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Erschienen in: Acta Mechanica 1/2024

23.10.2023 | Original Paper

Dynamic response of a piezoelectric quasicrystal rod with the generalized thermoelasticity

verfasst von: Ying Li, Yanbin Zhou

Erschienen in: Acta Mechanica | Ausgabe 1/2024

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Abstract

Based on the generalized thermoelastic theory, the physical changes of a finite length rod, which is composed of one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) fixed on both sides and subjected to a moving heat source, are studied. The numerical solutions are obtained using the Laplace transform and its numerical inversion. The effects of displacement, stress, temperature and electric potential on velocity of moving heat source and time were studied. It can be seen from the distribution that the temperature, displacement, electric potential and stress of the rod all increase when the time increases, while the influence of the heat source velocity is opposite.
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Literatur
1.
Zurück zum Zitat Shechtman, D., Blech, I., Gratias, D., Cahn, J.W.: Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951–1953 (1984) Shechtman, D., Blech, I., Gratias, D., Cahn, J.W.: Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53(20), 1951–1953 (1984)
2.
Zurück zum Zitat Levine, D., Steinhardt, P.J.: Quasicrystals. J. Non-cryst. Solids 75(1–3), 85–89 (1985) Levine, D., Steinhardt, P.J.: Quasicrystals. J. Non-cryst. Solids 75(1–3), 85–89 (1985)
3.
Zurück zum Zitat Louzguine-Luzgin, D.V., Inoue, A.: Formation and properties of quasicrystals. Annu. Rev. Mater. Res. 38(1), 403–423 (2008) Louzguine-Luzgin, D.V., Inoue, A.: Formation and properties of quasicrystals. Annu. Rev. Mater. Res. 38(1), 403–423 (2008)
4.
Zurück zum Zitat Li, L.H., Liu, G.T.: Stroh formalism for icosahedral quasicrystal and its application. Phys. Lett. A 376(8), 987–990 (2012) Li, L.H., Liu, G.T.: Stroh formalism for icosahedral quasicrystal and its application. Phys. Lett. A 376(8), 987–990 (2012)
5.
Zurück zum Zitat Li, X.F.: Elastohydrodynamic problems in quasicrystal elasticity theory and wave propagation. Philos. Mag. 93(13), 1500–1519 (2013) Li, X.F.: Elastohydrodynamic problems in quasicrystal elasticity theory and wave propagation. Philos. Mag. 93(13), 1500–1519 (2013)
6.
Zurück zum Zitat Li, X.Y., Li, P.D., Wu, T.H., Shi, M.X., Zhu, Z.W.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378(10), 826–834 (2014)MathSciNet Li, X.Y., Li, P.D., Wu, T.H., Shi, M.X., Zhu, Z.W.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378(10), 826–834 (2014)MathSciNet
7.
Zurück zum Zitat Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and its Applications. Science Press, Beijing (2011) Fan, T.Y.: Mathematical Theory of Elasticity of Quasicrystals and its Applications. Science Press, Beijing (2011)
8.
Zurück zum Zitat Hu, C.Z., Wang, R.H., Ding, D.H., Yang, W.G.: Piezoelectric effects in quasicrystals. Phys. Rev. B 56(5), 2463–2468 (1997) Hu, C.Z., Wang, R.H., Ding, D.H., Yang, W.G.: Piezoelectric effects in quasicrystals. Phys. Rev. B 56(5), 2463–2468 (1997)
9.
Zurück zum Zitat Altay, G., Dömeci, M.C.: On the fundamental equations of piezoelasticity of quasicrystal media. Int. J. Solids Struct. 49(23–24), 3255–3262 (2012) Altay, G., Dömeci, M.C.: On the fundamental equations of piezoelasticity of quasicrystal media. Int. J. Solids Struct. 49(23–24), 3255–3262 (2012)
10.
Zurück zum Zitat Guo, J.H., Zhang, Z.Y., Xing, Y.M.: Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites. Philos. Mag. 96(4), 349–369 (2016) Guo, J.H., Zhang, Z.Y., Xing, Y.M.: Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites. Philos. Mag. 96(4), 349–369 (2016)
