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Effect of non-homogeneity on natural frequencies of vibration of elliptic plates

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Abstract

This paper presents the effect of non-homogeneity of the material of plate structures on the vibration frequencies. The non-homogeneity of the plate is characterized by taking a variety of combinations of linear as well as quadratic variations in the Young’s modulus and density of the material. Boundary characteristic orthogonal polynomials using Gram-Schmidt procedure have been employed in the Rayleigh Ritz method. The results have been included for the first few frequencies of the plate element for all the boundary conditions viz. clamped, simply supported and free. Related Tables and graphs are incorporated to show the effect of the non-homogeneity parameter on the frequencies of the vibration of elliptic and circular plates.

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References

  1. Leissa AW (1969) Vibration of plates. NASA SP160. US Government Printing Office, Washington

    Google Scholar 

  2. Rebeiro P (2003) A hierarchical finite element for geometrically non-linear vibration of thick plates. Meccanica 38(1):117–132.

    Google Scholar 

  3. Awrejcewicz J, Krysko VA, Krysko AV (2004) Complex parametric vibrations of flexible rectangular plates. Meccanica 39(3):221–244

    Article  MATH  MathSciNet  Google Scholar 

  4. Paroni R (2006) The equations of motion of a plate with residual stress. Meccanica 41(1):1–21

    Article  MATH  MathSciNet  Google Scholar 

  5. Leissa AW (1978) Recent research in plate vibrations: 1973–1976: complicating effects. Shock Vib Dig 10(12):21–35

    Article  Google Scholar 

  6. Leissa AW (1981) Plate vibration research: 1976–1980: complicating effects. Shock Vib Dig 13(10):19–36

    Article  Google Scholar 

  7. Leissa AW (1987) Recent studies in plate vibrations: 1981–1985. Part II: complicating effects. Shock Vib Dig 19(3): 10–24

    Article  Google Scholar 

  8. Tomar JS, Gupta DC, Jain NC (1982) Vibrations of non homogeneous plates of variable thickness. J Acoust Soc Am 72(3):851–855

    Article  MATH  ADS  Google Scholar 

  9. Laura PAA, Gutierrez RH (1984) Transverse vibrations of orthotropic, non homogeneous rectangular plates. Fibre Sci Tech 133:125–133

    Article  Google Scholar 

  10. Tomar JS, Sharma RK, Gupta DC (1983) Transverse vibrations of non uniform rectangular orthotropic plates. AIAA J 21(7):1050–1053

    MATH  Google Scholar 

  11. Tomar JS, Gupta DC, Jain NC (1982) Axisymmetric vibrations of an isotropic elastic nonhomogeneous circular plate of linearly varying thickness. J Sound Vib 85(3):365–370

    Article  ADS  Google Scholar 

  12. Pan M (1976) Note on the transverse vibrations of an isotropic circular plate with density varying parabolically. Indian J Theor Phys 24(4):179–182

    Google Scholar 

  13. Mishra DM, Das AK (1971) Free vibrations of an isotropic nonhomogeneous circular plate. AIAA J 9(5):963–964

    Article  Google Scholar 

  14. Bhat RB (1985) Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method. J Sound Vib 102:493–499

    Article  ADS  Google Scholar 

  15. Bhat RB (1987) Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables. J Sound Vib 114:65–71

    ADS  Google Scholar 

  16. Singh B, Chakraverty S (1994) Boundary characteristic orthogonal polynomials in numerical approximation. Commun Numer Methods Eng 10:1027–1043

    Article  MATH  MathSciNet  Google Scholar 

  17. Bhat RB, Chakraverty S, Stiharu I (1998) Reccurence scheme for the generation of two-dimensional boundary characteristic orthogonal polynomials to study vibration of plates. J Sound Vib 216(2):321–327

    Article  ADS  Google Scholar 

  18. Singh B, Chakraverty S (1992) On the use of orthogonal polynomials in Rayleigh–Ritz method for the study of transverse vibration of elliptic plates. J Comput Struct 43(3):439–443

    Article  MATH  ADS  Google Scholar 

  19. Singh B, Chakraverty S (1992) Transverse vibrations of simply supported elliptic and circular plates using boundary characteristic orthogonal polynomials in two variables. J Sound Vib 152(1):149–155

    Article  MATH  ADS  Google Scholar 

  20. Singh B, Chakraverty S (1991) Transverse vibrations of completely free elliptic and circular plates using orthogonal polynomials in Rayleigh Ritz method. Int J Mech Sci 33(9):741–751

    Article  MATH  Google Scholar 

  21. Chakraverty S, Petyt M (1997) Natural frequencies for free vibration of nonhomogeneous elliptic and circular plates using two-dimensional orthogonal polynomials. Appl Math Model 21:399–417

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. BPPP Divn., Central Building Research Institute, Roorkee, 247 667, UA, India

    S. Chakraverty

  2. Dept. of Mathematics, Bhaskaracharya College of Applied Sciences (University of Delhi), Sector-2, Phase-1, Dwarka, New Delhi, 110045, India

    Ragini Jindal

  3. ex Principal, D.N. College, Meerut, UP, India

    V. K. Agarwal

Authors
  1. S. Chakraverty
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  2. Ragini Jindal
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  3. V. K. Agarwal
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Correspondence to S. Chakraverty.

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Chakraverty, S., Jindal, R. & Agarwal, V.K. Effect of non-homogeneity on natural frequencies of vibration of elliptic plates. Meccanica 42, 585–599 (2007). https://doi.org/10.1007/s11012-007-9077-3

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  • DOI: https://doi.org/10.1007/s11012-007-9077-3

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