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Prestress Effect on the Thermomechanical Response of Viscoelastic Plate Under Harmonic Loading

Received: 23 March 2020     Accepted: 13 April 2020     Published: 23 April 2020
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Abstract

A statement of the coupled thermomechanical problem on forced resonant vibrations and dissipative heating of hinged viscoelastic elastomeric plate is given with account of prestresses present in the plate. It is assumed the prestress is generated as a result of the manufacturing process or preliminary plate service. The problem statement is based on the standard Kirchhoff-Love hypotheses and concept of complex moduli that are used to describe the viscoelastic material response to harmonic loading. Under these circumstances, the prestress manifests itself as a membrane forces applied in the plane of the rectangular plate. Therefore, the problem of in-plane stress state and problem of forced transverse vibration of the plate can be solved separately. Both steady-state and transient thermal response is investigated. Influence of the prestress is studied in details. Dissipative heating temperature histories are calculated for the variety of the prestress and loading parameters. Temperature criterion is adopted to determine the critical state. The data obtained are used for the plate fatigue life prediction as well as for the investigation of prestress effect on the plate response. The reliability of the values of frequencies on the several lowest resonances was checked. For the most energy-intensive first mode of transverse vibrations, the influence of the preliminary tensile stress state, as well as the amplitude of the transverse distributed load on the amplitude–frequency characteristics and temperature evolution was studied.

Published in Advances in Applied Sciences (Volume 5, Issue 2)
DOI 10.11648/j.aas.20200502.11
Page(s) 20-27
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Thermomechanical Coupling, Viscoelastic Plate, Complex Moduli, Prestress, Dissipative Heating

References
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[2] R. Steinberger, T. I. Valadas Leit˜ao, E. Landstatter, G. Pinter, W. Billinger, R. W. Lang, “Infrared thermographic techniques for non-destructive damage characterization of carbon fibre reinforced polymers during tensile fatigue testing”, Int. J. Fatigue 28, 1340 (2006).
[3] D. Rittel, “On the conversion of plastic work to heat during high strain rate deformation of glassy polymers”, Mech. Mater. 31, 131 (1999).
[4] S. Moissa, G. Landsberg, D. Rittel, J. L. Halary, “Hysteretic thermal behavior of amorphous semi-aromatic polyamides”, Polymer 45, 11870 (2005).
[5] S. Mortazavian., A. Fatemi, “Fatigue behavior and modeling of short fiber reinforced polymer composites: A literature review”, Int. J. Fatigue 70, 297 (2015).
[6] R. N. Haward, “Heating effects in the deformation of thermoplastics”, Thermochim. Acta 247, 87 (1994).
[7] M. Hashemi, Y. Zhuk, “The influence of strain amplitude, temperature and frequency on complex shear moduli of polymer materials under kinematic harmonic loading”, Mech. Mech. Eng. 21, 157 (2017).
[8] M. Mehdizadeh, M. M. Khonsari, “On the application of fracture fatigue entropy to variable frequency and loading amplitude”, Theor. Appl. Fract. Mech. 98, 30 (2018).
[9] A. Krairi, I. Doghri, “A thermodynamically-based constitutive model for thermoplastic polymers coupling viscoelasticity, viscoplasticity and ductile damage”, Int. J. Plast. 60, 163 (2014).
[10] A. Katunin, M. Fidali, “Fatigue and thermal failure of polymeric composites subjected to cyclic loading”, Adv. Compos. Lett. 21, 64 (2012).
[11] S. Mortazavian, A. Fatemi, “Fatigue of short fiber thermoplastic composites: A review of recent experimental results and analysis”, Int. J. Fatigue 102, 171 (2017).
[12] A. Katunin. Criticality of the Self-Heating Effect in Polymers and Polymer Matrix Composites during Fatigue, and Their Application in Non-Destructive Testing. Polymers 11, DOI: org/10.3390/polym11010019 (2019).
[13] I. K. Senchenkov, Ya. A. Zhuk, and V. G. Karnaukhov, “Modeling the Thermomechanical Behavior of Physically Nonlinear Materials under Monoharmonic Loading”, Int. Appl. Mech. 40, 943 (2004).
[14] Y. A. Zhuk, I. K. Senchenkov, “On Linearization of the Stiffness Characteristics of Flexible Beams Made of Physically Nonlinear Materials”, Int. Appl. Mech. 42, 196 (2006).
[15] Y. A. Zhuk, I. K. Senchenkov, “Monoharmonic approach to investigation of the vibrations and self-heating of thin-wall inelastic members”, J. Civil EngrgManag. 15, 67 (2009).
[16] V. G. Karnaukhov, I. F. Kirichok, “Forced Harmonic Vibrations and Dissipative Heating-up of Viscoelastic Thin-Walled Elements (Review)”, Int. Appl. Mech. 36, 174 (2000).
[17] M. Hashemi, Y. A. Zhuk, “The Influence of Temperature on the Cyclic Properties of the Transversely Isotropic Nanocomposite System Under Kinematic Harmonic Loading”, J. Mat. Sci. 236, 185 (2019).
[18] Y. A. Zhuk, “Damping characteristics of three-layer beam-damper under harmonic loading”, Mat. Mod. Comp. 1, 109 (2014).
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  • APA Style

