Finite Hollow Cylinder Research Articles

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective non-Fourier thermal behavior is studied.

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.

Non-fourier temperature field in a solid homogeneous finite hollow cylinder

Analytical solution of the non-Fourier Axisymmetric temperature field within a finite hollow cylinder is investigated considering the Cattaneo-Vernotte constitutive heat flux relation. The solution is found for the most general linear time-independent boundary conditions. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used. The present solution can be reduced to special problems of interest by choosing appropriate boundary condition parameters. The solution is applied for two special cases including constant heat flux and the Gaussian distribution heating of a cylinder, and their respective non-Fourier thermal behavior is studied.

Transient torsional vibration responses of finite, semi-infinite and infinite hollow cylinders

Torsional guided waves are often used to detect the defects in a hollow cylinder. To realize the excitation of the torsional guided waves with high efficiency, the transient vibration responses of finite, semi-infinite and infinite hollow cylinders to external torsional forces must be clarified theoretically. In this study, the method of eigenfunction expansion is employed to solve the above problems. The exact analytical solutions derived by this method are not only explicit but also concise. Furthermore, the analytical solution of the transient torsional vibration of the finite hollow cylinder is numerically evaluated. The results obtained agree well with those simulated by the finite element method.

Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders

Exact solutions are obtained for transient torsional responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder with its external surface fixed is subjected to a dynamic shearing stress at the internal surface. The material properties are assumed to vary in the radial direction in a power law form, while keep invariant in the axial direction. With expansion in the axial direction in terms of trigonometric series, the governing equations for the unknown functions about the radial coordinate r and time t are deduced. By applying the variable substitution technique, the superposition method and the separation of variables consecutively, series-form solutions of the equations are obtained. Natural frequencies and the transient torsional responses are finally discussed for a functionally graded finite hollow cylinder.

Exact solution for forced torsional vibration of finite piezoelectric hollow cylinder

An exact solution is obtained for forced torsional vibration of a finite class 622 piezoelectric hollow cylinder with free-free ends subjected to dynamic shearing stress and time dependent electric potential at both internal and external surfaces. The solution is first expanded in axial direction with trigonometric series and the governing equations for the new variables about radial coordinate r and time t are derived with the aid of Fourier series expansion technique. By means of the superposition method and the separation of variables technique, the solution for torsional vibration is finally obtained. Natural frequencies and the transient torsional responses for finite class 622 piezoelectric hollow cylinder with free-free ends are computed and illustrated.

Transient torsional wave in finite hollow cylinder with initial axial stress

An analytical solution is obtained for transient torsional vibration of a finite hollow cylinder with initial axial stress. The cylinder is subjected to dynamic shearing stress at the internal surface and is fixed at the external surface. The basic equations are presented and the solution is obtained by means of Fourier series expansion technique and the separation of variables method. The effects of the initial stress on the natural frequencies and transient torsional responses are presented and discussed.

Transient response in a finite hollow cylinder from time-delayed prescribed motion at the boundary

Previous work (Int. J. Solids Struct. 41(18–19) (2004) 5051 on transient response of a hollow cylinder to time-dependent radial motion is extended to include motion of the excitation along the axis of the cylinder.

Singular integral equations in the problem of diffraction of an electromagnetic plane wave by a perfectly conducting finite hollow cylinder

Singular integral equations in the problem of diffraction of an electromagnetic plane wave by a perfectly conducting finite hollow cylinder

About the role of hysteresis in magnetic penetration at extremely low frequency

In this paper a discussion about the role of magnetic hysteresis on the magnetic field distortion and attenuation is presented. A one-dimensional FDITD algorithm has been used to evaluate the weight of hysteresis in determining the magnetic field attenuation for a magnetic iron hollow indefinite thin cylinder. On the basis of such an analysis a second 2D-FEM numerical algorithm has been implemented taking into account only the virgin magnetization curve, therefore, not describing the hysteretic cycles and simulations have been done for a finite thin hollow cylinder geometry. To investigate the approximation due to such a strategy an experimental setup has been implemented and results have been compared. Data have shown that for the investigated geometry and materials the error remains small validating the simplified methodology at least from an engineering point of view.

A general integration method for radiative transfer in 3-D non-homogeneous cylindrical media with anisotropic scattering

A general set of integral equations is presented to solve 3-D radiative heat transfer problems in emitting, absorbing and linear anisotropic scattering finite hollow or solid cylinders with non-homogeneous media. By tracing a ray to compute the intensity,it is much easier to handle the spatial change properties including extinction coefficient. Both the continuous change property and step-change property are dealt with without difficulties. The solid angle integration in getting the incident radiation and heat fluxes is represented by the bounding surface integration. In order to avoid the singularity problem near the bounding surface, the surface integrations are transformed to new modified integral equations by mathematical methods. By doing so, we get more flexible general integral equations applicable to all cases (3-D solid cylinders, 3-D hollow cylinders, finite cylinders or infinite cylinders). This scheme has been verified by comparing the results with published data in the literature. It is believed that this method will be useful in combined radiation and convection heat transfer problems.

