ANALYTICAL SOLUTION OF A PYROELECTRIC HOLLOW CYLINDER FOR PIEZOTHERMOELASTIC AXISYMMETRIC DYNAMIC PROBLEMS

By virtue of the separation of variables technique, the piezothermoelastic axisymmetric dynamic problem of a pyroelectric hollow cylinder is transformed to a second kind of Volterra integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a pyroelectric hollow cylinder with an arbitrary thickness subjected to arbitrary thermal loads. Numerical results are presented.     

TRANSIENT THERMOELASTIC SOLUTION OF A MULTILAYERED ORTHOTROPIC HOLLOW CYLINDER FOR AXISYMMETRIC PROBLEMS

The thermoelastic dynamic solution of a multilayered orthotropic hollow cylinder in the state of axisymmetric plane strain is obtained. By the method of superposition, the displacement is divided into two parts: one is quasi static and the other is dynamic. The quasi-static solution is derived by the state-space method, and the dynamic solution is obtained by the separation-of-variables method coupled with the initial parameter method as well as the orthogonal expansion technique. The present method is suitable for a multilayered orthotropic hollow cylinder consisting of arbitrary layers and subjected to arbitrary axisymmetric thermal loads. Numerical results are finally presented and discussed.     

Dynamic Thermoelastic Behavior of a Double-layered Hollow Cylinder with an FGM Layer

In this article, dynamic thermoelastic behavior of a double-layered cylinder with an FGM layer under mechanical and thermal loadings are investigated. The double-layered hollow cylinder is constructed by an FGM layer and a homogenous layer. Utilizing the Finite difference method and Newmark method, the governing equation of the double-layered hollow cylinder under both dynamic mechanical and thermal loads is solved. The accuracy of the approach is validated by comparing the results with the existing analytical ones. Numerical results show that volume exponent of the FGM layer, the thickness ratio of two layers and temperature change have significant effect on the dynamic behaviors of the double-layered hollow cylinder.     

Thermoviscoelastic Dynamic Behavior of a Double-Layered Hollow Cylinder Under Thermal Shocking

In this article, thermoviscoelastic dynamic behavior of a double-layered cylinder with a thermal barrier coating under radially symmetric mechanic and thermal loadings is investigated. The double-layered hollow cylinder is constructed of a viscoelastic layer and a homogenous layer, and the cylinder is subjected to thermal shocking. The material parameters of the cylinder are assumed to be temperature-dependent. The governing equation of the motion of the double-layered hollow cylinder under both dynamic mechanical and thermal loads is obtained based on the plane-stain theory, meanwhile, the transient heat transfer problems are solved by the finite difference method (FDM), Newmark method (NM), and iterative method. Numerical results show that mechanical load, boundary conditions, temperature field and whether considering the viscoelasticity of the inner layer each have a great influence on the dynamic behavior of the double-layered hollow cylinder.     

Thermoelastic analysis of a cylindrical vessel of functionally graded materials

This paper presents a novel method for analyzing steady thermal stresses in a functionally graded hollow cylinder. The thermal and thermoelastic parameters are assumed to arbitrarily vary along the radial direction of the hollow cylinder. The boundary value problem associated with a thermoelastic problem is converted to a Fredholm integral equation. By numerically solving the resulting equation, the distribution of the thermal stresses and radial displacement is obtained. The numerical results obtained are presented graphically and the influence of the gradient variation of the material properties on thermal stresses is investigated. It is found that appropriate gradient can make the distribution of thermal stresses more gentle in the whole structure.     

MAGNETOTHERMODYNAMIC STRESS AND PERTURBATION OF MAGNETIC FIELD VECTOR IN A HOLLOW CYLINDER

An analytical method is presented to investigate magnetothermoelastic waves and perturbation of the magnetic field vector produced by thermal shock in a hollow conducting cylinder. By means of finite integral transforms the exact expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in a hollow cylinder were obtained. From sample numerical calculations the dynamic effect on both magnetothermostress and perturbation of the axial magnetic field vector is revealed and is discussed.     