    Oleksandr Ostos, Yaroslav Zhuk. (2020). Prestress Effect on the Thermomechanical Response of Viscoelastic Plate Under Harmonic Loading. Advances in Applied Sciences, 5(2), 20-27. https://doi.org/10.11648/j.aas.20200502.11

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    ACS Style

    Oleksandr Ostos; Yaroslav Zhuk. Prestress Effect on the Thermomechanical Response of Viscoelastic Plate Under Harmonic Loading. Adv. Appl. Sci. 2020, 5(2), 20-27. doi: 10.11648/j.aas.20200502.11

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    AMA Style

    Oleksandr Ostos, Yaroslav Zhuk. Prestress Effect on the Thermomechanical Response of Viscoelastic Plate Under Harmonic Loading. Adv Appl Sci. 2020;5(2):20-27. doi: 10.11648/j.aas.20200502.11

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  • @article{10.11648/j.aas.20200502.11,
      author = {Oleksandr Ostos and Yaroslav Zhuk},
      title = {Prestress Effect on the Thermomechanical Response of Viscoelastic Plate Under Harmonic Loading},
      journal = {Advances in Applied Sciences},
      volume = {5},
      number = {2},
      pages = {20-27},
      doi = {10.11648/j.aas.20200502.11},
      url = {https://doi.org/10.11648/j.aas.20200502.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20200502.11},
      abstract = {A statement of the coupled thermomechanical problem on forced resonant vibrations and dissipative heating of hinged viscoelastic elastomeric plate is given with account of prestresses present in the plate. It is assumed the prestress is generated as a result of the manufacturing process or preliminary plate service. The problem statement is based on the standard Kirchhoff-Love hypotheses and concept of complex moduli that are used to describe the viscoelastic material response to harmonic loading. Under these circumstances, the prestress manifests itself as a membrane forces applied in the plane of the rectangular plate. Therefore, the problem of in-plane stress state and problem of forced transverse vibration of the plate can be solved separately. Both steady-state and transient thermal response is investigated. Influence of the prestress is studied in details. Dissipative heating temperature histories are calculated for the variety of the prestress and loading parameters. Temperature criterion is adopted to determine the critical state. The data obtained are used for the plate fatigue life prediction as well as for the investigation of prestress effect on the plate response. The reliability of the values of frequencies on the several lowest resonances was checked. For the most energy-intensive first mode of transverse vibrations, the influence of the preliminary tensile stress state, as well as the amplitude of the transverse distributed load on the amplitude–frequency characteristics and temperature evolution was studied.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Prestress Effect on the Thermomechanical Response of Viscoelastic Plate Under Harmonic Loading
    AU  - Oleksandr Ostos
    AU  - Yaroslav Zhuk
    Y1  - 2020/04/23
    PY  - 2020
    N1  - https://doi.org/10.11648/j.aas.20200502.11
    DO  - 10.11648/j.aas.20200502.11
    T2  - Advances in Applied Sciences
    JF  - Advances in Applied Sciences
    JO  - Advances in Applied Sciences
    SP  - 20
    EP  - 27
    PB  - Science Publishing Group
    SN  - 2575-1514
    UR  - https://doi.org/10.11648/j.aas.20200502.11
    AB  - A statement of the coupled thermomechanical problem on forced resonant vibrations and dissipative heating of hinged viscoelastic elastomeric plate is given with account of prestresses present in the plate. It is assumed the prestress is generated as a result of the manufacturing process or preliminary plate service. The problem statement is based on the standard Kirchhoff-Love hypotheses and concept of complex moduli that are used to describe the viscoelastic material response to harmonic loading. Under these circumstances, the prestress manifests itself as a membrane forces applied in the plane of the rectangular plate. Therefore, the problem of in-plane stress state and problem of forced transverse vibration of the plate can be solved separately. Both steady-state and transient thermal response is investigated. Influence of the prestress is studied in details. Dissipative heating temperature histories are calculated for the variety of the prestress and loading parameters. Temperature criterion is adopted to determine the critical state. The data obtained are used for the plate fatigue life prediction as well as for the investigation of prestress effect on the plate response. The reliability of the values of frequencies on the several lowest resonances was checked. For the most energy-intensive first mode of transverse vibrations, the influence of the preliminary tensile stress state, as well as the amplitude of the transverse distributed load on the amplitude–frequency characteristics and temperature evolution was studied.
    VL  - 5
    IS  - 2
    ER  - 

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Author Information
  • Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

  • Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

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