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Thermoelastic damping analysis in microbeam resonators based on Moore–Gibson–Thompson generalized thermoelasticity theory

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Abstract

Microbeam resonators are widely used due to their scientific and engineering applications. The accurate prediction of thermoelastic damping (TED) is necessary to evaluate the performance of resonators at micro- and nanoscales with less energy dissipation. This article aims to present an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore–Gibson–Thompson (MGT) generalized thermoelasticity theory. The finite Fourier sine transform and Laplace transform methods are used to solve the coupled thermoelastic equations. The analytical solutions are obtained for deflection and thermal moment of beams. The vibration responses of deflection and thermal moment are established in microbeams with simply supported and isothermal boundary conditions. The responses of deflection and thermal moment in beams are analyzed by comparing the results obtained under the MGT model with the corresponding results under the Lord–Shulman (LS) and Green–Naghdi (GN-III) models. The obtained results show that the amplitudes of deflection and thermal moment are attenuated, and the vibration frequency is increased due to the effect of thermoelastic coupling. It has been observed that the amplitudes of deflection under these three models are approximately the same, while the amplitude of thermal moment under the MGT model is higher than under the GN-III model and agrees with the LS model. It has been further noticed that TED depends on the size of the beams when the thermoelastic coupling effect is considered.

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Acknowledgements

One of the authors (Harendra Kumar) acknowledges the full financial support from the Council of Scientific and Industrial Research (CSIR), India, to carry this work with file no.: 09/1217(0014)/2017-EMR-I.

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  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Harendra Kumar & Santwana Mukhopadhyay

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  1. Harendra Kumar
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  2. Santwana Mukhopadhyay
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Correspondence to Harendra Kumar.

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Kumar, H., Mukhopadhyay, S. Thermoelastic damping analysis in microbeam resonators based on Moore–Gibson–Thompson generalized thermoelasticity theory. Acta Mech 231, 3003–3015 (2020). https://doi.org/10.1007/s00707-020-02688-6

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  • DOI: https://doi.org/10.1007/s00707-020-02688-6

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