Skip to main content
SpringerLink
Log in

Evaluation of Transitional and Plastic Stresses in Transversely Isotropic Disk Made of Piezoelectric Material Subjected to Internal Pressure

  • Conference paper
  • First Online:
Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1440))

  • 151 Accesses

Abstract

This paper presents an analytical solution for transient stresses in a thin rotating disk consisting of transversely isotropic piezoelectric material under the influence of pressure on inner side of the disk. Apply concepts from Seth’s transition theory to evaluate rotational stresses in annular disk of transversely isotropic piezoelectric material. With the help of stress–strain relations of transversely isotropic materials, the electric displacement relations and stresses are derived. By using equilibrium equation describing the annular disk, a nonlinear differential equation is obtained. Transitional stresses, pressure and electric displacement are calculated from the governing equations. Analysis of stresses, angular velocity, and applied pressure is done on the basis of graphs and numerical calculations for transversely isotropic piezoelectric materials (Barium Titanate BaTiO3 and Lead Zirconate PZT-4) and transversely isotropic materials (Barium and Magnesium). On the basis of all the observations, it is concluded that transversely isotropic piezoelectric materials are better than transversely isotropic materials for designing purpose.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
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

References

  1. Abd-alladan, A.E.N.N., Hamdan, A.M., Almarashi A.A.: The mathematical modeling for bulk acoustic wave propagation velocities in transversely isotropic piezoelectric materials. J. Math. Mech. Solids 823–836 (2015)

    Google Scholar 

  2. Rawan, A.: Bossly: effect of initial stress on the electromechanical coupling and the Bleustein-Gulyaev wave in a transversely isotropic piezoelectric layered structure. J. Appl. Math. Inf. Sci. 13(6), 1059–1066 (2019)

    Article  Google Scholar 

  3. Atrian, A., Jafari-Fesharaki, J., Nourbakhsh, H.: Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads. Appl. Math. Mech. 35(7), 939–954 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Rahimi, G.H., Arefi, M., Khoshgoftar, M.J.: Application and analysis of functionally graded piezoelectrical rotating cylinder as mechanical sensor subjected to pressure and thermal loads. Appl. Math. Mech> (English Ed.) 32(8), 997–1008 (2011)

    Article  MATH  Google Scholar 

  5. Porcelli, E.B., Filho, V.S.: Induction of forces at distance performed by piezoelectric materials. J. Power Energy Eng. 6, 33–50 (2018)

    Article  Google Scholar 

  6. Borah, B.N.: Thermo elastic-plastic transition. Contemp. Math. 379, 93–111 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Sharma, S., Sahni, M.: Elastic-plastic transition of transversely isotropic thin rotating disc. Contemp. Eng. Sci. 2(9), 433–440 (2009)

    Google Scholar 

  8. Aggarwal, A.K., Sharma, R., Sharma, S.: Safety analysis using Lebesgue strain measure of thick-walled cylinder for functionally graded material under internal and external pressure. Sci. World J. 1–10 (2013)

    Google Scholar 

  9. Sharma, S., Sahai, I., Kumar, R.: Creep transition of a thin rotating annular disk of exponentially variable thickness with inclusion and edge load. Proc. Eng. 55, 348–354 (2013)

    Article  Google Scholar 

  10. Aggarwal, A.K., Sharma, R., Sharma, S.: Collapse pressure analysis of transversely isotropic thick-walled cylinder using lebesgue strain measure and transition theory. Sci. World J. 1–10 (2014)

    Google Scholar 

  11. Sharma, S.: Creep transition in bending of functionally graded transversely isotropic rectangular plates. Struct. Integrity Life 17(3), 187–192 (2014)

    Google Scholar 

  12. Sharma, S.: Thermal analysis of elastic-plastic thick-walled cylindrical pressure vessels subjected to temperature. Struct. Integrity Life 17(2), 105–112 (2017)

    Google Scholar 

  13. Sharma, S., Yadav, S., Sharma, R.: Thermal creep analysis of functionally graded thick-walled cylinder subjected to torsion and internal and external pressure. J. Solid Mech. 9(2), 302–318 (2017)

