Viscoelastic initially stressed microbeam heated by an intense pulse laser via photo-thermoelasticity with two-phase lag

Author(s):  
Ahmed E. Abouelregal ◽  
Kadry Zakaria ◽  
Magdy A. Sirwah ◽  
Hijaz Ahmad ◽  
Ali F. Rashid

This work aims to assess the response of viscoelastic Kelvin–Voigt microscale beams under initial stress. The microbeam is photostimulated by the light emitted by an intense picosecond pulsed laser. The photothermal elasticity model with dual-phase lags, the plasma wave equation and Euler–Bernoulli beam theory are utilized to construct the system equations governing the thermoelastic vibrations of microbeams. Using the Laplace transform technique, the problem is solved analytically and expressions are provided for the distributions of photothermal fields. Taking aluminum as a numerical example, the effect of the pulsed laser duration coefficient, viscoelasticity constants and initial stress on photothermal vibrations has been studied. In addition, a comparison has been made between different models of photo-thermoelasticity to validate the results of the current model. Photo-microdynamic systems might be monolithically integrated on aluminum microbeams using microsurface processing technology as a result of this research.

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sunita Deswal ◽  
Sandeep Singh Sheoran ◽  
Kapil Kumar Kalkal

The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation.


2021 ◽  
Vol 127 (9) ◽  
Author(s):  
Mohamed I. A. Othman ◽  
Sarhan Y. Atwa ◽  
Ebtesam E. M. Eraki ◽  
Mohamed F. Ismail

2007 ◽  
Vol 22 (1) ◽  
pp. 1-9
Author(s):  
Umberto Rizza ◽  
Jonas C. Carvalho ◽  
Davidson M. Moreira ◽  
Marcelo R. Moraes ◽  
Antônio G. Goulart

In this article is carried out a comparison between Lagrangian and Eulerian modelling of the turbulent transport of pollutants within the Planetary Boundary Layer (PBL). The Lagrangian model is based on a three-dimensional form of the Langevin equation for the random velocity. The Eulerian analytical model is based on a discretization of the PBL in N sub-layers; in each of the sub-layers the advection-diffusion equation is solved by the Laplace transform technique. In the Eulerian numerical model the advective terms are solved using the cubic spline method while a Crank-Nicholson scheme is used for the diffusive terms. The models use a turbulence parameterization that considers a spectrum model, which is given by a linear superposition of the buoyancy and mechanical effects. Observed ground-level concentrations measured in a dispersion field experiment are used to evaluate the simulations.


2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 285-299
Author(s):  
Jamel Bouslimi ◽  
Sayed Abo-Dahab ◽  
Khaled Lotfy ◽  
Sayed Abdel-Khalek ◽  
Eied Khalil ◽  
...  

In this paper is investigating the theory of generalized thermoelasticity under two temperature is used to solve boundary value problems of 2-D half-space its bound?ary with different types of heating under gravity effect. The governing equations are solved using new mathematical methods under the context of Lord-Shulman, Green-Naghdi theory of type III (G-N III) and the three-phase-lag model to inves?tigate the surface waves in an isotropic elastic medium subjected to gravity field, magnetic field, and initial stress. The general solution obtained is applied to a spe?cific problem of a half-space and the interaction with each other under the influence of gravity. The physical domain by using the harmonic vibrations is used to obtain the exact expressions for the Waves velocity and attenuation coefficients for Stoneley waves, Love waves, and Rayleigh waves. Comparisons are made with the results between the three theories. Numerical work is also performed for a suitable material with the aim of illustrating the results. The results obtained are calculated numerical?ly and presented graphically with some comparisons in the absence and the presence the influence of gravity, initial stress and magnetic field. It clears that the results ob?tained agree with the physical practical results and agree with the previous results if the gravity, two temperature, and initial stress neglect as special case from this study.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Rashid Ayub ◽  
Shahzad Ahmad ◽  
Muhammad Imran Asjad ◽  
Mushtaq Ahmad

In this article, an unsteady free convection flow of MHD viscous fluid over a vertical rotating plate with Newtonian heating and heat generation is analyzed. The dimensionless governing equations for temperature and velocity fields are solved using the Laplace transform technique. Analytical solutions are obtained for the temperature and components of velocity fields. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are presented graphically.


Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).


2008 ◽  
Vol 75 (1) ◽  
Author(s):  
C. J. Toki

An exact solution of the problem of the unsteady free convection and mass transfer flow near an infinite vertical porous plate, which moves with time-dependent velocity in a viscous and incompressible fluid, is presented here by the Laplace transform technique. All expressions of the new solutions of the present problem were obtained in closed forms with arbitrary Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), and mass Grashof number (Gm). Two applications of physical interest for porous or nonporous plate are discussed. Applying numerical values into the expressions of analytical solution, we was also discussed the vertical air flows—the usual phenomenon at plumes into the atmosphere.


2018 ◽  
Vol 27 (08) ◽  
pp. 1850071
Author(s):  
F. Teimoury Azadbakht ◽  
G. R. Boroun ◽  
B. Rezaei

In this paper, the polarized neutron structure function [Formula: see text] in the [Formula: see text] nucleus is investigated and an analytical solution based on the Laplace transform method for [Formula: see text] is presented. It is shown that the neutron spin structure function can be extracted directly from the polarized nuclear structure function of [Formula: see text]. The nuclear corrections due to the Fermi motion of the nucleons as well as the binding energy considerations are taken into account within the framework of the convolution approach and the polarized structure function of [Formula: see text] nucleus is expressed in terms of the spin structure functions of nucleons and the light-cone momentum distribution of the constituent nucleons. Then, the numerical results for [Formula: see text] are compared with experimental data of the SMC and HERMES collaborations. We found that there is an overall good agreement between the theory and experiments.


2021 ◽  
pp. 2150297
Author(s):  
Ahmed E. Abouelregal ◽  
Hijaz Ahmad ◽  
Taher A. Nofal ◽  
Hanaa Abu-Zinadah

This paper analyzes the thermoelastic dynamic behavior of simply supported viscoelastic nanobeams of fractional derivative type due to a dynamic strength load. The viscoelastic Kelvin–Voigt model with fractional derivative with Bernoulli–Euler beam theory is introduced. The generalized thermoelastic heat conduction model with a two-phase lag is also used. It is assumed that the beam is rotating at a uniform angular velocity and that the thermal conductivity varies linearly depending on the temperature. Due to a variable harmonic heat and retreating time-dependent load, the nanobeam is excited. The Laplace integral transformation technique is used as the solution method. The thermodynamic temperature, deflection function, bending moment, and displacement are numerically calculated. Results of fractional and integer viscoelastic material models are compared. In the studied system, the effect of the nonlocal parameter, viscosity and varying load on the solutions is shown, and the temperature-dependence of the thermal conductivity is analyzed.


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