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Multi-phase-lag model on forced vibrations of nonlocal thermoelastic diffusive cylinder with time-dependent heat flux

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Abstract

The nonlocal thermoelastic cylinder with diffusion has been depicted for thermal shock as forced vibrations to be an application for the present model. The main purpose of this manuscript is to investigate the forced vibrations of thermo-diffusive nonlocal elastic cylinder with time-dependent heat flux in the preview of three-phase-lag thermoelasticity theory. The internal and external boundary faces of the cylinder are kept free from stresses and concentration of diffusion. A heat flux with time-dependent heat source has been supplied on the internal face of the cylinder along radial direction and external face may be assumed isothermal. Simulations and computations have been employed to analytical outcomes by using MATLAB computer-based tools. The data generated from computations has been shown graphically which represent the different phase lag effects in temperature, stresses, dilatation, displacement and chemical potential. The analytical results have been verified by reduction/deduction and authenticated with earlier published literature. The study of the vibrations of nonlocal thermoelastic cylinder has been applied mostly in navigation, cosmetics industry, defence and also for the development of practical situations in optics, geo-magnetics, acoustics, cosmetics, etc.

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Data and code availability

The data and material that support the findings of this study are available with the corresponding author and may be produced on request.

Abbreviations

e :

Uniform cubical dilatation

T(r, t):

Temperature change

\(e_{ij} ;(i,j = r,\theta ,z)\) :

Strain components

u(r, t):

Displacement

C e :

Specific heat at constant strain

β 1, β 2 :

Material constants

λ, μ :

Lame’s constants

ω :

Circular frequency of vibrations,

α T :

Coefficient of linear thermal expansion

ω * :

Thermoelastic characteristic frequency

α c :

Coefficient of linear diffusion expansion

Ω* :

Characteristic frequency of vibrations

\(\zeta^{2} = (e_{0} a_{0} )^{2}\) :

Nonlocal elastic parameter, where e0 is material constant a0 is internal characteristic length

a :

Measure of thermoelastic diffusion

\(\sigma_{{{\text{rr}}}} ,\sigma_{\theta \theta }\) :

Stress components

c 1, c 2 :

Longitudinal, shear wave velocities

α t :

Linear thermal expansion coefficient

\(\overline{D},D^{*}\) :

Diffusion constants

t T, t q, t V :

Phase-lag thermal relaxation time parameters of the temperature gradient, heat flux, thermal displacement gradient, respectively.

P :

Chemical potential

b :

Measure of diffusive effect

R I and \(R_{{\text{O}}} = \eta R_{{\text{I}}}\) :

Inner radius and outer radius

K :

Thermal conductivity

ρ :

Mass density

\(\overline{t}_{{\text{T}}} ,\overline{t}_{{\text{q}}} ,\overline{t}_{{\text{V}}}\) :

Diffusion relaxation time parameters under TPL model of generalized thermoelasticity, respectively

ε T :

Thermoelastic coupling parameter

\(\eta = R_{{\text{O}}} /R_{{\text{I}}}\) :

Ratio of outer radius to inner radius

K * :

Additional characteristic material constant of TPL theory

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Authors and Affiliations

  1. Department of Mathematics, Maharaja Agrasen University, Baddi, Himachal Pradesh, 174103, India

    Dinesh Kumar Sharma

  2. School of Engineering and Technology, Chitkara University, Himachal Pradesh, 174103, India

    Sita Ram Sharma

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  1. Dinesh Kumar Sharma
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Sharma, D.K., Sharma, S.R. Multi-phase-lag model on forced vibrations of nonlocal thermoelastic diffusive cylinder with time-dependent heat flux. Int. J. Dynam. Control 11, 1494–1505 (2023). https://doi.org/10.1007/s40435-022-01081-6

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  • DOI: https://doi.org/10.1007/s40435-022-01081-6

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