Abstract
Purpose
The purpose of this paper is to study detection, microstretch function, temperature distribution function and thermoelastic damping analysis due to thermal variations and stretch forces in homogeneous, isotropic microstretch, generalized thermoelastic thin circular plate.
Method
This theory is based on the Kirchho-Love plate theory assumptions. The governing equations for the transverse vibrations of microstretch thermoelastic thin circular plate have been derived. The analytical expressions for detection, microstretch function, temperature distribution function and thermoelastic damping have been numerically analyzed for clamped and simply supported boundary conditions in case of both non-Fourier and Fourier microstretch thermoelastic circular plate with the help of MATLAB programming software.
Results
Finally the analytical development for thermoelastic damping have been illustrated numerically for Silicon-like material. The computer simulated results have been presented graphically under different boundary conditions.
Conclusion
It leads to the conclusion that thermal relaxation time and microstretch parameters contribute to an increase in the magnitude of the critical value of damping.
Similar content being viewed by others
References
Berry BS (1955) Precise investigation of the theory of damping by transverse thermal currents. J Appl Phys 26:1221–1224
Biswas D, Ray MC (2013) Active constrained layer damping of geometrically nonlinear vibration of rotating composite beams using 1–3 piezoelectric composite. Int J Mech Mater Des 9:83–104
Chandrashekhara K (2001) Theory Pates. Universities Press, India, Orient Blackswan
Dhaliwal RS, Singh A (1980) Dynamic coupled thermoelasticity. Hindustan Publication Corporation, New Delhi, India
Eringen AC (1966) Linear theory of micropolar elasticity. J Math Mech 909–923
Eringen AC (1971) Micropolar elastic solids with stretch. Ari Kitabevi Matbassi 24:1–18
Eringen AC (1990) Theory of thermo- microstretch elastic solids. Int J Eng Sci 28:1291–1301
Eringen AC (1999) Microcontinuum field theories I: Foundation and Solids. Springer, New York
Grover D (2013) Transverse vibrations in micro-scale viscothermoelastic beam resonators. Arch Appl Mech 83(2):303–314
Grover D (2015) Damping in thin circular viscothermoelastic plate resonators. Can J Phys 93(12):1597–1605
Grover D, Seth RK (2017) Viscothermoelastic micro-scale beam resonators based on dual-phase lagging model. Microsyst Technol. https://doi.org/10.1007/s00542-017-3515-5
Grover D, Seth RK (2018) Generalized viscothermoelasticity theory of dual-phase-lagging model for damping analysis in circular micro-plate resonators. Mech Time Depend Mater 23(1).https://doi.org/10.1007/s11043-018-9388-x
Kumar RS, Ray MC (2012) Active constrained layer damping of smart laminated composite sandwich plates using 1–3 piezoelectric composites. Int J Mech Mater Des 8:197–218
Leissa AW (1969) Vibration of Plates. Scientific and Technical Information Division (National Aeronautics and Space Administration), Washington
Lifshitz R, Roukes ML (2000) Thermoelastic damping in micro and nanomechanical systems. Phys. Rev. B 61:5600–5609
Lord HW, Shulman Y (1967) The generalized dynamical theory of thermoelasticity. J Mech Phys Solids 15:299–309
Nayfeh AH, Younis MI (2004) Modeling and simulations of thermoelastic damping in microplates. J Micromech Microeng 14:1711–1717
Alghamdi NA (2019) Vibration of circular micro-ceramic (Si 3 N4) plate resonators in the context of the generalized viscothermoelastic dual-phase-lagging theory. Adv Mech Eng 11(11):1. https://doi.org/10.1177/1687814019889480
Partap G, Chugh N (2017a) Deflection analysis of micro-scale microstretch thermoelastic beam resonators under harmonic loading. Appl Math Model 46:16–27
Partap G, Chugh N (2017b) Thermoelastic damping in microstretch thermoelastic rectangular plate. Microsyst Technol 23:5875–5886
Partap G, Chugh N (2017c) Study of deflection and damping in micro-beam resonator based on micro-stretch thermoelastic theory. Mech Adv Mater Struct. https://doi.org/10.1080/15376494.2017.1365988
Rao SS (2007) Vibration of continuous systems. Wiley, New Jersey, USA
Rashidifar MA, Rashidifar AA (2015) Vibrations Analysis of circulare plate with piezoelectric actuator using thin plate theory and bessel function. Am J Eng Technol Soc 2(6):140–156
Reddy JN (1999) Theory and analysis of elastic plates. Taylor and Francis, Philadelphia, PA
Sharma JN, Grover D (2012) Thermoelastic vibration analysis of Mems/ Nems plate resonators with void. Acta Mech 223:167–187
Sun YX, Tohmyoh H (2009) Thermoelastic damping of the axisymmetric vibration of circular plate resonators. J Sound Vib 319:392–405
Sun Y, Saka M (2010) Thermoelastic damping in micro-scale circular plate resonators. J Sound Vib 329:328–337
Ventsel E, Krauthammer T (2001) Thin plates and shells: theory, analysis, and applications. Marcel Dekker Inc., New York
Watson GN (1922) A Treatise on the theory of Bessel functions. Cambridge University Press, UK
Wong SJ, Fox CHJ, McWilliam S (2006) Thermoelastic damping of the in-plane vibration of thin silicon rings. J Sound Vib 293:266–285
Zener C (1937) Internal friction in solids I, Theory of internal friction in reeds. Phys Rev 52:230–235
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chugh, N., Partap, G. Study of Thermoelastic Damping in Microstretch Thermoelastic Thin Circular Plate. J. Vib. Eng. Technol. 9, 105–114 (2021). https://doi.org/10.1007/s42417-020-00213-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42417-020-00213-6