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The axial-flow-induced vibration of fuel rods in the nuclear power plant is closely related to nuclear safety. In this article, a numerical study is performed on vibration of two elastic cylinders arranged side-by-side in axial flow. Large eddy simulation is employed to predict the turbulent flow. The numerical method has been verified using the experimental root-mean-square vibration amplitude of a single cylinder. A wide range of inflow velocities u∗, incident turbulence intensity Tu and space ratio P/D have been examined, where D and P are the diameter and centre-to-centre distance of the cylinders, respectively. The results show that the vibration amplitudes increase with an increasing u∗, comparable to the case of a single cylinder in axial flow. However, the two cylinders could bend outwards during a relatively high u∗ and low Tu. Although Tu significantly affects the amplitudes of the cylinders, it does not change the vibration frequency and the critical velocity at which buckling instability occurs. As the gap between the two cylinders is sufficiently small, the vibration amplitude enhances significantly due to the pronounced hydrodynamic interaction between the two elastic cylinders and surrounding fluid. The direction of buckling is no longer random but fixed.

This article studies the mathematical modeling of an acoustic field, which is scattered by a homogeneous isotropic cylinder with a radially inhomogeneous elastic coating. The primary perturbation field is a cylindrical harmonic sound wave emitted by a linear source. It is assumed that the axes of the source and scatterer are not parallel and do not lie in the same plane. The density and elastic moduli of the coating material are described by continuous functions of the radial coordinate. The results of the calculations of the angular characteristics of the scattered acoustic field in the far zone for different positions of the linear source are presented. [ABSTRACT FROM AUTHOR]

We derive the compliance of an elastic cylinder submitted to a line Hertzian contact. The cylinder is maintained in static equilibrium by bulk forces that are proportional to rigid body motions. Displacements are measured by setting integral gauges that amount to prescribing zero net linear and angular momentum, if the problem were to depend upon time. Various cases are covered, representing either infinitesimal or finite contact displacements, including partial slip. The developments are illustrated by revisiting a classical example in what could be called The heavy cylinder on a vibrating soil. The four contact resonances and forced response of the system are given in closed form in the quasi-static approximation, and compared against a reference numerical solution. The formulae can also be used as building blocks to assemble the compliance matrix of a system comprising several cylinders. [ABSTRACT FROM AUTHOR]

An analytical solution is obtained for the problem of the diffraction of cylindrical sound waves at an elastic cylinder with an elastic radially-inhomogeneous coating located in the vicinity of the boundary of an elastic half-space. The calculation results of the acoustic field in the far zone are presented. [ABSTRACT FROM AUTHOR]

Rolling with the slipping of an infinite elastic cylinder with a horizontal axis in the gravity field on a flat surface made of the same material is considered. The angle between the nondeformed boundary of the surface and the horizon is nonzero. Based on solution of the corresponding contact problem in Carter's quasi-static formulation, the reaction of the flat surface in dynamic equations is determined. It is shown that if the tangent of the inclination angle does not exceed the product of the friction coefficient and the coefficient that depends on the elastic properties of the material and the mass distribution, motion with constant relative slip δ and a constant acceleration of the center of mass is possible; there is a region in the contact area where the materials stick together. This motion is found to be asymptotically stable with respect to δ. The dependence of the cylinder-axis acceleration on the mechanical properties of the material and the friction coefficient is examined. The results obtained are compared with those of the classical problem of rigid-disk motion along an inclined straight line. [ABSTRACT FROM AUTHOR]

The assembly of acoustically-engineered composite (meta)materials rely on the acousto-elastic radiation force of stationary waves to trap solid particles and form a stable structure. Accurate modeling of the time-averaged force on a particle is needed for experimental design purposes and basic physical understanding of the trapping effect and particle clustering. This work presents a rigorous formalism based on the integration of the time-averaged radial power flow density to derive analytically and calculate numerically the acousto-elastic radiation force induced by compressional (P) and shear (S) plane standing waves incident upon a circular elastic cylinder embedded in a linear lossless solid. Initially, the elastic scattering by the cylinder is determined and then used to derive the acousto-elastic radiation force. Particular emphasis is made on the contributions of elastic mode preservation (P → P, S → S) as well as mode conversion (P → S, S → P) to the radiation force of standing waves. Numerical computations for the dimensionless radiation force efficiency and its components demonstrate the importance of compressional-to-shear and shear-to-compressional mode conversions in scattering that occur in linear elastic media. The analytical formalism and exact solutions of the radiation force can be used to validate numerical methods and the results of the simulations can be utilized a priori in optimizing and designing acousto-elastic radiation force experiments involving standing waves and particle assembly in materials science, elasticity imaging methods, activation of implantable devices, non-destructive evaluation and other related applications.

