Generalized Thermoelastic Functionally Graded on a Thin Slim Strip Non-Gaussian Laser Beam

Abstract

<jats:p>The present study utilizes the generalized thermoelasticity theory, with one thermal relaxation time (TR), to examine the thermoelastic problem of a functionally graded thin slim strip (TSS). The authors heated the plane surface bounding using a non-Gaussian laser beam with a pulse length of 2 ps. The material characteristics varied continually based on exponential functions. Moreover, the equations governing the generalized thermoelasticity for a functionally graded material (FGM) are recognized. The problem’s ideal solution was primarily obtained in the Laplace transform (LT) space. The LTs were converted numerically because of the considerable importance of the response in the transient state. For a hypothetical substance, the numerical procedures calculating the displacement, stress, temperature and strain were given. The analogous problem solution to an isotropic homogeneous material was provided by defining the parameter of non-homogeneity adequately. The obtained results were displayed using graphs to illustrate the extent to which non-homogeneity affected displacement, stress, temperature and strain. A comparison was been made between the present study and those previously obtained by others, when the new parameters vanish to show the impact of the non-homogeneity, TSS and laser parameters on the phenomenon. The results obtained indicate a significant strong impact of FGM, TSS and laser parameters.</jats:p>

Analysis of the magneto-thermoelastic vibrations of rotating Euler–Bernoulli nanobeams using the nonlocal elasticity model

“…The nonlocal parameter nondependence on temperature has been observed in many investigations and previous studies Figure 6 The effect of nonlocality (ξ ) on the variation of the deflection w Figure 7 The effect of nonlocality (ξ ) on the variation of the temperature θ Figure 8 The effect of nonlocality (ξ ) on the variation of the displacement u [55]. Other aspects for media with microstructure can be found in [56][57][58][59][60][61]. It can be concluded further that the steady state of the mechanical waves within the beam depends on specific values of the nonlocal index ξ .…”

Thermodynamic modeling of a laser pulse heating in a rotating microelongated nonlocal thermoelastic solid due to G‐N theory

“…Where, 𝐾 n (n = 1, 2, 3, 4) are the roots of the characteristic equation of Equations ( 33)- (36). The characteristic equation of Equation ( 33) -for example-can be written as:…”

“…Othman et al [33][34][35] investigated the effect of the laser pulse in various problems of thermoelastic medium. Abo-Dahab et al [36] studied the generalized thermoelastic functionally graded on a thin slim strip under a laser beam. Hilal [37] discussed the reflection waves phenomena in a rotating magneto-micropolar thermoelastic medium with temperature dependency and gravity using Green-Naghdi theory.…”

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

“…Zhang et al [10] illustrated the outline of the prevailing literature on free vibration buckling and stability analysis of FGM. Abo-Dahab et al [11] discussed the FG thin slim strip with one thermal relaxation time in generalized thermoelasticity theory. The effects of vibrations on concrete structures can be reduced by special construction and material conditions [12,13].…”