Damage assessment based on the structural frequency-response function

A method is presented for determining both the amount and position of damage present in members which can be modeled as longitudinally vibrating uniform beams. The method is valid for all boundary conditions, and for simplicity, is applied to the free-free case. It uses the shift in the natural frequencies of vibration, which are determined from the structural frequency-response function, caused by the damage present in the beam. These altered values of frequency are then utilized in a graphical solution technique which predicts the damage location directly and provides a parameter whose value is related to the magnitude of the damage present.     

The acoustic field in a rigid cylindrical vessel excited by a sphere oscillating by a definite law

The problem on the interaction between a spherical body oscillating by a definite law and a rigid cylinder filled with an ideal compressible liquid is formulated. The geometrical center of the sphere is located on the cylinder axis. The solution is based on the possibility of representing the particular solutions of the Helmholtz equation in cylindrical coordinates in terms of particular solutions in spherical coordinates, and vice versa. As a result of satisfaction of the boundary conditions on the surfaces of the sphere and cylinder, an infinite system of linear algebraic equations is obtained to determine the coefficients of expansion of the potential of liquid velocities into a Fourier series in terms of Legendre polynomials. The use of the reduction technique for solving the infinite system obtained is substantiated. The hydrodynamic characteristics of the liquid filling the cylindrical cavity are determined and compared with the case of a sphere vibrating in an infinite liquid. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 88–97, June, 2000.     

Boundary conditions for axisymmetric circular cylinder in one-dimensional hexagonal quasicrystals

Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan, a set of necessary conditions on the end-data of axisymmetric circular cylinder in one-dimensional (1D) hexagonal quasicrystals (QCs) for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state, and using the reciprocal theorem and general solution, these necessary conditions for the end-data to induce only a decaying elastostatic state (boundary layer solution) will be translated into appropriate boundary conditions for the circular cylinder with axisymmetric deformations in 1D hexagonal QCs. The results of the present paper enable us to establish a set of correct boundary conditions, most of which are obtained for the first time. Furthermore, corresponding necessary conditions for the case of axisymmetric circular cylinder with transversely isotropic are derived subsequently, and their isotropic elastic counterparts are also obtained. The accuracy of mixed boundary conditions of isotropic axisymmertic circular cylinder is proved at last.     

Anti-plane dynamic problem of an electroelastic cylinder with thin rigid inclusions excited by a system of surface electrodes

Summary The anti-plane mixed boundary problem of electroelasticity for vibrations of an infinite piezoceramic cylinder with a thin rigid inclusion is considered. Using the developed integral representation of the solution, the boundary problem is reduced to a system of singular integro-differential equations of the second kind with resolvent kernels. Calculations yeild the amplitude-frequency characteristics of the piecewise homogeneous cylinder. The behaviour of electroelastic fields, both within the cylinder and on its boundary, is given.     

Modal characteristics of a flexible cylinder in turbulent axial flow from numerical simulations

In this paper the vibration behavior of a flexible cylinder subjected to an axial flow is investigated numerically. Therefore a methodology is constructed, which relies entirely on fluid–structure interaction calculations. Consequently, no force coefficients are necessary for the numerical simulations. Two different cases are studied. The first case is a brass cylinder vibrating in an axial water flow. This calculation is compared to experiments in literature and the results agree well. The second case is a hollow steel tube, subjected to liquid lead–bismuth flow. Different flow boundary conditions are tested on this case. Each type of boundary conditions leads to a different confinement and results in different eigenfrequencies and modal damping ratios. Wherever appropriate, a comparison has been made with an existing theory. Generally, this linear theory and the simulations in this paper agree well on the frequency of a mode. With respect to damping, the agreement is highly dependent on the correlation used for the normal friction coefficients in the linear theory.     

On the interactions of surface waves with immersed structures

The fluid forces resulting from wave interaction with large submerged structures may be calculated using numerical procedures based on the solution of the associated boundary-value problem. In this paper, the analysis of wave interaction with a fixed submerged object of arbitrary cross-section and infinite length using a two-dimensional boundary value formation based on linear diffraction theory is summarized. Subsequently, the application of the boundary element method to obtain a solution is presented. The numerical considerations are emphasized with particular reference to computational efficiency. Numerical results are presented in the form of dimensionless wave force plots for various structural shapes. In the case of a bottom-seated half cylinder, for which there exists a closed-form solution, comparisons are made between results generated using both boundary element and equivalent finite element approaches. In the case of a submerged cylinder, comparisons are made between boundary element derived values and experimental results. The boundary element results compare well with both the closed-form solution and the experimental values.     

