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Thermoelastic damping in a thin circular transversely isotropic Kirchhoff–Love plate due to GN theory of type III

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Abstract

This research deals with the study of thermoelastic damping in transversely isotropic thin circular Kirchhoff–Love plate. Mathematical model is formed for time-harmonic displacement and temperature fields due to the GN theory of thermoelasticity of type III. The model is solved to obtain the expressions for thermoelastic damping, displacement, and temperature fields for circumferential surface wave modes for simply supported and clamped plate resonators. The numerical results for both the simply supported and clamped boundary conditions for an axisymmetric circular plate are illustrated. It is observed that the damping of vibrations is considerably influenced by surface wave modes. The thickness of the plate also has major effects on the vibrations of resonators. The computer-simulated results to illustrate the effect of circumferential surface wave modes on thermoelastic damping for the GN III theory of thermoelasticity have been depicted graphically.

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Abbreviations

\(\omega\) :

Frequency

\(\delta_{ij}\) :

Kronecker delta

\(T\) :

Absolute temperature

\(e_{ij}\) :

Strain tensors

\(t_{ij}\) :

Stress tensors

\(\rho\) :

Medium density

\(C_{E}\) :

Specific heat

\(\beta_{ij}\) :

Thermal elastic coupling tensor

\(K_{ij}\) :

Thermal conductivity

\(c_{ijkl}\) :

Elastic parameters

\(\alpha_{ij}\) :

Linear thermal expansion coefficient

\({\varvec{u}}\) :

Displacement vector

\(T_{0}\) :

Reference temperature

\(K_{ij}^{*}\) :

Materialistic constant

\(u_{i}\) :

Components of displacement

\(J_{m}\) :

Bessel function of the first kind of order m

\(Y_{m}\) :

Bessel function of second kind of order m

\(I_{m}\) :

Hyperbolic or modified Bessel function of order m of the first kind

\(K_{m}\) :

Hyperbolic or modified Bessel function of order m of the second kind

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Authors and Affiliations

  1. Department of Mathematics, Government College for Girls, Palwal, Kurukshetra, India

    Iqbal Kaur

  2. Kurukshetra University, Kurukshetra, Haryana, India

    Kulvinder Singh

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  1. Iqbal Kaur
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Kaur, I., Singh, K. Thermoelastic damping in a thin circular transversely isotropic Kirchhoff–Love plate due to GN theory of type III. Arch Appl Mech 91, 2143–2157 (2021). https://doi.org/10.1007/s00419-020-01874-1

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