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Impact of temperature-dependent parameters on wave motion in a micropolar thermoelastic plate involving memory-dependent derivatives

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Abstract

This article presents a new model for homogeneous micropolar thermo-elastic plate after the introduction of memory-dependent derivatives into the constitutive relations applicable to the dual-phase-lag (DPL) model. The heat conduction equation for DPL model is derived by incorporating modified Fourier’s law into the heat energy equation. In the assumed model, the material parameters are taken to be temperature-dependent. The two dimensional resulting equations are normalized using non-dimensional quantities and are decomposed by using Helmholtz decomposition theorem. Normal mode analysis technique has been applied to solve the problem. The frequency equations for symmetric and skew-symmetric modes are determined by invoking suitable boundary conditions for the plate under consideration. Aluminium-epoxy material has been chosen to present the numerical solutions of frequency equations using MATLAB software. The variations of specific heat loss and penetration depth with wave number are shown graphically. Some special cases of the proposed model are also discussed.

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Acknowledgements

The first author (Sunil Kumar) is thankful to UGC, New Delhi, India, for providing Junior Research Fellowship (JRF) with reference number: 958/(CSIR-UGC NET DEC.2018). The authors are highly grateful to anonymous referees for providing their valuable comments, which helped to increase the quality of this work.

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Authors and Affiliations

  1. Department of Mathematics, Dr B R Ambedkar National Institute of Technology, Jalandhar, Punjab, 144011, India

    Sunil Kumar & Geeta Partap

  2. Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, 136119, India

    Rajneesh Kumar

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  1. Sunil Kumar
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Correspondence to Sunil Kumar.

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Kumar, S., Partap, G. & Kumar, R. Impact of temperature-dependent parameters on wave motion in a micropolar thermoelastic plate involving memory-dependent derivatives. Acta Mech 235, 429–439 (2024). https://doi.org/10.1007/s00707-023-03737-6

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  • DOI: https://doi.org/10.1007/s00707-023-03737-6

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