圆柱外表面受热冲击问题的广义热弹性分析

基于 L-S 广义热弹性理论, 针对实心圆柱体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析. 利用热冲击的瞬时特征, 借助于 Laplace 正、反变换技术及柱函数的渐近性质, 推导了热冲击作用周期内温度场、位移场和应力场的渐近表达式. 通过计算, 得到了热冲击条件下各物理场的分布规律以及延迟效应和耦合效应对热弹性响应的影响规律. 结果表明: 当考虑延迟效应和耦合效应时, 热扰动将以两组速度不同的波的形式向前传播, 延迟效应和耦合效应对各物理场的建立时间, 阶跃间隔和阶跃峰值均产生影响, 且延迟效应和耦合效应均在一定程度上削弱了热冲击的作用效果.      

Magneto–thermo–electro–elastic transient response in a piezoelectric hollow cylinder subjected to complex loadings

The article presents an analytical solution for magneto–thermo–electro–elastic problems of a piezoelectric hollow cylinder placed in an axial magnetic field subjected to arbitrary thermal shock, mechanical load and transient electric excitation. Using an interpolation method solves the Volterra integral equation of the second kind caused by interaction among magnetic, thermal, electric and mechanical fields, the electric displacement is determined. Thus, the exact expressions for the transient responses of displacement, stresses, electric displacement, electric potential and perturbation of the magnetic field vector in the piezoelectric hollow cylinder are obtained by means of Hankel transforms, Laplace transforms, and inverse Laplace transforms. From sample numerical calculations, it is seen that the present method is suitable for a piezoelectric hollow cylinder subjected to arbitrary thermal shock, mechanical load and transient electric excitation, and the result carried out may be used as a reference to solve other transient coupled problems of magneto–thermo–electro–elasticity.     

Dynamic solution of a multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems

The dynamic solution of a multilayered orthotropic piezoelectric infinite hollow cylinder in the state of axisymmetric plane strain is obtained. By the method of superposition, the solution is divided into two parts: one is quasi-static and the other is dynamic. The quasi-static part is derived by the state space method, and the dynamic part is obtained by the separation of variables method coupled with the initial parameter method as well as the orthogonal expansion technique. By using the obtained quasi-static and dynamic parts and the electric boundary conditions as well as the electric continuity conditions, a Volterra integral equation of the second kind with respect to a function of time is derived, which can be solved successfully by means of the interpolation method. The displacements, stresses and electric potentials are finally obtained. The present method is suitable for a multilayered orthotropic piezoelectric infinite hollow cylinder consisting of arbitrary layers and subjected to arbitrary axisymmetric dynamic loads. Numerical results are finally presented and discussed.     

Instability of the magnetic fluid shape in the field of a line conductor with current

The static shape of the surface of a finite magnetic fluid volume between horizontal plates is investigated theoretically. The nonuniform magnetic field is generated by a horizontal line conductor with current, which is placed above the upper plate. The variational problem of minimum energy relative to plane surface perturbations is considered for a simply connected magnetic fluid volume. The problem is solved for arbitrary magnetic fields in the noninductive approximation with account for the gravity force and surface tension. Unstable solutions are found. The possibility of stepwise behavior in response to quasi-static changes of the current in the conductor is investigated for the surface shape of a finite magnetic fluid volume.     

Exact Electromagnetothermoelastic Solution for a Transversely Isotropic Piezoelectric Hollow Sphere Subjected to Arbitrary Thermal Shock

This paper presents analytical study for electromagnetothermoelastic transient behavior of a transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Exact solutions for the transient responses of stresses, perturbation of magnetic field vector, electric displacement and electric potential in the transversely isotropic piezoelectric hollow sphere are obtained by means of the Hankel transform, the Laplace transform and their inverse transforms. An interpolation method is used to solve the Volterra integral equation of the second kind caused by interactions among electric, magnetic, thermal and elastic fields. From the sample numerical calculations, it is seen that the present method is suitable for the transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Finally, the result can be used as a reference to solve other transient coupling problems of electromagnetothermoelasticity.     

Non-linear vibration of bimaterial magneto-elastic cantilever beam with thermal loading

Formulas and numerical results are studied for the transient vibration and dynamic instability of a bimaterial magneto-elastic cantilever beam which is subjected to alternating magnetic field and thermal loading. Materials are assumed isotropic, and the physical properties are assumed to have unique values in each layer. The governing equation of motion is derived by the extended Hamilton's principle, in which the damping factor, the electromagnetic force, the electromagnetic torque, and the thermal load are considered. The solution of thermal effect is obtained by superposing certain fundamental linear elastic stress states which are compatible with the Euler–Bernoulli beam theory. The axial stresses results are found to be in good agreement with some known numerical solutions. Using Galerkin's method, the equation of motion is reduced to a time-dependent Mathieu equation. The numerical results of the regions of dynamic instability are determined by the incremental harmonic balance (IHB) method, and the transient vibratory behaviors are presented by the fourth-order Runge–Kutta method. The results show that the responses of the transient vibration and dynamic instability of the system are influenced by the magnetic field, the thickness ratio, the excitation frequency, but not by the temperature increase in this study.     

