Scholar 

  8. L. Sator, V. Sladek, J. Sladek, L. Young Sator, V. Sladek, J. Sladek, D.L. Young, Elastodynamics of FGM plates by mesh-free method, Composite Structures 140 (2016) 309–322.

    Article  MATH  Google Scholar 

  9. Z.X. Wanga, H.S. Shen, Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments, Ocean Engineering 57 (2013) 99–110.

    Article  Google Scholar 

  10. A.R. Mojdehi, A. Darvizeh, A. Basti, H. Rajabi, Three dimensional static and dynamic analysis of thick functionally graded plates by the meshless local Petrov– Galerkin (MLPG) method, Engineering Analysis with Boundary Elements 35 (2011) 1168–1180.

    Article  MathSciNet  MATH  Google Scholar 

  11. M.M. Alipour, M. Shariyat, Semi-analytical consistent zigzag-elasticity formulations with implicit layerwise shear correction factors for dynamic stress analysis of sandwich circular plates with FGM layers, Composites Part B: Engineering 49 (2013) 43–64.

    Article  Google Scholar 

  12. M.M. Alipour, M. Shariyat, Analytical zigzag-elasticity transient and forced dynamic stress and displacement response prediction of the annular FGM sandwich plates, Composite Structures 106 (2013) 426–445.

    Article  Google Scholar 

  13. T. Kocatürk, G. Altintas, Determination of the steady-state response of viscoelastically point-supported rectangular orthotropic plates, Mechanics of Composite Materials 39 (5) (2003) 455–466.

    Article  Google Scholar 

  14. T. Kocatürk, S. Sezer, C. Demir, The effect of support locations on the steady-state response of viscoelastically point-supported rectangular orthotropic plates, Archive of Applied Mechanics 75 (2005) 58–67.

    Article  MATH  Google Scholar 

  15. M. Stembalski, W. Skoczyński, A. Roszkowski, P. Preś, Testing the vibration damping of a glass gatherer robot arm using a friction damper, Archives of Civil and Mechanical Engineering 17 (2017) 240–248.

    Article  Google Scholar 

  16. F. Alinaghizadeh, M. Shariati, Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation, Composites Part B 86 (2016) 61–83.

    Article  Google Scholar 

  17. F. Alinaghizadeh, M. Shariati, Buckling analysis of variable thickness radially functionally graded annular sector plates resting on two-parameter elastic foundations by the GDQ method, International Journal of Applied Mechanics 7 (2015) 1550083.

    Article  Google Scholar 

  18. Sh. Hosseini-Hashemi, H. Rokni Damavandi Taher, H. Akhavan, Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations, Composite Structures 92 (2010) 1734–1743.

    Article  Google Scholar 

  19. Sh. Hosseini-Hashemi, H. Akhavan, H. Rokni Damavandi Taher, N. Daemi, A. Alibeigloo, Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation, Materials and Design 31 (2010) 1871–1880.

    Article  Google Scholar 

  20. A. Nosier, F. Fallah, Non-linear analysis of functionally graded circular plates under asymmetric transverse loading, International Journal of Non-Linear Mechanics 44 (2009) 928– 942.

    Article  MATH  Google Scholar 

  21. S.Y. Lee, S.M. Lin, Levy-type solution for the analysis of nonuniform plates, Computers & Structures 49 (6) (1993) 931– 939.

    Article  MATH  Google Scholar 

  22. L.G. Nallim, B.M. Luccioni, R.O. Grossi, Vibration of general triangular composite plates with elastically restrained edges, Thin-Walled Structures 43 (2005) 1711–1745.

    Article  Google Scholar 

  23. L.G. Nallim, R.O. Grossi, Vibration of angle-ply symmetric laminated composite plates with edges elastically restrained, Composite Structures 81 (2007) 80–83.

    Article  Google Scholar 

  24. L.G. Nallim, R.O. Grossi, Natural frequencies of symmetrically laminated elliptical and circular plates, International Journal of Mechanical Sciences 50 (2008) 1153–1167.

    Article  MATH  Google Scholar 

  25. R. Vescovini, C. Bisagni, Single-mode solution for post-buckling analysis of composite panels with elastic restraints loaded in compression, Composites Part B: Engineering 43 (2012) 1258–1274.

    Article  Google Scholar 

  26. E. Bahmyari, A. Rahbar-Ranji, Free vibration analysis of orthotropic plates with variable thickness resting on non-uniform elastic foundation by element free Galerkin method, Journal of Mechanical Science and Technology 26 (9) (2012) 2685–2694.

    Article  Google Scholar 

  27. A.S. Ashour, Vibration of angle-ply symmetric laminated composite plates with edges elastically restrained, Composite Structures 74 (2006) 294–302.

    Article  Google Scholar 

  28. L.B. Rao, C.K. Rao, Fundamental buckling of circular plates with elastically restrained edges and resting on concentric rigid ring support, Frontiers of Mechanical Engineering 8 (3) (2013) 291–297.

    Article  Google Scholar 

  29. L.B. Rao, C.K. Rao, Buckling of circular plate with foundation and elastic edge, International Journal of Mechanical and Materials Engineering 11 (2015) 149–156.

    Article  Google Scholar 

  30. L.B. Rao, C.K. Rao, Frequencies of circular plate with concentric ring and elastic edge support, Frontiers of Mechanical Engineering 9 (2) (2014) 168–176.

    Article  Google Scholar 

  31. L.B. Rao, C.K. Rao, Frequency analysis of annular plates with inner and outer edges elastically restrained and resting on Winkler foundation, International Journal of Mechanical Sciences 81 (2014) 184–194.

