Skip to main content
SpringerLink
Log in

Influence of Time Harmonic Source Frequency in a Fibre-Reinforced Magneto-Thermoelastic Material with New Modified Couple Stress and Hyperbolic Two-Temperature Theory

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

In this paper, the concept of the new modified couple stress theory (NMCST) for microstructures and the hyperbolic two-temperature (H2T) theory of thermoelasticity has been mixed with the Green and Nagdhi theory to obtain a new coupled theory of thermoelasticity with microstructures. A fibre-reinforced rotating media in a high magnetic field, under the action of linearly distributed load and time-harmonic source frequency, is studied as an application. The Fourier transform technique is used for solving this mathematical model and to derive the displacement components, temperature change, axial stress components and couple stress in the transformed domain. A numerical inversion technique is employed to obtain the solutions in the physical domain. The comparison of the effects of time harmonic frequency, the effect of thermoelasticity theory with and without energy dissipation, the effect of rotation, the Hall current effect, and the effect of hyperbolic two-temperature theory and classical two-temperature theory is represented graphically on the physical quantities.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Abbreviations

\({\delta }_{ij}\) :

Kronecker delta

\({\beta }_{ij}\) :

Thermal elastic coupling tensor

\({T}_{0}\) :

Reference temperature medium in its natural state such that \(\left|T/{T}_{0}\right|<<1\)

\(T\) :

Thermodynamic temperature

\(\varphi\) :

Conductive temperature

\({t}_{ij}\) :

Stress tensors (N m−2)

\({e}_{ij}\) :

Strain tensors (m m−1)

\({u}_{i}\) :

Components of displacement (m)

\(\rho\) :

Medium density (kg m−3)

\({C}_{E}\) :

Specific heat at constant strain

\({a}_{ij}\) :

Two-temperature parameters

\({\alpha }_{ij}\) :

Linear thermal expansion coefficient

\({K}_{ij}\) :

Thermal conductivity

\({m}_{ij}\) :

Couple stress moment tensor

\({\chi }_{ij}\) :

Curvature tensor

\(\epsilon_{ijk}\) :

Permutation symbol

\({\sigma }_{0}\) :

Electrical conductivity

\({n}_{\mathrm{e}}\) :

Electron number density

\({m}_{\mathrm{e}}\) :

Electron mass

\({\mu }_{0}\) :

Magnetic permeability

\(\omega\) :

Time harmonic source frequency

\(\overrightarrow{a}\) :

The direction of fibre reinforcement

\({\mu }_{\mathrm{T}}\) :

Shear modulus in transverse shear across the preferred direction

\({\mu }_{\mathrm{L}}\) :

Shear modulus in longitudinal shear in the preferred direction

\({\alpha }_{1},{\alpha }_{3}\) :

Components of linear thermal expansion

\({J}_{r}\) :

Conduction current density

\(\alpha ,\beta\) :

Fibre reinforcement elastic parameters

\(t\) :

Time

\(\lambda\) :

Elastic constants

\({K}_{ij}^{*}\) :

Conductivity rate tensor

\({\omega }_{i}\) :

Rotational vector components

\({H}_{r}\) :

Intensity tensor of the magnetic field

\({l}_{j}\) :

Material length scale parameters

\({G,G}_{i}\) :

The elasticity constants

\(e\) :

Electron charge

\({t}_{\mathrm{e}}\) :

Electron collision time

\({E}_{i}\) :

Intensity tensor of the electric field

\(\delta \left(\right)\) :

Dirac’s delta function

\(m\) :

Hall current parameter

\({F}_{i}\) :

Body force

\({\psi }_{1}\left({x}_{1}\right), {\psi }_{2}({x}_{1})\) :

Vertical and horizontal load distribution function along the x-axis

References

Download references

Acknowledgements

Not applicable.

Funding

No fund/grant/scholarship has been taken for the research work.

Author information

Authors and Affiliations

  1. Department of Mathematics, Government College for Girls, Palwal, Kurukshetra, Haryana, India

    Iqbal Kaur

  2. Faculty of Engineering, UIET, Kurukshetra University, Kurukshetra, Haryana, India

    Kulvinder Singh

Authors
  1. Iqbal Kaur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kulvinder Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iqbal Kaur.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaur, I., Singh, K. Influence of Time Harmonic Source Frequency in a Fibre-Reinforced Magneto-Thermoelastic Material with New Modified Couple Stress and Hyperbolic Two-Temperature Theory. Iran J Sci Technol Trans Mech Eng 47, 1093–1107 (2023). https://doi.org/10.1007/s40997-022-00562-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40997-022-00562-5

Keywords

Mathematics Subject Classification

Search

Navigation