Exact solutions of some mixed problems of uncoupled thermoelasticity theory for a finite hollow circular cylinder with a groove along the generatrix

Uncoupled problems of thermoelasticity for a finite hollow circular cylinder with a groove along the generatrix for different types of boundary conditions on all the surfaces are considered. These are the conditions for specifying displacements equal to zero or sliding clamping on the cylindrical surfaces and on the edges of the groove and the conditions for specifying stresses on the ends of the cylinder (shear stresses are assumed to be zero). It is assumed that the problem of thermoelasticity has been solved and the temperature is known. Certain auxiliary functions, related to the displacements, are initially introduced, and equations for these functions are derived using Lamé's equations. A finite integral Fourier transformation with respect to the polar angle and a finite Hankel transformation with respect to the radius are then used. As a result a one-dimensional boundary-value vector problem is obtained for a first-order differential equation, which is solved using Green's matrix constructed. Finally, exact solutions of the problems are constructed in series.

Thermal Stress Analysis of Pipe Flange Connections Combining Bolts with Adhesive Subjected to Heat Conduction from Contained Fluid.

Thermal stress distribution of adhesively bonded pipe flange connections subjected to heat conduction in steady state are analyzed by using the thermoelastic displacement potential and Michell's stress functions based on the axisymmetrical theory of elasticity. In the analysis, pipe flanges, hubs of pipe flange and an adhesive are replaced by finite hollow cylinders, respectively. In the numerical calculations, the effects of the ratios of linear thermal expansion coefficients, Young's moduli between the pipe flange and the adhesive layer and the adhesive thickness on the stress distribution at the interface between the flange and the adhesive layer are examined. As a result, it is seen that the thermal stress (compressive) at the inner and the outer surfaces of the adhesive layer increases with a decrease of Young's moduli ratio, the linear thermal expansion coefficient ratio and the adhesive thickness. In addition, stress analysis by using FEM (Finite Element Method) was also carried out. Fairly good agreement is seen between the numerical and FEM results. The characteristics are compared with those of the connections with gaskets. It is found that the stress at hub of the joint with adhesive is smaller than that of the joint with gasket.

Stress analysis of adhesive lap joints of dissimilar hollow shafts subjected to an axial load

The stress and strain distributions in adhesive lap joints of dissimilar hollow shafts subjected to an axial load have been examined using the axisymmetric theory of elasticity. In the analysis, the joint is modelled as an elastic three-body contact problem and the hollow shafts and the adhesive are replaced by finite hollow cylinders. In the numerical calculations, the effects of the ratio of Young's modulus of the adhesive to that of the shaft and of the thickness of the adhesive on the stress distributions at the interfaces in the joint are clarified. It is shown that the stresses in the radial and circumferential directions become singular at the ends of the interfaces and that the stress increases near the ends of the interfaces with a decrease of Young's modulus of the shaft and with an increase of the thickness of the adhesive. For verification of the stress analysis, the strain distribution at the outer surface of the outer hollow shaft of the joint was measured and satisfactory agreement was shown by comparing the experimental results with the analytical predictions.

Thermal Stress Analysis in Pipe Flange Connections with a Raised-face Gasket Subjected to Heat Conduction from Contained Fluid.

Thermal stress distribution of pipe flange connections with a raised-face gasket subjected to heat conduction in steady state are analyzed by using the thermoelastic displacement potential and Michell's stress function based on the axisymmetrical theory of elasticity. In the analysis, pipe flanges, hubs of pipe flange and a raised-face gasket are replaced by finite hollow cylinders, respectively. In the numerical calculations, the effects of the ratios of linear thermal expansion coefficients, Young's moduli and the thicknesses between the pipe flange and the gasket on the contact stress distribution are examined. As a result, it is seen that the thermal stress at the inner and the outer surfaces of the gasket increases with a decrease of Young's moduli ratio and the gasket thickness. In addition, experiments were performed to measure temperature, the variations of axial bolt force and strains at hubs of pipe flanges. Fairly good agreement is seen between the analytical and the experimental results.