Magneto-Thermo-Elastic Stresses Induced by a Transient Magnetic Field in a Conducting Hollow Circular Cylinder

We investigate the dynamic and quasi-static behavior of magneto-thermo-elastic stresses induced by a transient magnetic field in a conducting hollow circular cylinder. A transient magnetic field defined by an arbitrary function of time acts on the outer surface of the hollow cylinder and parallel to it. The fundamental equations of plane axisymmetrical electromagnetic, temperature and elastic fields are formulated, and solutions for the magnetic field, eddy current, temperature change and dynamic and quasi-static solutions for stresses and deformations are analytically derived in terms of the arbitrary function. The stress solutions are determined to be sums of a thermal stress component caused by eddy current loss and a magnetic stress component caused by the Lorentz force. The case of a magnetic field defined by a smoothed ramp function with a sine-function profile is examined in particular, and the dynamic and quasi-static behavior of the stresses and deformations are numerically calculated.     

DYNAMIC THERMAL STRESS IN A TRANSVERSELY ISOTROPIC HOLLOW SPHERE

A closed-form solution for the histories and distribution of dynamic themoelastic stress in a transversely isotropic hollow sphere is obtained. The field equation for a spherically symmetric transversely isotropic problem subjected to rapid arbitrary heating shock is derived and solved. Based on the results in this article, some phenomena in a transversely isotropic hollow sphere under thermal shock are shown.     

Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective–radiative surface cooling

This article investigates entropy generation in an asymmetrically cooled hollow cylinder with temperature dependent thermal conductivity and internal heat generation. The inside surface of the cylinder is cooled by convection on its inside surface while the outside surface experiences simultaneous convective–radiative cooling. The thermal conductivity of the cylinder as well as the internal heat generation within the cylinder are linear functions of temperature, introducing two nonlinearities in the one-dimensional steady state heat conduction equation. A third nonlinearity arises due to radiative heat loss from the outside surface of the cylinder. The nonlinear system is solved analytically using the differential transformation method (DTM) to obtain the temperature distribution which is then used to compute local and total entropy generation rates in the cylinder. The accuracy of DTM is verified by comparing its predictions with the analytical solution for the case of constant thermal conductivity and constant internal heat generation. The local and total entropy generations depend on six dimensionless parameters: heat generation parameter Q, thermal conductivity parameter β, conduction–convection parameters Nc₁ and Nc₂, conduction–radiation parameter Nr, convection sink temperature δ and radiation sink temperature η.     

UNSTEADY THERMAL STRESS ANALYSIS IN AXISYMMETRIC PROBLEMS BY MEANS OF BOUNDARY ELEMENT METHOD

The boundary integral formulation for unsteady thermal stresses in axisymmetric quasi-static problems is proposed. It is shown that axisymmetric unsteady thermal stress problems can be easily solved without the volume integral by means of the thermoelastic displacement potential and boundary element method. It is also shown that the time integral can be easily carried out analytically. In order to investigate the accuracy of rhis method, unsteady thermal stress distributions for a hollow circular cylinder and a torus are obtained.     

Thermo-fluid dynamics of Loop Heat Pipe operation

The paper presents a thermo-fluid dynamic model for the transient operations of a Loop Heat Pipe. The Fourier heat conduction equation in a hollow cylinder is solved to determine the temperature distribution of the compensation chamber and the cavity. A one-dimensional transient model is also derived for the vapor temperature in the condenser section of the Loop Heat Pipe. The thermo-fluid dynamic characteristic of a Stainless Steel/Ammonia Loop Heat Pipe is analyzed.     

A Unified Formulation for the Analysis of Temperature Field in a Thick Hollow Cylinder Made of Functionally Graded Materials With Various Grading Patterns

In this article, a unified formulation is presented to analyze the heat conduction and temperature field in a functionally graded thick hollow cylinder. To solve the heat transfer equation in a functionally graded thick hollow cylinder, an analytical method is presented using a nonlinear volume fraction law with variable exponent for mechanical properties. The new unified formulation is obtained based on various thermal boundary conditions such as heat convection at bounding surfaces and constant temperature of bounding surfaces. The functionally graded thick hollow cylinder is considered in axisymmetry condition and infinite length. The temperature field is discussed for various boundary conditions and different grading patterns in functionally graded materials. The presented results and data are verified with published literature.     

Axisymmetric thermoelastic analysis in a finite hollow cylinder due to nonuniform thermal shock

An exact solution is obtained for two-dimensional elastodynamic analysis of finite hollow cylinder excited by nonuniform thermal shock. The cylinder is simply-supported at the two ends and is traction-free at the internal and external cylindrical surfaces. Based on the uncoupled linear thermoelastic theory, the solution is developed by employing the expansion of trigonometric series method and the separation of variables technique. The obtained solution contains two infinite series. One is trigonometric function and the other is Bessel function. The coefficients in the series solution are determined by the orthogonal properties of the functions. Numerical experiments are presented for describing the thermal dynamic behaviors of finite hollow cylinder.     

