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Influence of the mechanical damage on vibration of a viscothermoelastic circular microplate resonator based on dual-phase-lag heat conduction

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Abstract

We establish a mathematical model of thermally conducting an isotropic, homogeneous, and circular microplate in the context of Kirchhoff’s Love plate theory. We define the governing equations in the context of the generalized dual-phase-lagging model and coupled viscothermoelastic plate. We illustrate the scaled viscothermoelasticity for the case of a circular plate for an aspect ratio for clamped boundary conditions. The bounding plane of the plate has been thermally shocked by ramp heating. We apply the Laplace transform and numerically calculate its inversions. The results are obtained for a ceramic plate. The effects of the damage variables and the thickness of the resonator on the temperature increment distribution are found to be minimal, whereas the effect of the ramp heat parameter on the temperature increment is significant. The damage variables and the thickness of the resonator have significant effects. We determine that the ramp heat parameter can be used as a controller to tune the energy damping.

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References

  • Al-Huniti, N.S., Al-Nimr, M.: Thermoelastic behavior of a composite slab under a rapid dual-phase-lag heating. J. Therm. Stresses 27(7), 607–623 (2004)

    Article  Google Scholar 

  • Al-Lehaibi, E.A., Youssef, H.M.: Vibration of gold nano-beam with variable Young’s modulus due to thermal shock. World J. Nano Sci. Eng. 5(04), 194 (2015)

    Article  Google Scholar 

  • Alghamdi, N.: Dual-phase-lagging thermoelastic damping vibration in micro-nano scale beam resonators with voids. Int. J. Multidisciplinary Current Res. 5, 71–78 (2017)

    Google Scholar 

  • Alghamdi, N.A.: Vibration of circular micro-ceramic (Si3N4) plate resonators in the context of the generalized viscothermoelastic dual-phase-lagging theory. Adv. Mech. Eng. 11(11), 1687814019889480 (2019)

    Article  Google Scholar 

  • Alghamdi, N.A., Youssef, H.M.: Dual-phase-lagging thermoelastic damping in-extensional vibration of rotating nano-ring. Microsyst. Technol. 23(10), 4333–4343 (2017)

    Article  Google Scholar 

  • Biot, M.A.: Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena. J. Appl. Phys. 25(11), 1385–1391 (1954)

    Article  MATH  Google Scholar 

  • Biot, M.A.: Variational principles in irreversible thermodynamics with application to viscoelasticity. Phys. Rev. 97(6), 1463 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  • Biot, M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27(3), 240–253 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  • Bland, D.R.: The Theory of Linear Viscoelasticity. Courier Dover Publications, Mineola, New York (2016)

    MATH  Google Scholar 

  • Carcione, J.M., Poletto, F., Gei, D.: 3-D wave simulation in anelastic media using the Kelvin–Voigt constitutive equation. J. Comput. Phys. 196(1), 282–297 (2004)

    Article  MATH  Google Scholar 

  • Chandrasekharaiah, D.: Thermoelasticity with second sound: a review. Appl. Mech. Rev. 39(3), 355–376 (1986)

    Article  MATH  Google Scholar 

  • Christensen, R.: Theory of Viscoelasticity, p. 48. Academic Press, New York (1982).

    Google Scholar 

  • Drozdov, A.: A constitutive model in finite thermoviscoelasticity based on the concept of transient networks. Acta Mech. 133(1–4), 13–37 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Eldesoky, I., Abdelsalam, S., El-Askary, W., El-Refaey, A., Ahmed, M.: Joint effect of thermal energy and magnetic field on particulate fluid suspension in a catheterized tube. BioNanoScience 9(3), 723–739 (2019a)

    Article  Google Scholar 

  • Eldesoky, I., Abdelsalam, S.I., El-Askary, W., Ahmed, M.: Concurrent development of thermal energy with magnetic field on a particle-fluid suspension through a porous conduit. BioNanoScience 9(1), 186–202 (2019b)

    Article  Google Scholar 

  • Ezzat, M.A., El-Karamany, A.S.: The relaxation effects of the volume properties of viscoelastic material in generalized thermoelasticity. Int. J. Eng. Sci. 41(19), 2281–2298 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Gross, D., Seelig, T.: Fracture Mechanics: with an Introduction to Micromechanics. Springer, Berlin (2017)

    MATH  Google Scholar 

  • Grover, D.: Viscothermoelastic vibrations in micro-scale beam resonators with linearly varying thickness. Can. J. Phys. 90(5), 487–496 (2012)

    Article  Google Scholar 

  • Grover, D.: Damping in thin circular viscothermoelastic plate resonators. Can. J. Phys. 93(12), 1597–1605 (2015)

    Article  Google Scholar 

  • Grover, D., Seth, R.: Generalized viscothermoelasticity theory of dual-phase-lagging model for damping analysis in circular micro-plate resonators. Mech. Time-Depend. Mater. 23(1), 119–132 (2019)

