Magnetothermoelastic transient response of multilayered conical shells

This paper considers problems of the three-dimensional axisymmetric quasi-static coupled magnetothermoelasticity for the laminated circular conical shells subjected to magnetic and temperature fields. The temperature and pressure relation are assumed for the inner boundary. The formulation begins with the basic equations of magnetothermoelasticity in curvilinear circular conical coordinates. Laplace transform and finite difference methods are used to analyze problems. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal deformation distributions in a transient and steady state. Moreover, the computational procedures established in this thesis, can solve the generalized magnetothermoelasticity problem for multilayered conical shells with nonhomogeneous materials.     

Thermoelastic transient response of multilayered conical shells subjected to vapor field

The problems of the three-dimensional axisymmetric quasi-static coupled thermoelastic for the laminated circular conical shells subjected to vapor field. The water vapor temperature and pressure relation assumed for the inner boundary. The water vapor temperature and pressure data were obtained from a thermodynamic steam table. The formulation begins with the basic equations of thermoelasticity in curvilinear circular conical coordinates. Laplace transform and finite difference methods are used to analyze problems. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal deformation distributions in a transient and steady state. Moreover, the computational procedures established in this thesis, can solve the generalized thermoelasticity problem for multilayered conical shells with nonhomogeneous materials.     

Magnetothermoelastic analysis of multilayered conical shells subjected to magnetic and vapor fields

This paper considers problems of the three-dimensional axisymmetric quasi-static coupled magnetothermoelasticity for the laminated circular conical shells subjected to magnetic and vapor fields. The water vapor temperature and pressure relation are assumed for the inner boundary. The water vapor temperature and pressure data were obtained from a thermodynamic steam table. The formulation begins with the basic equations of magnetothermoelasticity in curvilinear circular conical coordinates. Laplace transform and finite difference methods are used to analyze problems. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal deformation distributions in a transient and steady state. Moreover, the computational procedures established in this thesis, can solve the generalized magnetothermoelasticity problem for multilayered conical shells with nonhomogeneous materials.     

Generalized coupled transient thermoelastic problem of multilayered hollow cylinder with hybrid boundary conditions

The problems of the one-dimensional axisymmetric quasi-static coupled thermoelastic for multilayered hollow cylinder with clamped surface subjected to time-dependent boundary conditions. The formulation begins with the basic equations of thermoelasticity in polar coordinates. The results are obtained employing a method based on a hybrid Laplace transformation matrix similarity transformation and finite difference method. It was shown that the solutions are rapidly convergent. Solutions for the temperature, displacement and thermal stress distributions in both transient and steady state are obtained. The present method can obtain stable solutions at a specific time; thus it is a further concluded that the method and the computing process of the coupled transient thermoelastic problems of multilayered hollow cylinder are powerful and efficient.     

Generalized coupled transient response of 3-D multilayered hollow cylinder

This paper deals three-dimensional axisymmetric quasi-static coupled thermoelastic problems. Laplace transform and finite difference methods are used to analyze problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal deformation distributions in a transient and steady state. Moreover, the computational procedures established in this thesis, can solve the generalized thermoelasticity problem for different length hollow cylinder with nonhomogeneous materials.     

Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads

This paper considers the magnetothermoelastic problem of functionally graded material (FGM) hollow structures subjected to mechanical loads. Exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow cylinders and FGM hollow spheres are determined using the infinitesimal theory of magnetothermoelasticity. The material stiffness, thermal expansion coefficient and magnetic permeability are assumed to obey the same simple power-law variation through the structures’ wall thickness. The aim of this research is to understand the effect of composition on magneto- thermoelastic stresses and to design optimum FGM hollow cylinders and hollow spheres.     

Two-dimensional thermal shock problem of generalized thermoelastic multilayered structures considering interfacial conditions

A two-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting nondimensional coupled equations together with the Laplace and Fourier transform techniques are applied to a specific problem of multilayered structures considering thermal resistance subjected to thermal shock and traction-free surface. The solutions in the transformed domain are obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transform. Numerical results are represented graphically to estimate the effects of the thermal resistance and thermal conductivities on the temperature, displacement, and stress distributions.     