Analysis of residual stresses in a long hollow cylinder

This paper presents an analytical method for solving the axisymmetric stress problem for a long hollow cylinder subjected to locally-distributed residual (incompatible) strains. This method is based on direct integration of the equilibrium and compatibility equations, which thereby have been reduced to the set of two governing equations for two key functions with corresponding boundary and integral conditions. The governing equations were solved by making use of the Fourier integral transformation. Application of the method is illustrated with an analysis of the welding residual stresses in a butt-welded thick-walled pipe.     

Analysis of aerodynamic noise generated from inclined circular cylinder

IntroductionThe public attention to environment' has beenincreased in these days, and noise reduction of ventilationfan is extremely needed more than ever. We must reducethe generated noise and control the resources of thediscordant one. Recently, aerodynndc noise problems,e.g. wind-pass sound from high-speed mobiles, noisefrom cooling fan, are increased rapidly. Manyexperimental studies have been reported tO contfol thegenerated noise, and numerical prediction of aerodyntricsound (CAA; Comp…     

Circumferentially Cracked Bimaterial Hollow Cylinder Under Mechanical and Transient Thermal Loading

The analytical solution for the problem of a circumferential inner surface crack in an elastic, infinitely long composite hollow cylinder, made of two concentric perfectly bonded transversely isotropic cylinders is considered. Uniform axial loading and thermal loading in the form of a sudden cooling on the inner boundary are considered. Out of 10 material parameters involved, two bimaterial parameters and three material parameters for each layer upon which the stress intensity factor depends under uniform loading, are identified. The problem is reduced to a singular integral equation that is solved numerically. Stress intensity factors are presented for various values of material and geometric parameters.     

Quasi-Static Thermal Stresses Due to Heat Generation in a Thin Hollow Circular Disk

The present paper deals with the determination of displacement and thermal stresses in a thin hollow circular disk defined by a ≤ r ≤ b due to internal heat generation within it. Time dependent heat flux Q(t) is applied at the outer circular boundary (r = b), whereas inner circular boundary (r = a) is at zero heat flux. Also, initially the circular disk is at arbitrary temperature F(r). The governing heat conduction equation has been solved by the method of integral transform technique. The radial stress function σ_rr is zero at inner and outer circular boundaries (r = a and r = b). The results are obtained in a series form in terms of Bessel's functions. The results for displacement and stresses have been computed numerically and illustrated graphically.     

An integral equation approach to diffusion

A method of solution of transient diffusion, e.g. heat conduction, problems in homogeneous and isotropic media with internal sources and arbitrary (including nonlinear) boundary conditions and initial conditions is proposed. The method is based on the reduction of the problem to one only involving surface values of temperature and/or heat flux in the form of an integral equation through the introduction of fundamental solutions and the use of Green's theorem. The integral equation is solved numerically for a specific example.     

Axisymmetric Mechanical and Thermal Stresses in Thick Long FGM Cylinders

The analysis of axisymmetric mechanical and thermal stresses for a long hollow cylinder made of functionally graded material, as functions of radial and longitudinal directions, is developed. The material properties are graded along the radial direction according to power functions of radial direction. The temperature and Navier equations are solved analytically, using the generalized Bessel function and complex form of Fourier integral. A direct method of solution of Navier equations is presented, rather than potential functions method.     

Thermal fracture of cracked cylinders associated with nonclassical heat conduction: The effect of material property

The thermoelastic problem of a transversely isotropic hollow cylinder containing a circumferential crack is investigated in the present article based on the non-Fourier heat conduction theory. The temperature and stress fields are obtained by solving the coupled partial differential equations in the Laplace domain, and corresponding thermal axial stress with minus sign is then applied to the crack surface to form a mode I crack problem. Three different kinds of crack are considered, and the singular integral equation method is adopted to solve the fracture problem. Finally, with the definition of stress intensity factor, the effect of material properties, coupling parameter, and crack geometry on the hyperbolic thermal fracture responses of a transversely isotropic hollow cylinder excited by a thermal loading is visualized.