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Geometry and load effects on transient response of a VFGM annular plate: An analytical approach

  • Alavia, Seyed Hashem (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology) ;
  • Eipakchi, Hamidreza (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology)
  • Received : 2018.11.01
  • Accepted : 2019.02.11
  • Published : 2019.04.25

Abstract

In this article, the effect of different geometrical, materials and load parameters on the transient response of axisymmetric viscoelastic functionally graded annular plates with different boundary conditions are studied. The behavior of the plate is assumed the elastic in bulk and viscoelastic in shear with the standard linear solid model. Also, the graded properties vary through the thickness according to a power law function. Three types of mostly applied transient loading, i.e., step, impulse, and harmonic with different load distribution respect to radius coordinate are examined. The motion equations and the corresponding boundary conditions are extracted by applying the first order shear deformation theory which are three coupled partial differential equations with variable coefficients. The resulting motion equations are solved analytically using the perturbation technique and the generalized Fourier series. The sensitivity of the response to the graded indexes, different transverse loads, aspect ratios, boundary conditions and the material properties are investigated too. The results are compared with the finite element analysis.

Keywords

References

  1. Abaqus User Manual (2013), Hibbitt, Karlsson and Sorensen, Inc.
  2. Alavi, S.H. and Eipakchi, H.R. (2018), "An analytical approach for free vibrations analysis of viscoelastic circular and annular plates using FSDT", Mech. Adv. Mater. Struct., 1-15.
  3. Alipour, M. and Shariyat, M. (2014), "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(1), 235-259. https://doi.org/10.1016/j.ast.2013.10.007
  4. Ansari, R., Gholami, R., Shojaei, M.F., Mohammadi, V. and Sahmani, S. (2014), "Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular microplates based on the modified strain gradient elasticity theory", Eur. J. Mech. A-Sol., 49, 251-267.
  5. Barrett, R. (2012), "On the relative position of twist and shear centers in the orthotropic and fiberwise homogeneous Saint-Venant beam theory", Int. J. Sol. Struct., 49(21), 3038-3046. https://doi.org/10.1016/j.ijsolstr.2012.06.003
  6. Barretta, R. and Elast, J. (2013), "On cesaro-volterra method in orthotropic saint-venant neam", J. Elast., 112(2), 233-253. https://doi.org/10.1007/s10659-013-9432-7
  7. Barretta, R., Feo, L., Luciano, R., Sciarra, F. and Penna, R. (2016), "Functionally graded Timoshenko nanobeams: A novel nonlocal gradient formulation", Compo.. Part B, 100, 208-219. https://doi.org/10.1016/j.compositesb.2016.05.052
  8. Brinson, H.F. and Brinson, L.C. (2008), Polymer Engineering Science and Viscoelasticity; An Introduction, Springer Science Business Media LLC, U.S.A.
  9. Dai, H.L., Dai, T. and Cheng, S.K. (2015), "Transient response analysis for a circular sandwich plate with an FG central disk", J. Mech., 31(4), 417-426. https://doi.org/10.1017/jmech.2015.7
  10. Faghidian, S.A. (2017), "Unified formulations of the shear coefficients in Timoshenko beam theory", J. Eng. Mech., 143(9), 06017013. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001297
  11. Khadem-Moshir, S., Eipakchi, H.R. and Sohani, F. (2017), "Free vibration behavior of viscoelastic annular plates using first order shear deformation theory", Struct. Eng. Mech., 62(5), 607-618. https://doi.org/10.12989/sem.2017.62.5.607
  12. Liang, X., Kou, H., Wang, L., Palmer, A.C., Wang, Z. and Liu, G. (2015), "Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions", Compos. Struct., 132, 584-596. https://doi.org/10.1016/j.compstruct.2015.05.066
  13. Liang, X., Wang, Z., Wang, L. and Liu, G. (2014), "Semianalytical solution for three-dimensional transient response of functionally graded annular plate on a two parameter viscoelastic foundation", J. Sound Vibr., 333(12), 2649-2663. https://doi.org/10.1016/j.jsv.2014.01.021
  14. Liang, X., Wang, Z., Wang, L., Izzuddin, B. and Liu, G. (2015), "A semi-analytical method to evaluate the dynamic response of functionally graded plates subjected to underwater shock", J. Sound J. Sound Vibr., 336, 257-274. https://doi.org/10.1016/j.jsv.2014.10.013
  15. Liang, X., Wu, Z., Wang, L. and Liu, G. (2015), "Semianalytical three-dimensional solutions for the transient response of functionally graded material rectangular plates", J. Eng. Mech., 141(9), 1-17. https://doi.org/10.3901/JME.2015.05.001
  16. Malekzadeh, P., Setoodeh, R. and Shojaee, M. (2018), "Vibration of FG-GPLs eccentric annular plates embedded in piezoelectric layers using a transformed differential quadrature method", Comput. Meth. Appl. M., 340, 451-479. https://doi.org/10.1016/j.cma.2018.06.006
  17. Nayfeh, A.H. (1993), Introduction to Perturbation Techniques, John Wiley & Sons, New York, U.S.A.
  18. Pawlus, D. (2016), "Dynamic response control of three-layered annular plate due to various parameters of electrorheological core", Arch. Mech. Eng., 63(1), 74-90. https://doi.org/10.1515/meceng-2016-0004
  19. Rad, B.A. and Shariyat, M. (2016), "Thermo-magneto-elasticity analysis of variable thickness annular FGM plates with asymmetric shear and normal loads and non-uniform elastic foundations", Arch. Civil Mech. Eng., 16(3), 448-466. https://doi.org/10.1016/j.acme.2016.02.006
  20. Romano, G., Barretta, A. and Barretta, R. (2012), "On torsion and shear of saint-venant beams", Eur. J. Mech. A-Sol., 35, 47-60.
  21. Sadd, M.H. (2009), Elasticity Theory, Applications and Numeric, Elsevier Inc., U.S.A.
  22. Salehi, M. and Aghaei, H. (2005), "Dynamic relaxation large deflection analysis of non-axisymmetric circular viscoelastic plates", Compos. Struct., 83(23-24), 1878-1890. https://doi.org/10.1016/j.compstruc.2005.02.023
  23. Shariyat, M. and Alipour, M.M. (2013), "A power series solution for vibration and complex modal stress analyses of variable thickness viscoelastic two-directional FGM circular plates on elastic foundations", Appl. Math. Model., 37(5), 3063-3076. https://doi.org/10.1016/j.apm.2012.07.037
  24. Srividhya, S., Raghu, P., Rajagopal, A. and Reddy, J.N. (2018), "Nonlocal nonlinear analysis of functionally graded plates using third-order shear deformation theory", Int. J. Eng. Sci., 125, 1-22. https://doi.org/10.1016/j.ijengsci.2017.12.006
  25. Wang, H.J. and Chen, L.W. (2002), "Vibration and damping analysis of a three-layered composite annular plate with a viscoelastic mid-layer", Compos. Struct., 58(4), 563-570. https://doi.org/10.1016/S0263-8223(02)00165-4