Thermoelastic damping in a micro-beam based on the memory-dependent generalized thermoelasticity

References

• Bishop JE, Kinra VK. Elastothermodynamic damping in laminated composites. Int J Solids Struct. 1997;34(9):1075–1092.
   Web of Science ®Google Scholar
• Lin S-M. Analytical solutions for thermoelastic vibrations of beam resonators with viscous damping in non-Fourier model. Int J Mech Sci. 2014;87:26–35.
   Web of Science ®Google Scholar
• Tunvir K, Ru CQ, Mioduchowski A. Effect of cross-sectional shape on thermoelastic dissipation of micro/nano elastic beams. Int J Mech Sci. 2012;62(1):77–88.
   Web of Science ®Google Scholar
• Kinra VK, Milligan KB. A second-law analysis of thermoelastic damping. J Appl Mech. 1994;61(1):71–76.
   Web of Science ®Google Scholar
• Khisaeva ZF, Ostoja-Starzewski M. Theroelastic damping in nanomechanical resonators with finite wave speeds. J Therm Stress. 2006;29(3):201–216.
   Web of Science ®Google Scholar
• Li P, Fang Y, Hu R. Thermoelastic damping in rectangular and circular microplate resonators. J Sound Vib. 2012;331(3):721–733.
   Web of Science ®Google Scholar
• Bostani M, Mohammadi AK. Thermoelastic damping in microbeam resonators based on modified strain gradient elasticity and generalized thermoelasticity theories. Acta Mech. 2018;229(1):173–192.
   Web of Science ®Google Scholar
• Liu S, Sun Y, Ma J, et al. Theoretical analysis of thermoelastic damping in bilayered circular plate resonators with two-dimensional heat conduction. Int J Mech Sci. 2018;135:114–123.
   Web of Science ®Google Scholar
• Zuo W, Li P, Du J, et al. Thermoelastic damping in trilayered microplate resonators. Int J Mech Sci. 2019;151:595–608.
   Web of Science ®Google Scholar
• Lifshitz R, Roukes ML. Thermoelastic damping in micro- and nanomechanical systems. Phys Rev B. 2000;61:5600–5609.
   Web of Science ®Google Scholar
• Sun Y, Fang D, Soh AK. Thermoelastic damping in micro-beam resonators. Int J Solids Struct. 2006;43(10):3213–3229.
   Web of Science ®Google Scholar
• Vahdat AS, Rezazadeh G. Effects of axial and residual stresses on thermoelastic damping in capacitive micro-beam resonators. J Franklin Inst. 2011;348(4):622–639.
   Web of Science ®Google Scholar
• Croy A, Midtvedt D, Isacsson A, et al. Nonlinear damping in graphene resonators. Phys Rev B. 2012;86(23):235435.
   Google Scholar
• Guo FL. Thermo-elastic dissipation of microbeam resonators in the framework of generalized thermo-elasticity theory. J Therm Stress. 2013;36(11):1156–1168.
   Web of Science ®Google Scholar
• Tai Y, Li P, Fang Y. Thermoelastic damping in torsion microresonators with coupling effect between torsion and bending. J Sound Vib. 2014;333(5):1509–1525.
   Web of Science ®Google Scholar
• Hendou RH, Mohammadi AK. Transient analysis of nonlinear Euler–Bernoulli micro-beam with thermoelastic damping via nonlinear normal modes. J Sound Vib. 2014;333(23):6224–6236.
   Web of Science ®Google Scholar
• Emami AA, Alibeigloo A. Thermoelastic damping analysis of FG Mindlin microplates using strain gradient theory. J Therm Stress. 2016;39(12):1499–1522.
   Web of Science ®Google Scholar
• Zhang H, Kim T, Choi G, et al.Thermoelastic damping in micro- and nanomechanical beam resonators considering size effects. Int J Heat Mass Transfer. 2016;103:783–790.
   Web of Science ®Google Scholar
• Deng W, Li L, Hu Y, et al. Thermoelastic damping of graphene nanobeams by considering the size effects of nanostructure and heat conduction. J Therm Stress. 2018;41(9):1182–1200.
   Web of Science ®Google Scholar
• Borjalilou V, Asghari M, Bagheri E. Small-scale thermoelastic damping in micro-beams utilizing the modified couple stress theory and the dual-phase-lag heat conduction model. J Therm Stress. 2019;42(7):801–814.
   Web of Science ®Google Scholar
• Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. J Mech Phys Solids. 1967;15(5):299–309.
   Web of Science ®Google Scholar
• Kumar H, Mukhopadhyay S. Thermoelastic damping analysis for size-dependent microplate resonators utilizing the modified couple stress theory and the three-phase-lag heat conduction model. Int J Heat Mass Transfer. 2020;148:118997.
   Web of Science ®Google Scholar
• Abbas IA, Hobiny AD. Analytical solution of thermoelastic damping in a nanoscale beam using the fractional order theory of thermoelasticity. Int J Struct Stab Dyn. 2016;16(9):1550064.
   Web of Science ®Google Scholar
• Wang J-L, Li H-F. Surpassing the fractional derivative: concept of the memory-dependent derivative. Comput Math Appl. 2011;62(3):1562–1567.
   Web of Science ®Google Scholar
• Yu Y-J, Hu W, Tian X-G. A novel generalized thermoelasticity model based on memory-dependent derivative. Int J Eng Sci. 2014;81:123–134.
   Web of Science ®Google Scholar
• Zhang P, He T. A generalized thermoelastic problem with nonlocal effect and memory-dependent derivative when subjected to a moving heat source. Waves Random Complex Media. 2018;30(1):142–156.
   Web of Science ®Google Scholar
• Sur A, Santra S, Kanoria M. Memory response on thermal wave propagation in an elastic solid with voids. Mech. Based Des. Struct. Mach. 2020; 48(3): 326–348.
   Web of Science ®Google Scholar
• Othman MIA, Sur A. Transient response in an elasto-thermo-diffusive medium in the context of memory-dependent heat transfer. Waves Random Complex Media. 2020. in press, doi:10.1080/17455030.2020.1737758.
   Google Scholar
• Love AEH. A treatise on the mathematical theory of elasticity. Cambridge, UK: Cambridge University Press; 1927.
   Google Scholar
• Li X-F, Hu Z-L. Generalization of plane stress and plane strain states to elastic plates of finite thickness. J Elast. 2020;140(2):243–256.
   Web of Science ®Google Scholar
• Wong S, Fox C, McWilliam S. Thermoelastic damping of the in-plane vibration of thin silicon rings. J Sound Vib. 2006;293(1–2):266–285.
   Web of Science ®Google Scholar
• Nowacki W. Thermoelasticity. Amsterdam, Netherlands: Elsevier; 2013.
   Google Scholar
• Rao SS. Vibration of continuous systems. New York: John Wiley & Sons; 2007.
   Google Scholar
• Tzou DY. Macro-to microscale heat transfer: the lagging behavior. West Sussex, UK: John Wiley and Sons; 2014.
   Google Scholar