    Article  Google Scholar 

  32. Q. Chen, P. Qiao, Post-buckling behavior of imperfect laminated composite plates with rotationally-restrained edges, Composite Structures 125 (2015) 117–126.

    Article  Google Scholar 

  33. G. Jin, H. Chen, J. Du, T. Yang, W. Li, The influence of edge restraining stiffness on the transverse vibrations of rectangular plate structures, Journal of Marine Science and Application 9 (2010) 393–402.

    Article  Google Scholar 

  34. P. Malekzadeh, M.R. Golbahar Haghighi, M.M. Atashi, Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment, Meccanica 46 (2011) 893–913.

    Article  MathSciNet  MATH  Google Scholar 

  35. A. Sharma, Free vibration of moderately thick antisymmetric laminated annular sector plates with elastic edge constraints, International Journal of Mechanical Sciences 83 (2014) 124–132.

    Article  Google Scholar 

  36. P.C. Dumir, C.H.R. Kumar, M.L. Gandhi, Nonlinear axisymmetric vibration of orthotropic thin circular plates with elastically restrained edges, Computers & Structures 22 (4) (1986) 677–686.

    Article  Google Scholar 

  37. M.L. Gandhi, P.C. Dumir, Y. Nath, Nonlinear axisymmetric static analysis of orthotropic thin circular plates with elastically restrained edge, Computers & Structures 20 (5) (1985) 841–853.

    Article  Google Scholar 

  38. Q. Wang, D. Shi, Q. Liang, X. Shi, A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions, Composites Part B: Engineering 88 (2016) 264–294.

    Article  Google Scholar 

  39. T. Ye, G. Jin, Z. Su, Y. Chen, A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports, International Journal of Mechanical Sciences 80 (2014) 29–46.

    Article  Google Scholar 

  40. Y. Zhang, J. Du, T. Yang, Z. Liu, A series solution for the in-plane vibration analysis of orthotropic rectangular plates with elastically restrained edges, International Journal of Mechanical Sciences 79 (2014) 15–24.

    Article  Google Scholar 

  41. D. Shi, Q. Wang, X. Shi, F. Pang, A series solution for the in-plane vibration analysis of orthotropic rectangular plates with non-uniform elastic boundary constraints and internal line supports, Archive of Applied Mechanics 85 (2015) 51–73.

    Article  Google Scholar 

  42. F.A. Fazzolaria, E. Carrera, Free vibration analysis of sandwich plates with anisotropic face sheets in thermal environment by using the hierarchical trigonometric Ritz formulation, Composites Part B: Engineering 50 (2013) 67–81.

    Article  Google Scholar 

  43. E. Carrera, S. Brischetto, A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Applied Mechanics Reviews 62 (1) (2008) 010803– 010819.

    Article  Google Scholar 

  44. E. Carrera, On the use of the Murakami’s zig-zag function in the modeling of layered plates and shells, Computers and Structures 82 (2004) 541–554.

    Article  Google Scholar 

  45. M.M. Alipour, A novel economical analytical method for bending and stress analysis of functionally graded sandwich circular plates with general elastic edge conditions, subjected to various loads, Composites Part B: Engineering 95 (2016) 48–63.

    Article  Google Scholar 

  46. M.M. Alipour, Effects of elastically restrained edges on FG sandwich annular plates by using a novel solution procedure based on layerwise formulation, Archives of Civil and Mechanical Engineering 16 (2016) 678–694.

    Article  Google Scholar 

  47. M.M. Alipour, M. Shariyat, An analytical global-local Taylor transformation-based vibration solution for annular FGM sandwich plates supported by nonuniform elastic foundations, Archives of Civil and Mechanical Engineering 14 (2014) 6–24.

    Article  Google Scholar 

  48. M.M. Alipour, An analytical approach for bending and stress analysis of cross/angle-ply laminated composite plates under arbitrary non-uniform loads and elastic foundations, Archives of Civil and Mechanical Engineering 16 (2) (2016) 193–210.

    Article  Google Scholar 

  49. M.M. Alipour, M. Shariyat, Analytical zigzag formulation with 3D elasticity corrections for bending and stress analysis of circular/annular composite sandwich plates with auxetic cores, Composite Structures 132 (2015) 175–197.

    Article  Google Scholar 

  50. M.M. Alipour, M. Shariyat, Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores, International Journal of Mechanical and Materials Engineering 13 (2017) 125–157.

    Article  Google Scholar 

  51. M. Shariyat, M.M. Alipour, Analytical bending and stress analysis of variable thickness FGM auxetic conical/cylindrical shells with general tractions, Latin American Journal of Solids and Structures 14 (2017) 805–843.

    Article  Google Scholar 

  52. J. Reddy, An Introduction to the Finite Element Method, 2nd ed., Wiley, New York, 2006.

    Google Scholar 

  53. A.J.M. Ferreira, Analysis of composite plates using a layerwise theory and multiquadrics discretization, Mechanics of Advanced Materials and Structures 12 (2005) 99–112.

    Article  Google Scholar 

  54. B. Liu, A.J.M. Ferreira, Y.F. Xing, A.M.A. Neves, Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method, Composite Structures 136 (2016) 546–553.

    Article  Google Scholar 

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Alipour, M. Transient forced vibration response analysis of heterogeneous sandwich circular plates under viscoelastic boundary support. Archiv.Civ.Mech.Eng 18, 12–31 (2018). https://doi.org/10.1016/j.acme.2017.05.007

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  • DOI: https://doi.org/10.1016/j.acme.2017.05.007

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