Analytical solution of generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads

In this article, a fully analytical solution of the generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads, based on Lord–Shulman model, is presented. The general forms of axisymmetric thermal and mechanical boundary conditions as arbitrary time-dependent heat transfer and traction, respectively, are considered at the inner and outer radii of the disk. The governing equations are solved analytically using the principle of superposition and the Fourier–Bessel transform. The general closed form solutions are presented for temperature and displacement fields. To validate the solutions, the results of this study are compared with the numerical results available in the literature, which show good agreement. For the temperature, displacement and stresses, radial distributions, and time histories are plotted and discussed. The propagation of thermoelastic waves and their reflection from the boundary of the disk are clearly shown. Moreover, effects of relaxation time and angular velocity on temperature, displacement, and stress fields are investigated.     

Transient hygrothermoelastic response in a porous cylinder subjected to ramp-type heat-moisture loading

Abstract

The classical theory of heat conduction (Fourier theory) predicts an infinite speed for thermal disturbance propagation, which is physically unrealistic. By extending the classical Fourier heat conduction and Fick’s diffusion, this article develops hyperbolic diffusion/heat conduction laws with phase lags of heat/moisture flux to simulate coupled heat-moisture diffusion-propagation behavior with the Defour and Soret effects. A porous cylinder subjected to a ramp-type heating and humidifying at the surface is studied. The Laplace transform is used to obtain a closed-form solution of the temperature, moisture, displacements and stresses in the cylinder. Numerical results are calculated via the inversion of the Laplace transform. Obtained results show that the thermal/moisture relaxation time or phase lag plays a significant role in affecting transient hygrothermoelastic field. For a non-vanishing phase lag, non-Fourier and non-Fickian effects exist and hygrothermal waves have finite propagation speeds. The influences of the phase lag of heat/moisture flux and ramp-type time parameter on the transient response of hygrothermoelastic field are presented graphically. A comparison of the numerical results based on the classical model and the present one is made. The non-Fourier heat conduction and non-Fickian diffusion can effectively avoid the shortcomings induced by the classical Fourier and Fick laws.     

Numerical and experimental thermal analysis for a metallic hollow cylinder subjected to step-wise electro-magnetic induction heating

In this study, basic electro-magnetic and heat transfer theories were applied to simulate the electro-magnetic and temperature fields in a steel hollow cylinder subjected to step-wise induction heating from outside. Three different sizes (Pipe A, D_o × D_i × L = 95 mm × 29 mm × 1000 mm, Pipe B, D_o × D_i × L = 110 mm × 39 mm × 1120 mm, Pipe C, D_o × D_i × L = 131 mm × 47 mm × 1450 mm) of the workpieces were numerically and experimentally investigated and compared. The temperatures on the inside and outside surface of the workpiece during the induction heating process were measured by thermocouples and an infrared thermal imaging system, respectively. The applied power input is a steep-wise function (constant high power, 0–8 min, and decrease to it 60%, 8–12 min, and then increase it original high power, 12–20 min). The process of induction heating heats the hollow cylinder from ambient temperature above the Curie point. It is shown that the inside temperature of the hollow cylinder is below the outside temperature initially (0–8 min), and then a constant temperature is held for approximately 4 min and finally the inside temperature is higher than the outside temperature. The numerical results agreed with the experimental data within 15%. The numerical simulation of three different air gaps (5 mm, 15 mm and 25 mm) between the coil and the workpiece were also performed. It is found that the temperature is increased as the air gap is decreased. The average temperatures of the hollow steel for air gap = 5 mm are 10 °C and 15 °C higher those for air gap = 15 mm, 25 mm, respectively.     

Transient stability analysis of a power system with one generator connected to an infinite bus system

This paper presents a novel method to identify the fault that would affect the transient stability of one machine to an infinite bus. Here, the swing equation of each machine is expressed in the form of a closed-loop transfer function in Laplace ss-domain. In the transfer function, the duration of the fault and the changes in maximum electrical power output of the machine during and after the fault are considered. Then, the real value of the dominant root of each machine's characteristic equation is identified on the real axis of the s-plane. In this method, the generator has been considered unstable based on the position of the real value of the dominant root in the left half or very close to the imaginary axis or in the right half of the s-plane. The results obtained by the proposed method are compared with those of the conventional step-by-step method on the basis of different fault clearing times, and good agreements have been demonstrated.     

Nonsymmetric thermomechanical analysis of a functionally graded cylinder subjected to mechanical,thermal, and magnetic loads

Thermoelastic analysis of a functionally graded cylinder under nonsymmetric thermal and mechanical loadings subjected to uniform magnetic field is presented in this article. All material properties are assumed to be variable along the thickness direction based on the power law. Due to nonsymmetric thermal and mechanical loadings and boundary conditions, a two-dimensional displacement field along the radial and circumferential directions is assumed for our analysis. The complex form of Fourier series is used as the method of solution. The nonsymmetric analysis of this problem for Lorentz force leads to radial and circumferential force components. The obtained results of this analysis indicate that the different parameters of material and loading have a considerable effect on the nonsymmetric behavior of cylinder.     