    Article  Google Scholar 

  • Guo, F., Song, J., Wang, G., Zhou, Y.: Analysis of thermoelastic dissipation in circular micro-plate resonators using the generalized thermoelasticity theory of dual-phase-lagging model. J. Sound Vib. 333(11), 2465–2474 (2014)

    Article  Google Scholar 

  • Guo, F., Wang, G., Rogerson, G.: Analysis of thermoelastic damping in micro- and nanomechanical resonators based on dual-phase-lagging generalized thermoelasticity theory. Int. J. Eng. Sci. 60, 59–65 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Hao, Z.: Thermoelastic damping in the contour-mode vibrations of micro- and nano-electromechanical circular thin-plate resonators. J. Sound Vib. 313(1–2), 77–96 (2008)

    Article  Google Scholar 

  • Ho, J.-R., Kuo, C.-P., Jiaung, W.-S.: Study of heat transfer in multilayered structure within the framework of dual-phase-lag heat conduction model using lattice Boltzmann method. Int. J. Heat Mass Transf. 46(1), 55–69 (2003)

    Article  MATH  Google Scholar 

  • Khatir, A., Tehami, M., Khatir, S., Abdel Wahab, M.: Multiple damage detection and localization in beam-like and complex structures using co-ordinate modal assurance criterion combined with firefly and genetic algorithms. J. Vibroeng. 18(8), 5063–5073 (2016)

    Article  Google Scholar 

  • Lee, Y.-M., Tsai, T.-W.: Ultra-fast pulse-laser heating on a two-layered semi-infinite material with interfacial contact conductance. Int. Commun. Heat Mass Transf. 34(1), 45–51 (2007)

    Article  Google Scholar 

  • Liu, K.-C.: Numerical analysis of dual-phase-lag heat transfer in a layered cylinder with nonlinear interface boundary conditions. Comput. Phys. Commun. 177(3), 307–314 (2007)

    Article  MATH  Google Scholar 

  • Öchsner, A.: Continuum damage mechanics. In: Continuum Damage and Fracture Mechanics, pp. 65–84. Springer, Berlin (2016)

    Chapter  Google Scholar 

  • Ramadan, K.: Semi-analytical solutions for the dual phase lag heat conduction in multilayered media. Int. J. Therm. Sci. 48(1), 14–25 (2009)

    Article  Google Scholar 

  • Rao, S.S.: Vibration of Continuous Systems. John Wiley & Sons, New York (2019)

    Book  Google Scholar 

  • Sharma, J., Grover, D.: Thermoelastic vibrations in micro-/nano-scale beam resonators with voids. J. Sound Vib. 330(12), 2964–2977 (2011)

    Article  Google Scholar 

  • Sun, Y., Saka, M.: Thermoelastic damping in micro-scale circular plate resonators. J. Sound Vib. 329(3), 328–337 (2010)

    Article  Google Scholar 

  • Sun, Y., Tohmyoh, H.: Thermoelastic damping of the axisymmetric vibration of circular plate resonators. J. Sound Vib. 319(1–2), 392–405 (2009)

    Article  Google Scholar 

  • Tzou, D.: On the thermal shock wave induced by a moving heat source. J. Heat Transf. 111(2), 232–238 (1989)

    Article  Google Scholar 

  • Tzou, D., Transfer, M.-t.M.H.: The Lagging Behavior. Taylor Francis, Washington (1997)

    Google Scholar 

  • Ventsel, E., Krauthammer, T.: Thin Plates and Shells: Theory: Analysis, and Applications. CRC Press, Boca Raton (2001)

    Book  Google Scholar 

  • Voyiadjis, G.Z.: Handbook of Damage Mechanics: Nano to Macro Scale for Materials and Structures. Springer, Berlin (2015)

    Google Scholar 

  • Voyiadjis, G.Z., Kattan, P.I.: Introducing damage mechanics templates for the systematic and consistent formulation of holistic material damage models. Acta Mech. 228(3), 951–990 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, M., Guo, J., Wang, L., Cheng, L.: Thermal wave interference as the origin of the overshooting phenomenon in dual-phase-lagging heat conduction. Int. J. Therm. Sci. 50(5), 825–830 (2011)

    Article  Google Scholar 

  • Yao, Y., He, X., Keer, L.M., Fine, M.E.: A continuum damage mechanics-based unified creep and plasticity model for solder materials. Acta Mater. 83, 160–168 (2015)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Mathematics Department, Faculty of Education, Alexandria University, Alexandria, Egypt

    Hamdy M. Youssef

  2. Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia

    Hamdy M. Youssef

  3. Basic Science Department, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt

    Alaa A. El-Bary

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  1. Hamdy M. Youssef
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  2. Alaa A. El-Bary
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Correspondence to Hamdy M. Youssef.

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Youssef, H.M., El-Bary, A.A. Influence of the mechanical damage on vibration of a viscothermoelastic circular microplate resonator based on dual-phase-lag heat conduction. Mech Time-Depend Mater 25, 473–493 (2021). https://doi.org/10.1007/s11043-020-09455-z

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