Skip to main content

Frequencies of Nonuniform Triangular Plate with Two-Dimensional Parabolic Temperature

  • Conference paper
  • First Online:
Soft Computing: Theories and Applications

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1381))

Abstract

Frequencies of nonuniform triangular plate (isosceles, right-angled, and scalene triangle) on clamped edges under temperature field are computed using Rayleigh–Ritz method. For non-uniformity, two-dimensional linear thickness variation on the plate is considered. The two-dimensional parabolic temperature is considered on the plate. First three modes of vibration are computed on different variation of plate parameters and presented with the help of tables. The objective of the study is to reduce the frequency of the plates. A comparative study of the frequencies with other available published results well presents the objective of the study.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Leissa, A.W.: Vibration of Plates. NASA, Washington DC (1969)

    Google Scholar 

  2. Leissa, A.W.: Recent research in plate vibrations 1973–1976: complicating effects. Shock Vibr. Dig. 10(12), 21–35 (1978)

    Article  Google Scholar 

  3. Leissa, A.W.: Plate vibration research, 1976–1980: classical theory. Shock Vibr. Dig. 13(9), 11–22 (1981)

    Article  Google Scholar 

  4. Vijayakar, S.M., Singh, R., Gunda, R.: Vibration analysis of triangular plates using the Ray Tracing technique. J. Acoust. Soc. Am. 97, 33–82 (1995)

    Google Scholar 

  5. Leissa, A.W., Jaber, N.A.: Vibrations of completely free triangular plates. Int. J. Mech. Sci. 34(8), 605–616 (1992)

    Article  Google Scholar 

  6. Sharma, A.: Free vibration of square plate with temperature effect. J. Measure. Eng. 5(4), 222–228 (2017)

    Article  Google Scholar 

  7. Sharma, A., Kumar, P.: Natural vibration of square plate with circular variation in thickness. Soft Comput. Theories Appl. Adv. Intell. Syst. Comput. 742, 311–319 (2019)

    Google Scholar 

  8. Khanna, A., Singhal, A.: Effect of plate’s parameters on vibration of isotropic tapered rectangular plate with different boundary conditions. J. Low Freq. Noise Vibr. Active Control 35(2), 139–151 (2016)

    Article  Google Scholar 

  9. Kaur, N.: Vibrational behavior of tapered triangular plate with clamped ends under thermal condition. J. Inst. Eng. (India): Series C 1-9 (2020)

    Google Scholar 

  10. Sarswat, N.K., Bansal, V., Singh, A.: Effect of temperature on vibrations of elastic circular plate under the influence of shear effect. Int. J. Pure Appl. Math. 120(6), 10577–10589 (2018)

    Google Scholar 

  11. Bhardwaj, R., Mani, N., Sharma, A.: Time period of transverse vibration of skew plate with parabolic temperature variation. J. Vibr. Control (2020). https://doi.org/10.1177/1077546320926887

  12. Bijlani, M., Mirza, S.: Vibration of triangular plates of variable thickness. Comput. Struct. 21(6), 1129–1135 (1985)

    Google Scholar 

  13. Chaudhary, R.R., Falak, Y.R.: Vibration analysis of laminated triangular plate by experimental and finite element analysis. Int. J. Eng. Res. Gen. Sci. 3(2), 786–791 (2015)

    Google Scholar 

  14. Sharma, A.: Natural vibration of parallelogram plate with circular variation in density. Acta Tech. 63(6), 763–774 (2019)

    Google Scholar 

  15. Sharma, A.: Vibration frequency of a rectangle plate with linear variation in thickness and circular variation in Poisson’s ratio. J. Theor. Appl. Mech. 57(3), 605–615 (2019)

    Article  Google Scholar 

  16. Bhardwaj, R., Mani, N.: Modelling on vibration of skew plate with thickness and temperature variation. Vibroengineering Procedia 22, 6–12 (2019)

    Article  Google Scholar 

  17. Rana, U.S.: Robin: effect of damping and thermal gradient on vibration of orthotropic rectangular plate of variable thickness. Appl. Appl. Math. Int. J. (AAM) 12(1), 201–216 (2017)

    MATH  Google Scholar 

  18. Kim, Y.W.: Temperature dependent vibration analysis of functionally graded rectangular plates. J. Sound Vib. 284(3–5), 531–549 (2005)

    Article  Google Scholar 

  19. Lather, N., Sharma, A.: Natural vibration of skew plate on different set of boundary conditions with temperature gradient. Vibroengineering Procedia 22, 74–80 (2019)

    Article  Google Scholar 

  20. Sharma, A.: Vibration of square plate with parabolic temperature variation. Romanian J. Acoust. Vibr. 14, 107–114 (2017)

    Google Scholar 

  21. Sharma, A.: Vibrational frequencies of parallelogram plate with circular variations in thickness. Soft Comput. Theores Appl. Adv. Intell. Syst. Comput. 583, 317–326 (2017)

    Google Scholar 

  22. Kitipornchai, S., Liew, K.M., Xiang, Y., Wang, C.M.: Free vibration of isosceles triangular Mindlin plates. Int. J. Mech. Sci. 35, 89–102 (1993)

    Article  Google Scholar 

  23. Chakraverty, S.: Vibration of Plates. CRC Press, Taylor and Francis Group, Boca Raton, London New York (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Snehlata, Mani, N., Kumar, K., Sharma, A., Bhardwaj, R., Kumar, P. (2021). Frequencies of Nonuniform Triangular Plate with Two-Dimensional Parabolic Temperature. In: Sharma, T.K., Ahn, C.W., Verma, O.P., Panigrahi, B.K. (eds) Soft Computing: Theories and Applications. Advances in Intelligent Systems and Computing, vol 1381. Springer, Singapore. https://doi.org/10.1007/978-981-16-1696-9_4

Download citation

Publish with us

Policies and ethics