Skip to main content
SpringerLink
Log in

On the Method of Low-Frequency Monitoring of the Initial Stress State of a Body

  • Chapter
  • First Online:
Dynamics and Control of Advanced Structures and Machines

  • 418 Accesses

Abstract

A method for low-frequency control of the stress state of structures is proposed, based on an analysis of the parameters of the surface wave field created by the impact. To process the recorded signal, a special method is used, based on the use of optimal orthogonal decompositions of the signal in the base, adaptively tuned to the training sample. A series of computational experiments on simulation of dynamic processes in a prestressed medium was carried out. Studies have shown a high degree of informativeness of the method to various types of initial stress state in the medium and also a high sensitivity to a change in the value of the initial deformation.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. Green, J.E.: A note on wave propagation in prestressed elastic solids. J. Mech. Phys. Solids 11(2), 119–126 (1963)

    Article  MathSciNet  Google Scholar 

  2. Guz, A.N.: Elastic waves in bodies with initial (residual) stresses. Int. Appl. Mech. 38(1), 23–59 (2002)

    Article  MathSciNet  Google Scholar 

  3. Shams, M., Destrade, M., Ogden, R.W.: Initial stresses in elastic solids: constitutive laws and acoustoelasticity. Wave Motion 48, 552–567 (2011)

    Article  MathSciNet  Google Scholar 

  4. Hayes, M., Rivlin, R.S.: Surface waves in deformed elastic materials. Arch. Ration. Mech. Anal. 8(5), 358–380 (1961)

    Article  MathSciNet  Google Scholar 

  5. Chadwick, P., Jarvis, D.A.: Surface waves in prestressed elastic body. Proc. R. Soc. Lond. A 336(1727), 517–536 (1979)

    Article  MathSciNet  Google Scholar 

  6. Nam, N.T., Merodio, J., Ogden, R.W., Vinh, P.C.: The effect of initial stress on the propagation of surface waves in a layered half-space. Int. J. Solids Struct. 88–89, 88–100 (2016)

    Article  Google Scholar 

  7. Iwashimizu, Y., Kobori, O.: The Rayleigh wave in a finitely deformed isotropic elastic material. J. Acoust. Soc. Am. 64(3), 910–916 (1978)

    Article  Google Scholar 

  8. Tanuma, K., Man, C.-S., Chen, Y.: Dispersion of Rayleigh waves in weakly anisotropic media with vertically-inhomogeneous initial stress. Int. J. Eng. Sci. 92, 63–82 (2015)

    Article  MathSciNet  Google Scholar 

  9. Wagh, D.K.: Propagation of SH waves in an infinite elastic plate with Cauchy’s initial transverse stress. Pure Appl. Geophys. 99(7), 95–115 (1979)

    Google Scholar 

  10. Shams, M.: Effect of initial stress on Love wave propagation at the boundary between a layer and a half-space. Wave Motion 65, 92–104 (2016)

    Article  MathSciNet  Google Scholar 

  11. Kalinchuk, V.V., Polyakova, I.B.: Vibration of a die on the surface of a prestressed half-space. Sov. Appl. Mech. 18(6), 504–509 (1982)

    Article  Google Scholar 

  12. Anan’ev, I.V., Kalinchuk, V.V., Poliakova, I.B.: On wave excitation by a vibrating stamp in a medium with inhomogeneous initial stresses. J. Appl. Math. Mech. 47(3), 408–413 (1983)

    Article  Google Scholar 

  13. Kalinchuk, V.V., Lysenko, I.V., Polyakova, I.B.: Singularities of the interaction of a vibrating stamp with an inhomogeneous heavy base. J. Appl. Math. Mech. 53(2), 235–241 (1989)

    Article  MathSciNet  Google Scholar 

  14. Belyankova, T.I., Kalinchuk, V.V.: On the interaction between an oscillating die and a prestressed half-space. J. Appl. Math. Mech. 57(4), 123–134 (1993)

    Article  MathSciNet  Google Scholar 

  15. Belyankova, T.I., Vorovich, I.I., Kalinchuk, V.V.: Low-frequency resonances in the dynamic interaction of an elastic solid with a semi-bounded medium. J. Appl. Math. Mech. 62(5), 797–801 (1998)

    Article  MathSciNet  Google Scholar 

  16. Esipov, Y.V., Mukhortov, V.M., Kalinchuk, V.V.: Test equipment for analyzing the deformation of models of three-dimensional structures. Meas. Tech. 51(10), 1104–1109 (2008)

    Article  Google Scholar 

  17. Sedov, A.V.: Objects with Discrete-Distributed Parameters: A Decomposition Approach (in Russian). Nauka Publishing, Moscow (2010)

    Google Scholar 

Download references

Acknowledgements

This study was supported by the Russian Science Foundation (grant number 14-19-01676).

Author information

Authors and Affiliations

  1. Southern Scientific Center of Russian Academy of Sciences and Southern Federal University, Rostov-on-Don, Russia

    T. I. Belyankova & V. V. Kalinchuk

  2. Southern Scientific Center of Russian Academy of Sciences, Rostov-on-Don, Russia

    O. V. Bocharova & A. V. Sedov

Authors
  1. T. I. Belyankova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. V. Bocharova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Sedov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. V. Kalinchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Kalinchuk .

Editor information

Editors and Affiliations

  1. Institute of Continuous Media Mechanics, Russian Academy of Sciences, Perm, Russia

    Valerii P. Matveenko

  2. Institute of Mechanics and Mechatronics, Vienna University of Technology, Vienna, Austria

    Michael Krommer

  3. Institute of Problems in Mech. Eng., Russian Academy of Sciences, St. Petersburg, Russia

    Alexander K. Belyaev

  4. Institute for Technical Mechanics, Johannes Kepler University of Linz, Linz, Austria

    Hans Irschik

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Belyankova, T.I., Bocharova, O.V., Sedov, A.V., Kalinchuk, V.V. (2019). On the Method of Low-Frequency Monitoring of the Initial Stress State of a Body. In: Matveenko, V., Krommer, M., Belyaev, A., Irschik, H. (eds) Dynamics and Control of Advanced Structures and Machines. Springer, Cham. https://doi.org/10.1007/978-3-319-90884-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-90884-7_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90883-0

  • Online ISBN: 978-3-319-90884-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation