Axisymmetric deformation of thick circular plate under Moore-Gibson-Thompson photothermoelastic model

The deformation in photothermoelastic thick circular plate under Moore-Gibson-Thompson thermoelasticity involving fractional order time derivative is explored. The fractional order parameters reclassify semiconductor materials in terms of photoelastic thermal conductivity. The considered equations are non-dimensionalised and further simplified with the use of potential functions. The significance of the method of potential function is that it decoupled the governing equations to determine the unknowns of photothermoelastic problems. Integral transform involving Laplace and Hankel transform reduced the governing equations into ordinary differential equation. The arbitrary constants in the solution are determined by considering the loading environment on the surface. Three different categories of the sources are considered to explore the application as (i) normal force (ii) ramp type thermal source (iii) carrier density source. In the new domain, the closed form expressions of physical quantities like displacement, normal stress, temperature field and carrier density distribution are derived. Numerical results are computed and presented in the form of Fig.s to know the impact of various models: (i) Sherief, El-Sayed and El-Latief (MGTS)(2010), (ii) Youssuf (MGTY)(2010), (iii) Ezzat (MGTEZ)(2010), (iv)Moore-Gibson-Thomson thermoelastic (MGTE)(2019), (v) Coupled thermoelastic (CTE)(1983), (vi) Lord and Shulman's (LS)(1967), (vii) Green and Naghdi type-II(GN-II)(1993) and (viii) Green and Naghdi type-III(GN-III)(1992) on physical field quantities w.r.t radial distance (photothermomechanical model with a hyperbolic partial differential equation for variations of the displacement, temperature and carrier density field.). Also, the response of fractional order photothermoelastic theories under MGTE model with different values of time is depicted in the form of Fig.s. The work presented in this model can be applied to thermoelastic material with nanostructures and plasmonic structures. The results obtained are helpful in designing the semiconductor materials through the course of coupled thermoelastic, plasma waves, also find application in the material and engineering sciences.