Periodic heat conduction with relaxation time in cylindrical geometry

Steady-periodic heat conduction with relaxation time in an infinitely long hollow cylinder is considered. Four boundary value problems, with boundary conditions of the first and of the second kind, are solved analytically. The solution for a solid cylinder with a sinusoidally varying surface temperature is obtained as a special case of a solution found for the hollow cylinder. The effects of the relaxation time on the steady-periodic temperature field are analysed, in details, for a solid cylinder with a sinusoidally varying surface temperature and for a hollow cylinder with a sinusoidally varying heat flux at the inner surface and with a constant temperature at the outer surface. The results show that thermal resonances may occur and suggest that accurate measurements of the relaxation time could be obtained by means of experiments on steady-periodic heat conduction in cylindrical geometry. Received on 15 April 1997     

A note on the translation of a thin rod inside a cylinder

The problem of a thin rod moving longitudinally along the axis of symmetry of a cylindrical vessel is examined for Newtonian and non-Newtonian liquids. For non-Newtonian fluids, the inelastic power-law type solution predicts the experimental results particularly well. On account of wall effects, the induced pressure gradients are much greater for a Newtonian fluid than for a viscoelastic fluid. In fact, in the latter case, they may be considered negligible when the radius of the inner cylinder is small compared to the one of the outer 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.     

Laminar boundary layer on a yawed infinite cylinder

Using mixed momentum and energy integral equations, a simple quadrature method is developed to compute incompressible laminar boundary layer on a yawed infinite cylinder. As an illustration, the results — including various boundary layer thicknesses, form parameters and potential and surface streamlines — are obtained for a circular cylinder and compared with a known solution.     

Fracture analysis for torsion problems of a composite cylinder with curvilinear cracks

The Salnt-Venant torsion problems of a composite cylinder with curvilinear cracks were investigated. By considering the bimaterial interface as a boundary of the outer bar or inner one, the problem was reduced to the solution of boundary integral equations on the crack, external boundary and interface. Using the new boundary element method, some typical torsion problems of a composite cylinder involving a straight or kinked crack were calculated. The obtained results were compared with data in the literature to show validity and applicability of the present method.     

Axial acoustic radiation force on a rigid cylinder near an impedance boundary for on-axis Gaussian beam

This work presents a theoretical model to calculate the acoustic radiation force on a rigid cylindrical particle immersed in an ideal fluid near a boundary for an on-axis Gaussian beam. An exact solution of the axial acoustic radiation force function is derived for a cylindrical particle by applying the translation addition theorem of cylindrical Bessel function. We analyzed the effects of the impedance boundary on acoustic radiation force of a rigid cylinder immersed in water near an impedance boundary with particular emphasis on the radius of the rigid cylinder and the distance from the cylinder center to impedance boundary. Simulation results reveal that the existence of particle trapping behavior depends on the choice of nondimensional frequency as well as the offset distance from the impedance boundary. The value of the radiation force function varies when the cylinder lies at the different position of the on-axis Gaussian beam. For the particle with different radius, the acoustic radiation force functions vary significantly with frequency. This study provides a theoretical basis for acoustic manipulation, which may benefit to the improvement and development of the acoustic control technology.     

Elastodynamic solution of a non-homogeneous orthotropic hollow cylinder

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure. The project supported by the National Natural Science Foundation of China (10172075 and 10002016)     

Three-Dimensional Analytical Solution for an Axisymmetric Biharmonic Problem

In this paper, we propose a method for the solution of the axisymmetric boundary value problem for a finite elastic cylinder with assigned stress and/or displacements acting on the ends and side. The technique utilizes the Love representation, which allows for reduction of the solution of the elastic problem to the search for a biharmonic function on a cylindrical domain. In the solution method suggested here, we write the Love function with a Bessel expansion and analyze in detail the conditions under which it is possible to differentiate the expansion term by term. We show that this is possible only for a restricted class of elastic solutions. In the general case, we introduce two new auxiliary functions of the z-coordinate. In this way, we obtain the general form of the axisymmetric biharmonic function, which is discussed in relation to certain specific boundary conditions applied on the side and ends of the cylinder. We obtain an exact explicit solution of practical interest for a cylinder with free ends and assigned displacements applied to the side.     

A continuous shape sensitivity equation method for unsteady laminar flows

This paper presents the application of a general shape sensitivity equation method (SEM) to unsteady laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The flow and sensitivity equations are solved on 3D meshes using a Streamline-Upwind Petrov Galerkin (SUPG) finite element method. In the case of shape parameters, boundary conditions for sensitivities depend on the flow gradient at the boundary. Therefore, an accurate recovery of solution gradients is crucial to the success of shape sensitivity computations. In this work, solution gradients at boundary points are extracted using the Finite Node Displacement (FiND) method on which the finite element discretization is enriched locally via the insertion of nodes close to the boundary points. The normal derivative of the solution is then determined using finite differences. This approach to evaluate shape sensitivity boundary conditions is embedded in the continuous SEM. The methodology is applied to the flow past a cylinder in ground proximity. First, the proposed method is verified on a steady state problem. The computed sensitivity is compared to the actual change in the solution when a small perturbation is imposed to the shape parameter. Then, the study investigates the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. A reduction of the gap causes damping of the vortex shedding while an increase amplifies the unsteadiness.     