Transient thermal stress analysis of a functionally graded thick hollow cylinder with temperature-dependent material properties

This article deals with the study of temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature and spatial coordinate z. The two-dimensional transient heat conduction equation is solved under convective heat transfer condition with varying point heat source. The influence of inhomogeneity parameters on the thermal and mechanical behavior is examined. Numerical computations are performed for ceramic-metal-based functionally graded material, in which alumina is selected as ceramic and nickel as metal.     

Transient response analysis of a spherical shell embedded in an infinite thermoelastic medium based on a memory-dependent generalized thermoelasticity

In the context of a memory-dependent generalized thermoelasticity, the thermal-induced transient response in an infinite elastic body containing a spherical shell is investigated. A thermal shock is applied on the inner surface of the spherical shell. The infinite body and the spherical shell are assumed to be isotropic but two dissimilar materials. By using an analytical technique based on the Laplace transform along with its numerical inversion, the governing equations of the problem are solved and the non-dimensional physical quantities in the two materials, i.e., temperature, displacement and stress, are obtained and illustrated graphically respectively. In simulation, the accuracy of memory-dependent derivative (MDD) is verified by degrading the present model into L-S model to compare the results obtained from the cases with interfacial thermal resistance and without interfacial thermal resistance. In addition, the effects of the different kernel functions as well as the ratios of the two materials, including the ratios of the density, the thermal-conductivity and the time-delay, on the distributions of the considered variables are obtained and demonstrated graphically respectively.     

Effect of stochastic thermal input on elastic and thermal properties of an infinitely long annular cylinder

Random elastic and thermal properties for an infinitely long solid conducting circular cylinder are investigated under the effect of random thermal input. The problem is considered in the context of a generalized thermoelasticity theory with one relaxation time. The lateral surface of the solid is traction free and subjected to known stochastic temperature, driven by an additive Gaussian white noise. Laplace transform technique is used to obtain the solution in the transformed domain. Statistically, we derive and analyze the mean and variance for temperature, displacement and stress. Numerical inversion of the transformed solution is carried out, represented graphically and discussed.     

Integral transform methods for inverse problem of heat conduction with known boundary of a thin rectangular object and its stresses

The three-dimensional inverse transient thermoelastic problem for a thin rectangular object is considered within the context of the theory of generalized thermoelasticity. The upper surface of the rectangular object occupying the space D: a≤x≤a; b≤y≤b; 0≤z≤h; with the known boundary conditions. Laplace and Finite Marchi-Fasulo transform techniques are used to determine the unknown temperature, temperature distribution, displacement and thermal stresses on upper plane surface of a thin rectangular object. The distributions of the considered physical variables are obtained and represented graphically.     

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

In this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.     

Transient response of a hygrothermoelastic cylinder based on fractional diffusion wave theory

A coupled fractional hygrothermoelasticity theory is formulated within the framework of fractional calculus. Both the classical Fourier’s and Fick’s laws are generalized to anomalous diffusion which is characterized by the time- fractional diffusion-wave equation. Based on the fractional hygrothermoelasticity theory, the transient response of an infinitely long cylinder subjected to hygrothermal loadings at the surface is analyzed. The finite Hankel integral transform method and decoupled technique are used to derive closed-form expressions for temperature, moisture, displacement, and hygrothermal stresses in the solid. The coupling effect of temperature and moisture on elastic fields is discussed. Numerical results of transient response of hygrothermoelastic fields are presented graphically for the cases of subdiffusion, normal diffusion, and superdiffusion, respectively.     

Transient thermal fracture analysis of a penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder

The problem of penny-shaped magnetic and dielectric crack in a magnetoelectroelastic cylinder is investigated under thermal shock load. The problem is reduced to solve three coupled Fredholm integral equations. The field intensity factors are derived. Numerical results of crack opening displacement intensity factors are presented, and the effects of thermal shock time, crack configuration, and magnetoelectrical crack surface conditions on crack propagation and growth are evaluated. Among others, the larger cylinder's radius, the easier to propagate the crack is. For a fixed crack configuration, magnetoelectrical crack surface conditions have different effects on crack propagation as well.