Abstract
In this article, the closed form expressions for the transverse vibrations of a homogenous isotropic, thermally conducting, Kelvin–Voigt type viscothermoelastic thin beam, based on Euler– Bernoulli theory have been derived. The effects of relaxation times, thermomechanical coupling, surface conditions, and beam dimensions on energy dissipation induced by thermoelastic damping in MEMS (micro-electromechanical systems) resonators are investigated for beams under clamped and simply supported conditions. Analytical expressions for deflection, temperature change, frequency shifts, and thermoelastic damping in the beam have been derived. Some numerical results with the help of MATLAB programming software in case of Silicon Nitride have also been presented. The computer-simulated results in respect of damping factor and frequency shift have been presented graphically.
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References
Biot M.A.: Theory of stress-strain relations in an isotropic viscoelasticity and relaxation phenomenon. J. Appl. Phys. 18, 27–34 (1954)
Biot M.A.: Variational principle in irreversible thermodynamics with applications to viscoelasticity. Phys. Rev. 97, 1463–1469 (1955)
Drozdov A.D.: A constitutive model in thermoviscoelasticity. Mech. Res. Comm. 23, 543–548 (1996)
Bera R.K.: Propagation of waves in random rotating infinite magneto-thermo-visco-elastic medium. Comput. Math. Appl. 36, 85–102 (1998)
Ezaat M.A., El-Karmany A.S.: The relaxation effects of the volume properties of viscoelastic material in generalized thermoelasticity. Int. J. Eng. Sci. 41, 2281–2298 (2003)
Carcione J.M., Poletto F., Gei D.: 3-D wave simulation in anelastic media using the Kelvin–Voigt constitutive equation. J. Comput. Phys. 196, 282–297 (2004)
Zener C.: Internal friction in solids I. Theory of internal friction in reeds. Phys. Rev. 52, 230–235 (1937)
Lifshitz R., Roukes M.L.: Thermoelastic damping in micro and nanomechanical systems. Phys. Rev. B 61, 5600–5609 (2000)
Guo F.L., Rogerson G.A.: Thermoelastic coupling effect on a micro-machined beam resonator. Mech. Res. Commun. 30, 513–518 (2003)
Sun Y.X., Fang D.N., Soh A.K.: Thermoelastic damping in micro-beam resonators. Int. J. Solids Struct. 43, 3213–3229 (2006)
Sun Y., Saka M.: Thermoelastic damping in micro-scale circular plate resonators. J. Sound Vib. 329, 328–337 (2010)
Sun Y.X., Tohmyoh H.: Thermoelastic damping of the axisymmetric vibration of circular plate resonators. J. Sound Vib. 319, 392–405 (2009)
Sharma J.N., Grover D.: Thermoelastic vibrations in micro and nano-scale beam resonators with voids. J. Sound Vib. 330, 2964–2977 (2011)
Sharma J.N., Grover D.: Thermoelastic vibration analysis of Mems/Nems plate resonators with voids. Acta Mech. 223, 167–187 (2012)
Grover D., Sharma J.N.: Transverse vibration in piezothermoelastic beam resonators. J. Intell. Mater. Syst. Struct. 23, 77–84 (2012)
Lord H.W., Shulman Y.: The generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)
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Grover, D. Transverse vibrations in micro-scale viscothermoelastic beam resonators. Arch Appl Mech 83, 303–314 (2013). https://doi.org/10.1007/s00419-012-0656-y
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DOI: https://doi.org/10.1007/s00419-012-0656-y