Structural Engineering and Mechanics

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Eigenfrequencies of simply supported taper plates with cut-outs

  • Kalita, Kanak (Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology) ;
  • Haldar, Salil (Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology)
  • Received : 2016.07.14
  • Accepted : 2017.06.05
  • Published : 2017.07.10
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Abstract

Free vibration analysis of plates is necessary for the field of structural engineering because of its wide applications in practical life. Free vibration of plates is largely dependent on its thickness, aspect ratios, and boundary conditions. Here we investigate the natural frequencies of simply supported tapered isotropic rectangular plates with internal cutouts using a nine node isoparametric element. The effect of rotary inertia on Eigenfrequencies was demonstrated by calculating with- and without rotary inertia. We found that rotary inertia has a significant effect on thick plates, while rotary inertia term can be ignored in thin plates. Based on comparison with literature data, we propose that the present formulation is capable of yielding highly accurate results. Internal cutouts at various positions in tapered rectangular simply supported plates were also studied. Novel data are also reported for skew taper plates.

Keywords

References

  1. Aksu, G. and Al-Kaabi, S.A. (1987), "Free vibration analysis of Mindlin plates with linearly varying thickness", J. Sound Vib., 119(2), 189-205. https://doi.org/10.1016/0022-460X(87)90448-2
  2. Algazin, S.D. (2010), "Numerical algorithms of classical mathematical physics", Dialog-MIFI, Moscow.
  3. Bert, C.W. and Malik, M. (1996), "Free vibration analysis of tapered rectangular plates by differential quadrature method: a semi-analytical approach", J. Sound Vib., 190(1), 41-63. https://doi.org/10.1006/jsvi.1996.0046
  4. Bhat, R.B., Laura, P.A., Gutierrez, R.G., Cortinez, V.H. and Sanzi, H.C. (1990), "Numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non-uniform thickness", J. Sound Vib., 138(2), 205-219. https://doi.org/10.1016/0022-460X(90)90538-B
  5. Chakraverty, S. (2008), Vibration of plates, CRC press.
  6. Cheung, K.Y. and Zhou, D. (1999a), "The free vibrations of tapered rectangular plates using a new set of beam functions with the Rayleigh-Ritz method", J. Sound Vib., 223(5), 703-722. https://doi.org/10.1006/jsvi.1998.2160
  7. Cheung, Y.K. and Ding, Z. (1999b), "Eigenfrequencies of tapered rectangular plates with intermediate line supports", Int. J. Solids Struct., 36(1), 143-166. https://doi.org/10.1016/S0020-7683(97)00272-2
  8. Cheung, Y.K. and Zhou, D. (2003), "Vibration of tapered Mindlin plates in terms of static Timoshenko beam functions", J. Sound Vib., 260(4), 693-709. https://doi.org/10.1016/S0022-460X(02)01008-8
  9. Dalir, M.A. and Shooshtari, A. (2015), "Exact mathematical solution for free vibration of thick laminated plates", Struct. Eng. Mech., 56(5), 835-854. https://doi.org/10.12989/sem.2015.56.5.835
  10. Fantuzzi, N., Bacciocchi, M., Tornabene, F., Viola, E. and Ferreira, A.J. (2015), "Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates", Compos. Part B-Eng., 78, 65-78. https://doi.org/10.1016/j.compositesb.2015.03.027
  11. Jin, G., Ye, T., Jia, X. and Gao, S. (2014), "A general Fourier solution for the vibration analysis of composite laminated structure elements of revolution with general elastic restraints", Compos. Struct., 109, 150-168. https://doi.org/10.1016/j.compstruct.2013.10.052
  12. Kalita, K. and Haldar, S. (2015), "Parametric study on thick plate vibration using FSDT", Mech. Mechanic. Eng., 19(2), 81-90.
  13. Kalita, K. and Haldar, S. (2016), "Free vibration analysis of rectangular plates with central cutout", Cogent Eng., 3(1), 1163781.
  14. Kandelousi, M.S. (2014), "Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition", Eur. Phys. J. Plus, 129(11), 1-12. https://doi.org/10.1140/epjp/i2014-14001-y
  15. Kirchhoff, G. (1850), "Ueber die Schwingungen einer kreisf\"ormigen elastischen Scheibe", Annalen der Physik, 157(10), 258-264. https://doi.org/10.1002/andp.18501571005
  16. Kirchhoff, G.R. (1850), Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe.