Electromagnetic twisting of a penny-shaped crack in an elastic conducting cylinder

This paper deals with the electromagnetoelastic problem of an elastic, conducting circular cylinder with a penny-shaped crack under a uniform axial current flow and a constant axial magnetic field. The current flow is disturbed by the presence of the crack and the torsional stresses are caused by the interactions between the magnetic field and the disturbed current. Two problems concerning the electric current density field and the electromagnetoelastic field are formulated by means of integral transform techniques and reduced to two Fredholm integral equations of the second kind. Numerical calculations are carried out and stress intensity factors are obtained for several values of the geometric parameters.     

Magneto-thermoelastic problem in non-homogeneous isotropic cylinder

The present paper concerns the investigation of the stress, temperature and magnetic fields in an isotropic elastic cylinder in a primary magenetic field when the curved surface of the cylinder subject to certain boundary conditions.The system of fundamental equations is solved by means of a finite difference method and the numerical calculations are carried out for the temperature, the components of displacement and the components of stresses with time and through the thickness of the cylinder. The results indicate that the effects of inhomogeneity and magnetic field are very pronounced.     

Transient thermal elastic fracture of a piezoelectric cylinder specimen

A finite piezoelectric cylinder with an embedded penny-shaped crack is investigated for a thermal shock load on the outer surface of the cylinder. The theory of linear electro-elasticity is applied to solve the transient temperature field and the associated thermal stresses and electrical displacements without crack. These thermal stresses and electrical displacements are added to the surfaces of the crack to form an electromechanical coupling and mixed mode boundary-value problem. The electrically permeable crack face boundary condition assumption is used, and the thermal stress intensity factor and electrical displacement intensity factor at the crack border are evaluated. The thermal shock resistance of the piezoelectric cylinder is evaluated for the analysis of piezoelectric material failure in practical engineering applications.     

Temperature and thermal stresses in material of a pad during braking

The transient temperature field and corresponding quasi-static thermal stresses are analysed in a system consisting of a semi-space and a strip. The strip is heated on its outer surface by a heat flux with the intensity equal to the specific power of friction during braking with a uniform retardation. The evolution and distribution in depth from a surface of friction for temperatures and thermal stresses were investigated for the metal-ceramic FMK-11 material of the strip.     

Magnetothermoelastic transient response of a functionally graded thick hollow sphere subjected to magnetic and thermoelastic fields

In this article, an analytical method is developed to obtain the response of magnetothermoelastic stress and perturbation of the magnetic field vector for a thick-walled spherical functionally graded materials (FGM) vessel. The vessel, which is placed in a uniform magnetic field, is subjected to an internal pressure and transient temperature gradient. Using the Hankel and Laplace transform techniques, the dynamic equation of magnetothermoelastic is solved and the radial and circumferential stresses as well as the perturbation of the magnetic field vector for a typical material are obtained. Moreover, the effect of magnetic field vector and material inhomogeneity on the stresses is investigated.     

Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system

This paper studies the fracture behavior of a thermoelastic cylinder subjected to a sudden temperature change on its outer surface within the framework of non-classical heat conduction.The heat conduction equation is solved by separation of variable technique.Closed form solution for the temperature field and the associated thermal stress are established.The critical parameter governing the level of the transient thermal stress is identified.Exact expression for the transient stress intensity factor is obtained for a crack in the cylinder.The difference between the non-classical solutions and the classical solution are discussed.It is found that the traditional classical heat conduction considerably underestimates the transient thermal stress and thermal stress intensity factor.     

Crack spacing effect for a piezoelectric cylinder under electro-mechanical loading or transient heating

This paper investigates the fracture problem of a piezoelectric cylinder with a periodic array of embedded circular cracks. An electro-mechanical fracture mechanics model is established first. The model is further used to the thermal fracture analysis of a piezoelectric cylinder subjected to a sudden heating on its outer surface. The temperature field and the associated thermal stresses and electric displacements are obtained and are added to the crack surface to form a mixed-mode boundary value problem for the electro-mechanical coupling fracture. The stress and stress intensities are investigated for the effect of crack spacing. Strength evaluation of piezoelectric materials under the transient thermal environment is made and thermal shock resistance of the medium is given.     

