The analysis and validation of natural frequencies and mode shapes of 3D plates in the framework of the generalized thermoelastic theory

References

• N. V. Vuong and C. H. Lee, “Quasi-3D isogeometric buckling analysis method for advanced composite plates in thermal environments,” Aerosp. Sci. Technol., vol. 92, pp. 34–54, 2019. DOI: 10.1016/j.ast.2019.05.056.
   Web of Science ®Google Scholar
• W. Yu, X. Wang, and X. Huang, “Dynamic modelling of heat transfer in thermal-acoustic fatigue tests,” Aerosp. Sci. Technol., vol. 71, pp. 675–684, 2017. DOI: 10.1016/j.ast.2017.10.025.
   Web of Science ®Google Scholar
• T. M. Tu, T. H. Quoc, and L. N. Van, “Vibration analysis of functionally graded plates using the eight-unknown higher order shear deformation theory in thermal environments,” Aerosp. Sci. Technol., vol. 84, pp. 698–711, 2019. DOI: 10.1016/j.ast.2018.11.010.
   Web of Science ®Google Scholar
• W. Zhang, R. Q. Wu, and K. Behdinan, “Nonlinear dynamic analysis near resonance of a beam-ring structure for modelling circular truss antenna under time-dependent thermal excitation,” Aerosp. Sci. Technol., vol. 86, pp. 296–311, 2019. DOI: 10.1016/j.ast.2019.01.018.
   Web of Science ®Google Scholar
• A. E. Abouelregal and R. Tiwari, “The thermoelastic vibration of nano-sized rotating beams with variable thermal properties under axial load via memory-dependent heat conduction,” Meccanica, vol. 57, no. 8, pp. 2001–2025, 2022. DOI: 10.1007/s11012-022-01543-3.
   Web of Science ®Google Scholar
• H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids, vol. 15, no. 5, pp. 299–309, 1967. DOI: 10.1016/0022-5096(67)90024-5.
   Web of Science ®Google Scholar
• A. E. Green and K. A. Lindsay, “Thermoelasticity,” J. Elasticity, vol. 2, no. 1, pp. 1–7, 1972. DOI: 10.1007/BF00045689.
   Google Scholar
• A. E. Green and P. M. Naghdi, “Thermoelasticity without energy dissipation,” J. Elasticity, vol. 31, no. 3, pp. 189–208, 1993. DOI: 10.1007/BF00044969.
   Web of Science ®Google Scholar
• P. Pal and M. Kanoria, “Thermo-elastic wave propagation in a transversely isotropic thick plate under Greena Naghdi theory due to gravitational field,” J. Therm. Stresses, vol. 40, no. 4, pp. 470–485, 2017. DOI: 10.1080/01495739.2016.1253438.
   Web of Science ®Google Scholar
• K. L. Verma, “Thermo-elastic waves in anisotropic plates using normal mode expansion method with thermal relaxation time,” Int. J. Mech. Syst. Sci. Eng., vol. 2, no. 2, pp. 86–93, 2013.
   Google Scholar
• K. L. Verma, “Thermo-elastic wave propagation in laminated composites plates,” Appl. Comput. Mech., vol. 6, no. 2, pp. 197–208, 2012.
   Google Scholar
• S. M. Hsu and C. C. Yin, “Numerical study of characteristic equations of thermo-elastic waves propagating in a uniaxial pre-stressed isotropic plate,” Isrn Appl. Math., vol. 2011, pp. 532–547, 2013.
   Google Scholar
• M. D. Sharma, “Propagation and attenuation of Rayleigh waves in generalized thermo-elastic media,” J. Seismol., vol. 18, no. 1, pp. 61–79, 2014. DOI: 10.1007/s10950-013-9401-4.
   Web of Science ®Google Scholar
• F. Bayones, A. Abd-Alla, R. Alfatta, and H. Al-Nefaie, “Propagation of thermoelastic wave in a half-space of a homogeneous isotropic material subjected to the effect of rotation and initial stress,” Comput. Mater. Contin., vol. 62, no. 2, pp. 551–567, 2020. DOI: 10.32604/cmc.2020.08420.
   Web of Science ®Google Scholar
• A. E. N. Abd-Alla and A. Al-Dawy, “Thermal relaxation times effect on Rayleigh waves in Generalized Thermoelastic Media,” J. Therm. Stress., vol. 24, pp. 367–382, 2001.
   Web of Science ®Google Scholar
• M. Marin, M. I. A. Othman, and I. A. Abbas, “An extension of the domain of influence theorem for generalized thermoelasticity of anisotropic material with voids,” J. Comput. Theor. Nanosci., vol. 12, no. 8, pp. 1594–1598, 2015. DOI: 10.1166/jctn.2015.3934.
   Google Scholar
• I. A. Abbas, A. Abdalla, F. S. Alzahrani, and M. Spagnuolo, “Wave propagation in a generalized thermo-elastic plate using eigenvalue approach,” J. Therm. Stress., vol. 39, no. 11, pp. 1367–1377, 2016. DOI: 10.1080/01495739.2016.1218229.
   Web of Science ®Google Scholar
• M. I. A. Othman and E. E. M. Eraki, “Effect of gravity on generalized thermoelastic diffusion due to laser pulse using dual-phase-lag model,” MMMS., vol. 14, no. 3, pp. 457–481, 2018. DOI: 10.1108/MMMS-08-2017-0087.