11.
Zurück zum Zitat Zhou, Y.B., Li, X.F.: Two collinear mode-\(III\) cracks in one-dimensional hexagonal piezoelectric quasicrystal strip. Eng. Fract. Mech 189, 133–147 (2017) Zhou, Y.B., Li, X.F.: Two collinear mode-\(III\) cracks in one-dimensional hexagonal piezoelectric quasicrystal strip. Eng. Fract. Mech 189, 133–147 (2017)
12.
Zurück zum Zitat Zhou, Y.B., Li, X.F.: A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals. Appl. Math. Model. 65, 148–163 (2019)MathSciNet Zhou, Y.B., Li, X.F.: A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals. Appl. Math. Model. 65, 148–163 (2019)MathSciNet
13.
Zurück zum Zitat Zhou, Y.B., Li, X.F.: Elasto-hydrodynamics of quasicrystals with a crack under sudden impacts. Philos. Mag. Lett. 1–18 (2019) Zhou, Y.B., Li, X.F.: Elasto-hydrodynamics of quasicrystals with a crack under sudden impacts. Philos. Mag. Lett. 1–18 (2019)
14.
Zurück zum Zitat Zhao, M.H., Dang, H.Y., Fan, C.Y., Chen, Z.T.: Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: theoretical solution. Eng. Fract. Mech. 179, 59–78 (2017) Zhao, M.H., Dang, H.Y., Fan, C.Y., Chen, Z.T.: Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: theoretical solution. Eng. Fract. Mech. 179, 59–78 (2017)
15.
Zurück zum Zitat Dang, H.Y., Zhao, M.H., Fan, C.Y., Chen, Z.T.: Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 2: numerical method. Eng. Fract. Mech. 180, 268–281 (2017) Dang, H.Y., Zhao, M.H., Fan, C.Y., Chen, Z.T.: Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 2: numerical method. Eng. Fract. Mech. 180, 268–281 (2017)
16.
Zurück zum Zitat Sun, T.Y., Guo, J.H., Zhan, X.Y.: Static deformation of a multilayered one-dimensional hexagonal quasicrystal plate with piezoelectric effect. Appl. Math. Mech. 39(3), 335–352 (2018)MathSciNet Sun, T.Y., Guo, J.H., Zhan, X.Y.: Static deformation of a multilayered one-dimensional hexagonal quasicrystal plate with piezoelectric effect. Appl. Math. Mech. 39(3), 335–352 (2018)MathSciNet
17.
Zurück zum Zitat Zhou, Y.B., Li, X.F.: Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal. Philos. Mag. 98(19), 1780–1798 (2018) Zhou, Y.B., Li, X.F.: Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal. Philos. Mag. 98(19), 1780–1798 (2018)
18.
Zurück zum Zitat Suo, Y.R., Zhou, Y.B., Liu, G.T.: Effect of T-stress on the fracture in an infinite two-dimensional decagonal quasicrystals of a cruciform crack with unequal arms. Int. J. Solids Struct. 232, 111181 (2021) Suo, Y.R., Zhou, Y.B., Liu, G.T.: Effect of T-stress on the fracture in an infinite two-dimensional decagonal quasicrystals of a cruciform crack with unequal arms. Int. J. Solids Struct. 232, 111181 (2021)
19.
Zurück zum Zitat Zhao, Z.N., Guo, J.H.: Surface effects on a mode-\(III\) reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals. Appl. Math. Mech. 42(5), 625–640 (2021)MathSciNet Zhao, Z.N., Guo, J.H.: Surface effects on a mode-\(III\) reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals. Appl. Math. Mech. 42(5), 625–640 (2021)MathSciNet
20.
Zurück zum Zitat Cheng, J.X., Liu, B.J., Huang, X.Z., Li, Z.X.: Anti-plane fracture analysis of 1D hexagonal piezoelectric quasicrystals with the effects of damage due to materials degradation. Theor. Appl. Fract. Mech. 113, 102939 (2021) Cheng, J.X., Liu, B.J., Huang, X.Z., Li, Z.X.: Anti-plane fracture analysis of 1D hexagonal piezoelectric quasicrystals with the effects of damage due to materials degradation. Theor. Appl. Fract. Mech. 113, 102939 (2021)
21.
