An Analytical Investigation on Thermally Induced Vibrations of Non-homogeneous Tapered Rectangular Plate

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 258)


The goal of the present investigation is to study the temperature-thickness coupling problem of non-homogeneous rectangular plate with varying thickness. Authors assumed that temperature and thickness of the plate vary exponentially in x-direction only. Four sided clamped boundary condition with two term deflection function is considered. Due to non-homogeneity present in the plate’s material, variation in poisson’s ratio is assumed exponential in x-direction. An authentic and quite convenient Rayleigh–Ritz technique has been applied to obtain the fundamental frequencies for the first two modes of vibration. The effect of structural parameters such as taper constant, thermal gradient, non-homogeneity constant and aspect ratio on time period and deflection has been illustrated for first two modes of vibration. Results are calculated with great accuracy and presented in tabular form.


Vibration Thermal gradient Taper constant Aspect ratio Non-homogeneity constant Deflection 


  1. 1.
    Abu, A.I., Turhan, D., Mengi, D.: Two dimensional transient wave propagation in visco-elastic layered media. J. Sound Vib. 244, 837–858 (2001)CrossRefGoogle Scholar
  2. 2.
    Algazin, S.D.: Vibrations of free edge variable thickness plate of arbitrary shape in plane. J. Appl. Mech. Tech. Phys. 5, 126–131 (2011)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Alijani, F., Amabili, M.: Theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges. J. Sound Vib. 332, 3564–3588 (2013)CrossRefGoogle Scholar
  4. 4.
    Avalos, D.R., Laura, P.A.: Transverse vibrations of a simply supported plate of generalized anisotropy with an oblique cut-out. J. Sound Vib. 258, 773–776 (2002)CrossRefGoogle Scholar
  5. 5.
    Bhardwaj, N., Gupta, A.P., Choong, K.K., Ohmori, H.: Transverse vibrations of clamped and simply-supported circular plates with two dimensional thickness variation. Shock Vib. 19(2012), 273–285 (2012)CrossRefGoogle Scholar
  6. 6.
    Chakraverty, S.: Vibrations of Plate, vol. 10. Taylor and Francis, Boca Raton (2009)Google Scholar
  7. 7.
    Gupta, A.K., Khanna, A.: Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions. J. Sound Vib. 301, 450–457 (2007)CrossRefMATHGoogle Scholar
  8. 8.
    Gupta, A.K., Kumar, L.: Effect of thermal gradient on vibration of non-homogeneous visco-elastic elliptic plate of variable thickness. Meccanica 44, 507–518 (2009)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Khodzhaev, D.A., Eshmatov, BKh: Non linear vibrations of a visco-elastic plate with concentrated masses. J. Appl. Mech. Tech. Phys. 48, 905–914 (2007)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Lal, R., Kumar, Y.: Characteristic orthogonal of nonhomogeneous rectangular polynomials in the study of transverse vibrations orthotropic plates of bilinearly varying thickness. Meccanica 47, 175–193 (2012)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Leissa, A.W.: Vibrations of plate. In: NASA SP-160 in U. S. Govt, Printing Office (1969)Google Scholar
  12. 12.
    Leissa, A.W.: Recent studies in plate vibration 1981–1985. Part II, complicating effects. Shock Vib. Dig. 19, 10–24 (1987)CrossRefGoogle Scholar
  13. 13.
    Li, W.L.: Vibration analysis of rectangular plate with general elastic boundary supports. J. Sound Vib. 273, 619–635 (2004)Google Scholar
  14. 14.
    Patel, D.S., Pathan, S.S., Bhoraniya, I.H.: Influence of stiffeners on the natural frequencies of rectangular plate with simply supported edges. Int. J. Eng. Res. Technol. 1, 1–6 (2012)Google Scholar
  15. 15.
    Rezaee, M., Fekrmandi, H.: A theoretical and experimental investigation on free vibration behavior of a cantilever beam with a breathing crack. Shock Vib. 19, 175–186 (2012)CrossRefGoogle Scholar
  16. 16.
    Sharma, S., Gupta, U.S., Lal, R.: Effect of pasternak foundation on axisymmetric vibration of polar orthotropic annular plates of varying thickness. J. Vib. Acoust 132, 1–13 (2012)CrossRefGoogle Scholar
  17. 17.
    Singh, B., Chakraverty, S.: Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method. J. Sound Vib. 33, 741–751 (1991)MATHGoogle Scholar
  18. 18.
    Singh, B., Saxena, V.: Transverse vibration of rectangular plate with bidirectional thickness variation. J. Sound Vib. 198, 51–65 (1996)CrossRefGoogle Scholar
  19. 19.
    Wang, H.J., Chen, W.L.: Axisymmetric vibration and damping analysis of rotating annular plates with constrained damping layer treatments. J. Sound Vib. 271, 25–45 (2004)CrossRefGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of MathematicsMaharishi Markandeshwar UniversityMullana, AmbalaIndia

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