MODELLING AND CALCULATION OF THE TURBULENT BOUNDARY LAYER ON A ROTATING CYLINDER SURFACE WITH STRONG SUCTION 1)

提出了湍流边界层的一种简单、快速计算方法, 用以求解强吸气作用下旋转圆筒表面边界层流动. 首先, 理论分析了同心圆筒间的旋转流体运动, 外筒静止、内筒旋转且为多孔吸气条件. 强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动, 基于这一事实得到了周向速度分布的解析表达式. 其次, 通过引入新参数扩展Cebeci-Smith代数湍流模型, 使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素. 针对这些因素的综合影响, 采用解析修正和经验参数对模型进行调整. 同时, 基于Reynolds应力湍流模型的仿真结果, 校准代数湍流模型中的经验参数. 最后, 给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法, 该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况. 计算了不同旋转速度和吸气强度组合工况下的边界层流动, 其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近. 并且表明, 当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时, 该方法也再现了相同初始条件下的层流边界层.     

LATTICE BOLTZMANN SIMULATION OF POWER-LAW FLOW PAST AN ELLIPTIC CYLINDER

基于格子波尔兹曼方法(lattice Boltzmann method) 和幂律流体本构方程, 建立二维流动模型, 将充分发展的速度分布与理论解进行对比, 吻合良好. 对幂律流体的圆柱绕流进行模拟, 采用了反弹格式的无滑移圆柱边界, 并使用应力积分法计算阻力系数, 分析了稳态圆柱绕流时, 阻力系数随幂律指数n 以及雷诺数Re 的变化规律. 分析了椭圆横轴/纵轴长度比和幂律指数n, 对压力系数C_p 和黏度系数C_v 的影响. 得到的变化规律与有限元方法规律一致, 验证了格子波尔兹曼模型的可行性.     

On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number

We numerically investigate flow-induced vibrations of circular cylinders arranged in a tandem configuration at low Reynolds number. Results on the coupled force dynamics are presented for an isolated cylinder and a pair of rigid cylinders in a tandem configuration where the downstream cylinder is elastically mounted and free to vibrate transversely. Contrary to turbulent flows at high Reynolds number, low frequency component with respect to shedding frequency is absent in laminar flows. Appearance and disappearance of the vorticity regions due to reverse flow on the aft part of the vibrating cylinder is characterized by a higher harmonic in transverse load, which is nearly three times of the shedding frequency. We next analyze the significance of pressure and viscous forces in the composition of lift and their phase relations with respect to the structural velocity. For both the isolated and tandem vibrating cylinders, the pressure force supplies energy to the moving cylinder, whereas the viscous force dissipates the energy. Close to the excitation frequency ratio of one, the ratio of transverse viscous force to pressure force is found to be maximum. In addition, movement of stagnation point plays a major role on the force dynamics of both configurations. In the case of isolated cylinder, displacement of the stagnation point is nearly in-phase with the velocity. During vortex-body interaction, the phase difference between the transverse pressure force and velocity and the location of stagnation point determines the loads acting on the cylinder. When the transverse pressure force is in-phase with velocity, the stagnation point moves to higher suction region of the cylinder. In the case of the tandem cylinder arrangement, upstream vortex shifts the stagnation point on the downstream cylinder to the low suction region. Thus a larger lift force is observed for the downstream cylinder as compared to the vibrating isolated cylinder. Phase difference between the transverse load and the velocity of the downstream cylinder determines the extent of upstream wake interaction with the downstream cylinder. When the cylinder velocity is in-phase with the transverse pressure load component, interaction of wake vortex with the downstream cylinder is lower compared to other cases considered in this study. We extend our parametric study of tandem cylinders for the longitudinal center-to-center spacing ranging from 4 to 10 diameter.     

Stresses in an elastic circular cylinder with a prolate spheroidal cavity under torsion

This paper contains an exact solution for the stresses arising from torsion of an elastic circular cylinder with a prolate spheroidal cavity. The solution, which is represented as a combination of a solution that is regular outside the cavity and a solution regular in the solid infinite circular cylinder, is deduced with the aid of a harmonic displacement potential. The two harmonic functions needed are given by simple expressions referred to cylindrical and prolate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and of the cavity are satisfied by using the relations between cylindrical and prolate spheroidal harmonics. Numerical results are presented for different shapes and sizes of the cavity, and the ensuing stress distribution in the neighborhood of the cavity is illustrated graphically.     

Dynamic thermal shock in a layered cylinder with initial interface pressure

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