Zurück zum Zitat Huang, R.K., Ding, S.H., Zhang, X., Li, X.: Frictional contact problem of a rigid charged indenter on two dimensional hexagonal piezoelectric quasicrystals coating. Philos. Mag. 101(19), 2123–2156 (2021) Huang, R.K., Ding, S.H., Zhang, X., Li, X.: Frictional contact problem of a rigid charged indenter on two dimensional hexagonal piezoelectric quasicrystals coating. Philos. Mag. 101(19), 2123–2156 (2021)
22.
Zurück zum Zitat Tzou, D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transf. 38(17), 3231–3240 (1995) Tzou, D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transf. 38(17), 3231–3240 (1995)
23.
Zurück zum Zitat Tzou, D.Y.: A unified field approach for heat conduction from macro- to micro-scales. J. Heat Transf. 117(1), 8–16 (1995) Tzou, D.Y.: A unified field approach for heat conduction from macro- to micro-scales. J. Heat Transf. 117(1), 8–16 (1995)
24.
Zurück zum Zitat Roy Choudhuri, S.K.: On A Thermoelastic Three-Phase-Lag Model. J Therm Stress 30(3), 231–238 (2007) Roy Choudhuri, S.K.: On A Thermoelastic Three-Phase-Lag Model. J Therm Stress 30(3), 231–238 (2007)
25.
Zurück zum Zitat Guo, Z.Y., Hou, Q.W.: On a thermoelastic three-phase-lag model. J. Heat Transf. 132(7), 072403 (2010) Guo, Z.Y., Hou, Q.W.: On a thermoelastic three-phase-lag model. J. Heat Transf. 132(7), 072403 (2010)
26.
Zurück zum Zitat Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967) Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)
27.
Zurück zum Zitat Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972) Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972)
28.
Zurück zum Zitat Green, A.E., Naghdi, P.M.: Thermoelasticity without energy dissipation. J. Elast. 31(3), 189–208 (1993)MathSciNet Green, A.E., Naghdi, P.M.: Thermoelasticity without energy dissipation. J. Elast. 31(3), 189–208 (1993)MathSciNet
29.
Zurück zum Zitat Hetnarski, R.B., Ignacza, J.: Greneralized thermoelasticity. J. Therm. Stress. 22(4–5), 451–476 (1999) Hetnarski, R.B., Ignacza, J.: Greneralized thermoelasticity. J. Therm. Stress. 22(4–5), 451–476 (1999)
30.
Zurück zum Zitat Abbas, I.A., Zenkour, A.M.: Two-temperature generalized thermoelastic interaction in an infinite fiber-reinforced anisotropic plate containing a circular cavity with two relaxation Times. J. Comput. Theor. Nanosci. 11(2), 331–338 (2014) Abbas, I.A., Zenkour, A.M.: Two-temperature generalized thermoelastic interaction in an infinite fiber-reinforced anisotropic plate containing a circular cavity with two relaxation Times. J. Comput. Theor. Nanosci. 11(2), 331–338 (2014)
31.
Zurück zum Zitat Li, X.Y., Li, P.D.: Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions. Phys. Lett. A 376(26–27), 2004–2009 (2012) Li, X.Y., Li, P.D.: Three-dimensional thermo-elastic general solutions of one-dimensional hexagonal quasi-crystal and fundamental solutions. Phys. Lett. A 376(26–27), 2004–2009 (2012)
32.
Zurück zum Zitat Li, X.Y., Wang, T., Zheng, R.F., Kang, G.Z.: Fundamental thermo-electro-elastic solutions for 1D hexagonal QC. Z. Angew. Math. Mech. 95(5), 457–468 (2013)MathSciNet Li, X.Y., Wang, T., Zheng, R.F., Kang, G.Z.: Fundamental thermo-electro-elastic solutions for 1D hexagonal QC. Z. Angew. Math. Mech. 95(5), 457–468 (2013)MathSciNet
33.
Zurück zum Zitat Yang, L.Z., Li, Y., Gao, Y., Pan, E.N.: Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates. Appl. Math. Model. 63, 203–218 (2018)MathSciNet Yang, L.Z., Li, Y., Gao, Y., Pan, E.N.: Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates. Appl. Math. Model. 63, 203–218 (2018)MathSciNet
34.
