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Magneto-thermoelastic plane wave at the interface of pre-stressed water-aluminum-epoxy composite using Green and Lindsay’s model

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Abstract

The reflection and refraction of magneto-thermoelastic plane wave at the interface of water-aluminum-epoxy composite in Green and Lindsay’s theory under initial stress has been investigated. Numerical computations are performed for the developed amplitude ratios of P-, SV- and thermal magneto-thermoelastic waves. For the values of relevant physical constants of water-aluminum-epoxy composite, the system of developed equations is solved by the application of the MATLAB software at different angles of incidence and the numerical computations are put graphically.

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Abbreviations

λ, μ :

Lame’s constants

ρ :

Density

σ :

Poisson’s ratio

c v :

Specific heat at constant strain

s ij :

Components of stress tensor

T:

Absolute temperature

T0 :

Reference temperature chosen so that |T − T0/T0| ≪ 1

P :

Initial pressure (s yy  − s xx )

e ij :

Components of strain tensor

K:

Thermal conductivity

J:

Current density vector

μ e :

1/[2(1 + σ)] magnetic permeability

ɛ e :

Electric permittivity

H:

Initial uniform magnetic intensity vector

h:

Induced magnetic field

H0 :

Magnetic field component

E:

Induced electric field vector

D:

Electric displacement vector

B:

Magnetic displacement vector

F :

Lorentz force

δ ij :

Kronecker delta

τ T :

Thermoelastic coupling constant

u i :

Components of displacement vector

τ 0, τ :

Relaxation times

t :

Time

e :

Cubical dilatation

Ω :

1/2( ∂v/∂x − ∂u/∂y)rotational component

α t :

Coefficient of linear thermal expansion

γ:

3λ + 2μ)α t

k :

Wave number

ω :

Angular frequency

c :

ω/k

c 21 :

(λ + 2μ +μ e H 20  + P)/ρ

c 22 :

μ − P/2)/ρ

c 23 :

K/ρc v

c 2 :

1/μ e ɛ e Light speed squared

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Acknowledgments

The authors are thankful to unknown reviewers for their valuable comments. This research has not received any specific grant from funding agency in the public, commercial, or not-for-profit sectors.

Conflict of interest

None declared.

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Authors and Affiliations

  1. Department of Physics, GNA University, Hargobindgarh, Phagwara, Chotti Baradari, 163/1, Jalandhar, 144022, India

    Rajneesh Kakar

  2. Department of Electronics, SBBS University, Padhiana, Chotti Baradari, 163/1, Jalandhar, 144022, India

    Shikha Kakar

Authors
  1. Rajneesh Kakar
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  2. Shikha Kakar
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Corresponding author

Correspondence to Rajneesh Kakar.

Appendix

Appendix

$$ c_{1}^{2} = \frac{{(\lambda + 2\mu + \mu_{e} {\rm H}_{0}^{2} + P)}}{\rho } = \frac{2\mu }{\rho }\left( {1 + a + \frac{\lambda }{2\mu } + \frac{{\mu_{e} {\rm H}_{0}^{2} }}{2\mu }} \right) $$
$$ c_{1}^{{{\prime }2}} = \frac{{(\lambda^{{\prime }} + \mu_{e}^{{\prime }} H_{0}^{{{\prime }2}} )}}{{\rho^{{\prime }} }} $$
$$ c_{2}^{2} = \frac{{\left( {\mu - \frac{P}{2}} \right)}}{\rho } = \frac{{\mu \left( {1 - a} \right)}}{\rho } $$
$$ \beta = \frac{P}{{\rho c_{2}^{2} }} = \frac{2a}{1 - a} $$
$$ c_{3}^{2} = \frac{\rm K}{{\rho c_{v} }} $$
$$ c_{3}^{{{\prime }2}} = \frac{{{\rm K}^{{\prime }} }}{{\rho^{{\prime }} c_{v}^{{\prime }} }} $$

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Kakar, R., Kakar, S. Magneto-thermoelastic plane wave at the interface of pre-stressed water-aluminum-epoxy composite using Green and Lindsay’s model. Meccanica 50, 3087–3102 (2015). https://doi.org/10.1007/s11012-015-0189-x

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