The gravitational coupling between longitudinal segments of a hollow cylinder and an arbitrary gravitational source: relevance to the STEP experiment

The gravitational interaction is derived between a solid longitudinal segment cut from a cylinder of uniform density, and an external point mass. The derivation is expressed in terms of the associated Legendre functions , and the parametric form of the coupling coefficients is presented. This theory is applied to the gravitational interaction between a point mass and a finite hollow cylinder, where the cylinder bears a number of `flats' cut into its outer surface. The `flats' are imagined to be regularly spaced in azimuth around the cylinder, each flat being treated as the removal of a solid segment from the full cylinder. Such forms of test mass have been proposed for the satellite test of the equivalence principle (STEP) experiment, since the masses may then be prevented from rotating in azimuth - a factor which is considered to be essential for this experiment. The gravitational theory developed here is applied to such STEP test masses, and two `low gravitational susceptibility' designs for test-mass pairs are considered, having four and six `flats', respectively. An expression for the axial force on such masses is derived which is more than times faster to compute than a Monte Carlo integration of similar accuracy, by virtue of which it is shown that a design with six or more `flats' is to be preferred. This theory is shown to have much wider applicability to gravitational problems involving general segmented cylindrical bodies, including square- and hexagonal-section prisms of finite length (hollow or solid).

Thermal Stress in Adhesive Butt Joints of Hollow Shafts in Steady Temperature Field.

This study deals with the thermal stress and strain distributions in an adhesive butt joint which is composed of two hollow shafts. The butt joints are joined by an epoxide-type adhesive and kept at a constant temperature. In the analysis, when the shafts and an adhesive are replaced with finite hollow cylinders respectively, the temperature distribution in a joint is calculated based on the thermal conditions of the joint. Then, thermal stresses are analyzed as a three-body contact problem by the axisymmetric theory of elasticity. The effects of the ratios of Young's modulus, the coefficient of thermal expansion and the thickness of the adhesive on the thermal stress distribution at the interface between the adherend and adhesive are studied as general cases. Moreover, thermal stress in the joints of hollow and solid shafts under uniform temperature change is examined by numerical calculations as special cases of the joints. In the experiments, an adhesive is modeled by an epoxide disc-shape plate and the thermal strains are measured by strain gages which are mounted on the outer surface of the shaft close to the interface between the shaft and the epoxide plate. The analytical results of the thermal strain distribution are compared with the experimental ones measured by the strain gages and it is shown that they are in fairly good agreement.

The dynamic problem of electroelasticity for a non-homogeneous cylinder

The non-stationary coupled problem of electroelasticity in connection with the dynamic twisting of a finite hollow cylinder of non-homogeneous piezoelectric material is considered in the case when the electric potential or shear stresses, which depend arbitrarily on time, are specified on its curvilinear surfaces. The method of expansion in eigen vector-valued functions in the form of a structural algorithm of finite integral transformations is used. It is shown that a closed solution can be obtained for a power law of the non-homogeneity of the electric, elastic and inertial characteristics of the material. The results obtained hold for crystals of tetragonal symmetry of class 422 and the hexagonal system of class 622.

Transient Brake Temperatures Found by use of Analytical Solutions for Finite Hollow Cylinders

A linear analytical model for calculating transient axisymmetric temperature distributions in finite hollow cylinders is established and adapted for practical use. A homogeneous isotropic material with temperature-independent thermal properties is assumed. Among possible applications are brake discs, brake drums and block braked railway wheels. The thermal power from braking is applied as prescribed heat influxes over parts of the lateral and radial surfaces of the cylinder. Bessel series solutions to the heat conduction equation are found where Newton's law for heat transfer is used in the boundary conditions. In addition to convection prescribed surface temperatures and insulated surfaces are also studied. Arbitrary thermal loading histories are treated by use of Duhamel's principle where step loadings are superposed. Convergence and limitations of the method and required computer times are discussed. Calculated numerical results for some typical braking operations are compared with those of other studies.

An axisymmetrical analysis of a bolted joint in a cover of the pressure vessel with a hub.

The contact stress distribution, the force ratio (the relationship between an increment of bolt axial force and an internal pressure) and the gasket properties (the gasket seating width and the moment arm) in a bolted joint of a cover of the pressure vessel with a raised face metallic gasket are analyzed as a four-body contact problem using an axisymmetrical theory of elasticity. In the analysis, a hub of the body is taken into consdieration, and a cover, a raised gasket, a body and a hub are replaced with a finite solid cylinder and finite hollow cylinders, respectively The effects of the stiffness and the thickness of gasket on the contact stress distribution and the gasket properties are obtained by numerical calculations. Experiments were carried out concerning the force ratio, the maximum stress produced in bolts and the stress producd on the hub. The analytical results are satisfactorily consistent with the experimental results.