Zurück zum Zitat Chen, Z.T., Akbarzadeh, A.: Advanced Thermal Stress Analysis of Smart Materials and Structures. Springer International Publishing, Berlin (2020) Chen, Z.T., Akbarzadeh, A.: Advanced Thermal Stress Analysis of Smart Materials and Structures. Springer International Publishing, Berlin (2020)
35.
Zurück zum Zitat Li, C.L., Liu, Y.Y.: The physical property tensors of one-dimensional quasicrystals. Chin. Phys. 13(6), 924–931 (2004) Li, C.L., Liu, Y.Y.: The physical property tensors of one-dimensional quasicrystals. Chin. Phys. 13(6), 924–931 (2004)
36.
Zurück zum Zitat Rochal, S.B., Lorman, V.L.: Anisotropy of acoustic-phonon properties of an icosahedral quasicrystal at high temperature due to phonon-phason coupling. Phys. Rev. B Condens. 62(2), 874–879 (2000) Rochal, S.B., Lorman, V.L.: Anisotropy of acoustic-phonon properties of an icosahedral quasicrystal at high temperature due to phonon-phason coupling. Phys. Rev. B Condens. 62(2), 874–879 (2000)
37.
Zurück zum Zitat Ding, D.H., Yang, W.G., Hu, C.Z., Wang, R.H.: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48(10), 7003–7010 (1993) Ding, D.H., Yang, W.G., Hu, C.Z., Wang, R.H.: Generalized elasticity theory of quasicrystals. Phys. Rev. B 48(10), 7003–7010 (1993)
38.
Zurück zum Zitat Li, X.F., Xie, L.Y., Fan, T.Y.: Elasticity and dislocations in quasicrystals with 18-fold symmetry. Phys. Rev. A 377(39), 2810–2814 (2013)MathSciNet Li, X.F., Xie, L.Y., Fan, T.Y.: Elasticity and dislocations in quasicrystals with 18-fold symmetry. Phys. Rev. A 377(39), 2810–2814 (2013)MathSciNet
39.
Zurück zum Zitat Hu, C.Z., Wang, R.H., Ding, D.H.: Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Rep. Prog. Phys. 63(2000), 1–39 (2000)MathSciNet Hu, C.Z., Wang, R.H., Ding, D.H.: Symmetry groups, physical property tensors, elasticity and dislocations in quasicrystals. Rep. Prog. Phys. 63(2000), 1–39 (2000)MathSciNet
40.
Zurück zum Zitat Fan, T.Y., Li, X.F., Sun, Y.F.: A moving screw dislocation in a one-dimensional hexagonal quasicrystal. Acta Phys. Sin-Ch Ed. 8(4), 288–295 (1999) Fan, T.Y., Li, X.F., Sun, Y.F.: A moving screw dislocation in a one-dimensional hexagonal quasicrystal. Acta Phys. Sin-Ch Ed. 8(4), 288–295 (1999)
41.
Zurück zum Zitat Babaei, M.H., Chen, Z.T.: Dynamic response of a thermopiezoelectric rod due to a moving heat source. Smart Mater. Struct. 18(2), 025003 (2009) Babaei, M.H., Chen, Z.T.: Dynamic response of a thermopiezoelectric rod due to a moving heat source. Smart Mater. Struct. 18(2), 025003 (2009)
42.
Zurück zum Zitat Durbin, F.: Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method. Comput. J. 17(4), 371–376 (1974)MathSciNet Durbin, F.: Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method. Comput. J. 17(4), 371–376 (1974)MathSciNet
43.
Zurück zum Zitat Honig, G., Hirdes, U.: A method for the numerical inversion of Laplace transforms. J. Comput. Appl. Math. 10(1), 113–132 (1984)MathSciNet Honig, G., Hirdes, U.: A method for the numerical inversion of Laplace transforms. J. Comput. Appl. Math. 10(1), 113–132 (1984)MathSciNet
44.
Zurück zum Zitat He, T.H., Cao, L., Li, S.R.: Dynamic response of a piezoelectric rod with thermal relaxation. J. Sound Vib. 306(3–5), 897–907 (2007) He, T.H., Cao, L., Li, S.R.: Dynamic response of a piezoelectric rod with thermal relaxation. J. Sound Vib. 306(3–5), 897–907 (2007)
Metadaten
Titel
Dynamic response of a piezoelectric quasicrystal rod with the generalized thermoelasticity
verfasst von
Ying Li
Yanbin Zhou
Publikationsdatum
23.10.2023
Verlag
Springer Vienna
Erschienen in
Acta Mechanica / Ausgabe 1/2024
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-023-03747-4

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