    Google Scholar 

  14. Sharma, S., Panchal, R.: Thermal creep deformation in pressurized thick walled functionally graded rotating shell. Int. J. Pure Appl. Math. 114(3), 435–444 (2017)

    Article  Google Scholar 

  15. Sharma, S., Sharma, R., Panchal, R.: Creep transition in transversely isotropic composite circular cylinder subjected to internal pressure. Int. J. Pure Appl. Math. 120(1), 87–96 (2018)

    Google Scholar 

  16. Sharma, S., Yadav, S., Sharma, R.: Creep torsion in thick-walled circular cylinder under internal and external pressure. Struct. Integrity Life-Integrity 18(2), 89–97 (2018)

    Google Scholar 

  17. Sharma, S., Panchal, R.: Creep stresses in functionally graded rotating orthotropic cylinder with varying thickness and density under internal and external pressure. Struct. Integrity Life-Integrity 18(2), 111–119 (2018)

    Google Scholar 

  18. Yadav, S., Sharma, S.: Torsion in microstructure hollow thick-walled circular cylinder made up of orthotropic material. J. Solid Mech. 10(3), 581–590 (2018)

    Google Scholar 

  19. Sharma, S., Panchal, R.: Elastic-plastic transition of pressurized functionally graded orthotropic cylinder using Seth’s transition theory. J. Solid Mech. 10(2), 450–463 (2018)

    Google Scholar 

  20. Sharma, R., Sharma, S., Radaković, Z.: Thermal creep analysis of pressurized thick-walled cylindrical vessels. Struct. Integrity Life 18(1), 7–14 (2018)

    Google Scholar 

  21. Sharma, S., Yadav, S., Radaković, Z.: Finite creep deformation in thick-walled circular cylinder with varying compressibility under external pressure. Struct. Integrity Life 18(1), 31–36 (2018)

    Google Scholar 

  22. Sharma, S., Yadav, S.: Numerical solution of thermal elastic-plastic functionally graded thin rotating disk with exponentially variable thickness and variable density. Therm. Sci. 23(1), 125–136 (2019)

    Article  Google Scholar 

  23. Sharma, R., Sahni, M.: Analysis of creep stresses in thin rotating disc composed of piezoelectric material. Struct. Integrity Life 20, Special Issue, S45–S49 (2020)

    Google Scholar 

  24. Sharma, R., Singhal, V., Sachan, P.: Elastic-plastic axi-symmetrical bending of functionally graded rectangular wide plates. Struct. Integrity Life 20, Special Issue, S65–S68 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jaypee Institute of Information Technology, Sector 62, Noida, India

    Richa Sharma

Authors
  1. Richa Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richa Sharma .

Editor information

Editors and Affiliations

  1. Pandit Deendayal Energy University, Gandhinagar, India

    Manoj Sahni

  2. School of Computer Science, University of Technology Sydney, Ultimo, NSW, Australia

    José M. Merigó

  3. Peter Faber Business School, Australian Catholic University, North Sydney, NSW, Australia

    Walayat Hussain

  4. Universidad Católica de la Santísima, Concepcion, Chile

    Ernesto León-Castro

  5. School of Economics and Business, Universidad de Talca, Talca, Chile

    Raj Kumar Verma

  6. Pandit Deendayal Energy University, Gandhinagar, India

    Ritu Sahni

Rights and permissions

Reprints and permissions

Copyright information

© 2023 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

Sharma, R. (2023). Evaluation of Transitional and Plastic Stresses in Transversely Isotropic Disk Made of Piezoelectric Material Subjected to Internal Pressure. In: Sahni, M., Merigó, J.M., Hussain, W., León-Castro, E., Verma, R.K., Sahni, R. (eds) Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy. Advances in Intelligent Systems and Computing, vol 1440. Springer, Singapore. https://doi.org/10.1007/978-981-19-9906-2_11

Download citation

Publish with us

Policies and ethics

Search

Navigation