   Google Scholar
• V. Borjalilou and M. Asghari, “Size-dependent strain gradient-based thermoelastic damping in micro-beams utilizing a generalized thermoelasticity theory,” Int. J. Appl. Mech., vol. 11, no. 01, pp. 1950007, 2019. DOI: 10.1142/S1758825119500078.
   Web of Science ®Google Scholar
• V. Borjalilou and M. Asghari, “Thermoelastic damping in strain gradient microplates according to a generalized theory of thermoelasticity,” J. Therm. Stress., vol. 43, no. 4, pp. 401–420, 2020. DOI: 10.1080/01495739.2020.1722771.
   Web of Science ®Google Scholar
• J. Alihemmati, Y. T. Beni, and Y. Kiani, “Application of Chebyshev collocation method to unified generalized thermoelasticity of a finite domain,” J. Therm. Stress., vol. 44, no. 5, pp. 547–565, 2021. DOI: 10.1080/01495739.2020.1867941.
   Web of Science ®Google Scholar
• B. Zhang, L. J. Li, J. G. Yu, and L. Elmaimouni, “Generalized thermo-elastic waves propagating in bars with a rectangular cross-section,” Arch. Appl. Mech., vol. 92, no. 3, pp. 785–799, 2022. DOI: 10.1007/s00419-021-02072-3.
   Web of Science ®Google Scholar
• M. Li, Y. Cai, R. Fan, H. Wang, and V. Borjalilou, “Generalized thermoelasticity model for thermoelastic damping in asymmetric vibrations of nonlocal tubular shells,” Thin-Walled Struct., vol. 174, pp. 109142, 2022. DOI: 10.1016/j.tws.2022.109142.
   Web of Science ®Google Scholar
• R. Tiwari and A. E. Abouelregal, “Memory response on magneto-thermoelastic vibrations on a viscoelastic micro-beam exposed to a laser pulse heat source,” Appl. Math. Model., vol. 99, pp. 328–345, 2021. DOI: 10.1016/j.apm.2021.06.033.
   Web of Science ®Google Scholar
• R. Tiwari, “Magneto-thermoelastic interactions in generalized thermoelastic half-space for varying thermal and electrical conductivity,” Waves Random Complex Media, pp. 1–17, 2021. DOI: 10.1080/17455030.2021.1948146.
   Web of Science ®Google Scholar
• R. Tiwari, J. C. Misra, and R. Prasad, “Magneto-thermoelastic wave propagation in a finitely conducting medium: a comparative study for three types of thermoelasticity I, II, and III,” J. Therm. Stress., vol. 44, no. 7, pp. 785–806, 2021. DOI: 10.1080/01495739.2021.1918594.
   Web of Science ®Google Scholar
• D. Zhou, Y. K. Cheung, F. T. K. Au, and S. H. Lo, “Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method,” Int. J. Solids Struct., vol. 39, no. 26, pp. 6339–6353, 2002. DOI: 10.1016/S0020-7683(02)00460-2.
   Web of Science ®Google Scholar
• S. Aydinlik and A. Kiris, “Fractional calculus approach to nonlocal three-dimensional vibration analysis of plates,” AIAA J., vol. 58, no. 1, pp. 355–361, 2020. DOI: 10.2514/1.J058629.
   Google Scholar
• A. Kiris and E. İnan, “3-D vibration analysis of the rectangular micro damaged plates,” Springer Proc. Phys., vol. 126, pp. 207–214, 2008.
   Google Scholar
• S. Aydinlik, A. Kiris, and W. Sumelka, “Nonlocal vibration analysis of microstretch plates in the framework of space-fractional mechanics—theory and validation,” Eur. Phys. J. Plus, vol. 136, no. 2, pp. 169, 2021. DOI: 10.1140/epjp/s13360-021-01110-x.
   Web of Science ®Google Scholar
• S. Aydinlik, A. Kiris, and W. Sumelka, “Three-dimensional analysis of nonlocal plate vibration in the framework of space-fractional mechanics—theory and validation,” Thin-Walled Struct., vol. 163, pp. 107645, 2021. DOI: 10.1016/j.tws.2021.107645.
   Web of Science ®Google Scholar
• H. T. Synder and M. W. Kehoe, Determination of the Effects of Heating on Modal Characteristics of an Aluminum Plate with Application to Hypersonic Vehicles. NASA, 1991.
   Google Scholar
• D. J. Godfrey, “The use of ceramics for engines,” Mater. Des., vol. 4, no. 3, pp. 759–765, 1983. DOI: 10.1016/0261-3069(83)90199-1.
   Google Scholar
• J. N. Sharma, D. Singh, and R. Kumar, “Generalized thermo-elastic waves in homogeneous isotropic plates,” J. Acoust. Soc. Am., vol. 108, no. 2, pp. 848–851, 2000. DOI: 10.1121/1.429619.
   PubMed Web of Science ®Google Scholar
• R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro- and nanomechanical systems,” Phys. Rev. B, vol. 61, no. 8, pp. 5600–5609, 2000. DOI: 10.1103/PhysRevB.61.5600.
   Web of Science ®Google Scholar
• C. M. Twinkle, J. Pitchaimani, and V. Rajamohan, “Free vibration modes of rectangular plate under non-uniform heating: an experimental investigation,” Structures, vol. 28, pp. 1802–1817, 2020.
   Web of Science ®Google Scholar