Abstract
The system of equations of the generalized piezothermoelasticity in anisotropic medium with dual-phase-lag model is established. The exact expressions for displacement components, the temperature, stress components, electric potential and electric displacements are given in the physical domain and illustrated graphically. These expressions are calculated numerically for the problem. Comparisons are made with the results predicted by Lord–Shulman theory and dual-phase-lag model. It is shown that the results from both theories are close to each other for thin slabs, while they differ considerably for thick ones. The present results are of interest in studying the thermomechanical response of piezoelectric sheets under different working thermal, mechanical and electrical conditions.
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References
D Y Tzou J. Heat Transf.117 8 (1995)
D Y Tzou Int. J. Heat Mass Transf.38 3231 (1995)
R Quintanilla and R Racke J. Appl. Math. 66 977 (2006)
R Quintanilla J. Non-Equilb. Thermodyn. 27 217 (2002)
R Quintanilla and R Racke Int. J. Heat Mass Transf. 49 1209 (2006)
S K Roy Choudhuri J. Therm. Stress.30 231 (2007)
B Singh, S Kumari and J Singh Mech. Mech. Eng. 21 105 (2017)
M I A Othman, W M Hasona and E E M Eraki Can. J. Phys. 92 149 (2014)
A F Ghaleb Enc. Therm. Stresses (C), Ed. R B Hetnarski, (Springer) p 767 (2014)
M S Abou-Dina, A R EL Dhaba, A F Ghaleb and E K Rawy Int. J. Eng. Sci. 119 29 (2017)
R D Mindlin in: N I Muskelishvili (Ed.), Mechanics, 70th Birthday Volume, SIAM, Philadelphia, p 282 (1961)
R D Mindlin Interactions in Elastic Solids (Wein: Springer) (1979)
P F Hou and A Y T Leung J. Intell. Mater. Syst. Struct. 16 1915 (2009)
G M Kulikov and S V Plotnikova J. Intell. Mater. Syst. Struct. 28 435 (2017)
W Q Chen J. Appl. Mech. 67 705 (2000)
W Q Chen, C W Lim and H J Ding Eng. Anal. Bound. Elem. 29 524 (2005)
M I A Othman, A Khan, R Jahangir and A Jahangir Appl. Math. Model. 65 535 (2019)
M I A Othman and E A A Ahmed J. Therm. Stress.474 (2016)
Y Tanigawa and Y Ootao J. Therm. Stress. 30 1003 (2007)
A N Abd-Alla and F A Alsheikh Arch. Appl. Mech. 79 843 (2009)
A N Abd-Alla, F A Alsheikh and A Y Al-Hossain Meccanica 47 731 (2012)
B Behjat, M Salehi, A Armin, M Sadighi and M Abbasi Sci. Iran Trans. B 18 986 (2011)
J N Sharma and M Kumar J. Eng. Mat. Sci. 7 434 (2000)
M Aouadi Int. J. Solids Struct. 43 6347 (2006)
H M Youssef and E Bassiouny Comput. Methods Sci. Technol.14 55 (2008)
E Bassiouny Appl. Math. Comput. 218 10009 (2012)
M I A Othman, S Y Atwa, W M Hasona and E A A Ahmed Int. J. Innov. Res. Sci. Eng. Technol. (IJIRSET) 4 2292 (2015)
M I A Othman and E A A Ahmed Struct. Eng. Mech. 56 649 (2015)
K M Liew, Z Z Jordan, C Li and S A Meguid Int. J. Solids Struct. 42 4239 (2005)
N Dhanesh and S Kapuria J. Therm. Stress. 41 1577 (2019)
M I A Othman and E M Abd -Elaziz J. Therm. Stress. 38 1068 (2015)
X J Yang Appl. Math. Lett. 64 193 (2017)
X J Yang and F Gao Therm. Sci. 21 133 (2017)
X-J Yang Therm. Sci. 21 S79 (2017)
X J Yang, Y Yang, C Cattani and M Zhu Therm. Sci. 21 S129 (2017)
R A Yadav, T K Yadav, M K Maurya, D P Yadav and N P Singh Indian J. Phys. 83 1421 (2009)
M I A Othman and E M Abd-Elaziz Indian J. Phys. 93 475 (2019)
M Marin, S Vlase , R Ellahi and M M Bhatti Symmetry 11 863 (2019)
M Marin, R Ellahi and A Chirila Carpath. J. Math. 33 219 (2017)
A Majeed, A Zeeshan, S Z Alamri and R Ellahi Neural Comput. Appl. 30 1947 (2018)
M Akbarzadeh, S Rashidi, N Karimi and R Ellahi Adv. Powder Technol. 29 2243 (2018)
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Appendices
Appendix 1
Some important coefficients appearing in the text:
and
Appendix 2
Some important coefficients appearing in the text for \(n=1,2,3,4\):
Appendix 3
This system is cast in the following matricial form:
where the superscript T is used here after to denote the transpose of the superscripted matrix and A is the matrix of coefficients given as
and F is the following vector of constants
The solution of this system of equations takes the form:
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Ahmed, E.A.A., Abou-Dina, M.S. Piezothermoelasticity in an infinite slab within the dual-phase-lag model. Indian J Phys 94, 1917–1929 (2020). https://doi.org/10.1007/s12648-019-01655-9
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DOI: https://doi.org/10.1007/s12648-019-01655-9
Keywords
- Piezothermoelasticity
- Dual-phase-lag model
- Normal modes method
- An infinite slab
- Generalized thermoelasticity