Transient response of an elastic conductor with a penny-shaped crack under electromagnetic force

The axisymmetric dynamic response of a penny-shaped crack in an elastic conductor under an impulsive electric current flow and a constant axial magnetic field is analyzed. The axial current flow is disturbed by the presence of the crack and the torsional shear stresses are caused by the interactions between the magnetic field and the disturbed current. Laplace and Hankel transforms are used to reduce the electromagnetoelastic problem to a Fredholm integral equation of the second kind in the Laplace transform plane. A numerical Laplace inversion routine is used to recover the time dependence of the solution. Numerical results on the dynamic stress intensity factor are obtained and are presented in a graphical form.     

Transient temperature and thermally induced stress distributions in a partly-circumferentially heated cylindrical workpiece

This paper presents the numerical solutions of the transient temperature and thermally induced stress distributions in a partly-circumferentially heated cylindrical hollow workpiece (steel) with conjugate heat transfer. Outer surface of the workpiece is heated partly-circumferentially heat flux as its remainder outer surface is circumferentially cooled with fluid (water). Three phenomena have been considered as; (1) conduction inside the cylinder, (2) convection from the cylinder surface to the surrounding fluid, and (3) thermal stress produced by high temperature gradient inside the cylinder. The governing flow and energy equations have been solved numerically by using a control volume approach. The PHOENICS 3.2 and HEATING7 computer codes have been used for the numerical evaluation. The transient calculations have been performed individually for four fluid inlet velocities, u_i = 0.005, 0.01, 0.015 and 0.020 m/s, until the system attains steady-state. The results of this study clearly demonstrate that the temperature contours in the low inlet velocity cases are more near to a symmetric case with respect to the y = 0 plane than that in the high inlet velocity cases, and the increment of the inlet velocity exponentially reduces the temperatures and thermally induced stresses in the workpiece. The effective thermal stress differences occurring in the workpiece can be significantly reduced by the high fluid inlet velocity.     

Dispersion of radial vibrations of an orthotropic cylindrical tube placed in a magnetic field

The present paper studies the dispersion relation of the radial vibrations of an orthotropic cylindrical tube. The effects of the magnetoelastic interaction on the problem are investigated. The problem is represented by the equations of elasticity taking into account the effect of the magnetic field as given by Maxwell's equations in the quasi-static approximation. The stress free conditions on the inner and outer surfaces of the hollow cylindrical cube are satisfied to form a dispersion relation in terms of the wavelength, the cylinder radii and the material constants. This study shows that waves in a solid body propagating under the influence of a superimposed magnetic field can differ significantly from those propagating in the absence of a magnetic field. The results have been verified numerically and represented graphically.     

Electromagnetoelastic behaviors of functionally graded piezoelectric

Analytical studies on electromagnetoelastic behaviors are presented for the functionally graded piezoelectric material (FGPM) solid cylinder and sphere placed in a uniform magnetic field and subjected to the external pressure and electric loading. When the mechanical, electric and magnetic properties of the material obey an identical power law in the radial direction, the exact displacements, stresses, electric potentials and perturbations of magnetic field vector in the FGPM solid cylinder and sphere are obtained by using the infinitesimal theory of electromagnetoelasticity. Numerical examples also show the significant influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter can optimize the electromagnetoelastic responses, which will be of particular importance in modern engineering designs.     

激光辐照下多层圆柱体中三维瞬态温度场的解析解

考虑外表面的气流影响和层间温度与传热的协调关系,建立了激光辐照下,层合圆柱体中的三维瞬态热传导解析模型。利用特征值法和Bessel函数,导出了各层柱体中三维瞬态温度场的封闭解析解。以一维轴对称问题为例计算了柱体中的瞬态温度场,给出了柱体内部温度随时间的变化和柱体表面换热系数对温度场的影响规律。本文的理论解可进一步用于分析层合圆柱体中的三维瞬态热-力效应,并可作为相应问题的数值模拟中数值模型的修正依据。     

Transient thermal stress analysis of a functionally graded magneto-electro-thermoelastic strip due to nonuniform surface heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic strip due to unsteady and nonuniform surface heating in the width direction. We analyze the transient thermal stress problem for a functionally graded strip constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the solution for the simply supported and functionally graded magneto-electro-thermoelastic strip under a plane strain state. As an illustration, we carried out numerical calculations for a functionally graded strip composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄, and examined the behaviors in the transient state for temperature change, stress, electric potential and magnetic potential distributions. Furthermore, the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.     

机械载荷作用下单边裂纹载流薄板的应力场

采用坐标变换的方式,将单边裂纹载流薄板通电瞬间由温度产生的应力场表达式中的各应力分量分离,并用极坐标进行表示．给出了Ⅰ型穿透裂纹尖端附近的应力场的表达式．最后将温度产生的应力场与单向拉伸载荷作用产生的应力场相叠加,推导出用极坐标表示的机械载荷作用下单边裂纹载流薄板的应力场的表达式,并给出算例．