  17. Larrondo, H.A., Avalos, D.R., Laura, P.A. and Rossi, R.E. (2001), "Vibrations of simply supported rectangular plates with varying thickness and same aspect ratio cutouts", J. Sound Vib., 244(4), 738-745. https://doi.org/10.1006/jsvi.2000.3492
  18. Lee, W.M. and Chen, J.T. (2010), "Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method", Int. J. Solids Struct., 47(9), 1118-1129. https://doi.org/10.1016/j.ijsolstr.2009.12.002
  19. Lee, W.M., Chen, J.T. and Lee, Y.T. (2007), "Free vibration analysis of circular plates with multiple circular holes using indirect BIEMs", J. Sound Vib., 304(3), 811-830. https://doi.org/10.1016/j.jsv.2007.03.026
  20. Liew, K.M., Xiang, Y. and Kitipornchai, S. (1995), "Research on thick plate vibration: a literature survey", J. Sound Vib., 180(1), 163-176. https://doi.org/10.1006/jsvi.1995.0072
  21. Majumdar, A., Manna, M.C. and Haldar, S. (2010), "Bending of skewed cylindrical shell panels", Int. J. Comput. Appl., 1(8), 89-93. https://doi.org/10.5120/175-302
  22. Manna, M.C. (2006), "A sub-parametric shear deformable element for free vibration analysis of thick/thin rectangular plates with tapered thickness", Appl. Mech. Eng., 11(4), 901.
  23. Manna, M.C. (2011), "Free vibration of tapered isotropic rectangular plates", J. Vib. Control, 18(1), 76-91. https://doi.org/10.1177/1077546310396800
  24. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic elastic plates".
  25. Mlzusawa, T. (1993), "Vibration of rectangular Mindlin plates with tapered thickness by the spline strip method", Comput. Struct., 46(3), 451-463. https://doi.org/10.1016/0045-7949(93)90215-Y
  26. Ozdemir, Y.I. and Ayvaz, Y. (2014), "Is it shear locking or mesh refinement problem?", Struct. Eng. Mech., 50(2), 181-199. https://doi.org/10.12989/sem.2014.50.2.181
  27. Pachenari, Z. and Attarnejad, R. (2014), "Analysis of Tapered Thin Plates Using Basic Displacement Functions", Arab J. Sci. Eng., 39(12), 8691-8708. https://doi.org/10.1007/s13369-014-1407-x
  28. Pachenari, Z. and Attarnejad, R. (2014), "Free vibration of tapered mindlin plates using basic displacement functions", Arab J. Sci. Eng., 39(6), 4433-4449. https://doi.org/10.1007/s13369-014-1071-1
  29. Pandit, M.K., Haldar, S. and Mukhopadhyay, M. (2007), "Free vibration analysis of laminated composite rectangular plate using finite element method", J. Reinf. Plast. Comp., 26(1), 69-80. https://doi.org/10.1177/0731684407069955
  30. Rajasekaran, S. and Wilson, A.J. (2013), "Buckling and vibration of rectangular plates of variable thickness with different end conditions by finite difference technique", Struct. Eng. Mech., 46(2), 269-294. https://doi.org/10.12989/sem.2013.46.2.269
  31. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  32. Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Phys. Camb., 23(1), 184-191. https://doi.org/10.1002/sapm1944231184
  33. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates".
  34. Saeedi, K., Leo, A., Bhat, R.B. and Stiharu, I. (2012), "Vibration of circular plate with multiple eccentric circular perforations by the Rayleigh-Ritz method", J. Mech. Sci. Technol., 26(5), 1439-1448. https://doi.org/10.1007/s12206-012-0325-7
  35. Sahoo, S. (2015), "Laminated composite stiffened cylindrical shell panels with cutouts under free vibration", Int. J. Manufact., Mater., Mech. Eng. (IJMMME), 5(3), 37-63. https://doi.org/10.4018/IJMMME.2015070103
  36. Viola, E., Tornabene, F. and Fantuzzi, N. (2013), "General higherorder shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels", Compos. Struct., 95, 639-666. https://doi.org/10.1016/j.compstruct.2012.08.005
  37. Ye, T., Jin, G., Chen, Y., Ma, X. and Su, Z. (2013), "Free vibration analysis of laminated composite shallow shells with general elastic boundaries", Compos. Struct., 106, 470-490. https://doi.org/10.1016/j.compstruct.2013.07.005
  38. Ye, T., Jin, G., Su, Z. and Chen, Y. (2014), "A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports", Int. J. Mech. Sci., 80, 29-46. https://doi.org/10.1016/j.ijmecsci.2014.01.001
  39. Zhou, D. (2002), "Vibrations of point-supported rectangular plates with variable thickness using a set of static tapered beam functions", Int. J. Mech. Sci., 44(1), 149-164. https://doi.org/10.1016/S0020-7403(01)00081-9