The paper presents a general solution of the isotropic elasticity problem for the sandwiched inclusion in an elastic cylinder and having axially varying eigenstrain. This problem is relevant in considerations of a cylinder with axially varying thermal expansion coefficient or a nanowire having an axial inhomogeneity of the crystal lattice parameter due to growth and processing conditions. The technique of the solution and the results for the elastic fields and energies of dilatational inclusions with different distribution of eigenstrain, namely, constant, trapezoidal, and diffusion-like, along the axis of the cylinder, are given in full details. The technique explores the axial superpositions of infinitely thin dilatation disks inserted in the cylinder, the elastic fields of which are found in analytical form. In addition, the energies of interfaces separated domains with constant eigenstrains in the cylinder are given. It is demonstrated that the blurring of the eigenstrain in the transition region leads to a decrease in interface energy. [ABSTRACT FROM AUTHOR]

A circular cylinder of finite height that is in the conditions of axial symmetric deformation is considered. Compressive loads are applied to the bases of the cylinder. The Erie stress function is represented in the form of Legendre polynomials. The behavior of a function describing the potential energy of formation in a cylinder is investigated. As a result of numerical experiments, the location of the zones, in which the potential energy is maximum, is clarified. The cases of a symmetric and asymmetric load on the cylinder bases are considered.

The quasi-static plane-parallel motion of an infinite elastic cylinder along a horizontal foundation made of the same material is studied (the cylinder axis is horizontal). The distribution of normal and tangential stresses in the region of contact interaction between the cylinder and plane is derived from the solution to the problem of the theory of elasticity, where the Amontons-Coulomb dry friction model is used in the slip area and the presence of a stick area is taken into account. The analytic solution to the problem is obtained and the phase portrait of the system is drawn. We compare this with the problem of the motion of a perfectly rigid cylinder along a rigid surface with dry friction and without slip. [ABSTRACT FROM AUTHOR]

This numerical study aims to investigate the effect of inlet turbulence intensity T u (0.05 – 5.0%) on flow-induced vibration of an elastic cylinder with fixed ends placed next to a rigid cylinder of the same diameter and length in axial flow. Turbulent flow structure and fluid-structure interaction are captured using large eddy simulation and two-way coupling calculation, respectively. It is found that T u produces a pronounced effect on vibration characteristics of the elastic cylinder. Given a dimensionless velocity U̅ (i.e., 3.49, less than critical U̅ for onset of buckling), root-mean-square vibration amplitude A rms ⁎ increases rapidly with increasing T u from 0.7% to 5.0% for any given center-to-center cylinder spacing P⁎ (1.20 – ∞). This change in A rms * is attributed to the interactions between turbulent structures of different scales, where interactions between large-scale eddies result in the formation of small-scale eddies in the interstitial flow between the cylinders, thus enhancing greatly the flow instability and hence A rms *. Another interesting phenomenon takes place at U̅ = 7.62 (beyond the critical U̅ for onset of buckling) and P⁎ = 1.80, where the elastic cylinder buckles into a new dynamic equilibrium state. As T u increases from 0.3% to 1.5%, the flutter instability occurs merely along the y direction that is normal to the plane of two cylinders axes and also normal to main stream direction. It has been found that the high- T u flow triggers two vortices in this direction, giving rise to two regions of different pressures around the cylinder. The two regions reposition quasi-periodically themselves, thus producing lateral forces that account for this flutter instability in the y direction. Scaling analysis of the dependence of A rms ⁎ on T u and U̅ reveals that the relationship A rms ⁎ = g 1 (T u , U̅) may be reduced to A rms ⁎ = g 2 (U̅ eff); g 1 and g 2 are different functions and the scaling factor U̅ eff = U̅ TF , where TF is the turbulence factor that accounts for the effect of T u on A rms ⁎. The scaling law is discussed in detail, along with the physical meanings of U̅ eff. [ABSTRACT FROM AUTHOR]

Abstract Numerical simulations of the axisymmetric response of a 2nd grade, fiber-reinforced, elastic cylinder are presented and discussed. The underlying model accounts for surface strain and for bending and twist, as in conventional theories, and also includes the non-standard effect of geodesic fiber bending at the constitutive level. [ABSTRACT FROM AUTHOR]

This paper considers the inverse problem of determining the inhomogeneity laws of the coating of an elastic cylinder that provide minimum reflection of a plane acoustic wave in a particular angular sector and in a given frequency range. A functional that expresses the reflection intensity is constructed by direct solution of the direct problem, and an algorithm for minimizing this functional is proposed. Analytical expressions describing the mechanical parameters of the inhomogeneous coating are obtained. [ABSTRACT FROM AUTHOR]

We examine frictional shakedown of an elastic contact of a cylinder pressed on a flat substrate. Slight oscillatory rolling of the cylinder varies the pressure distribution and the contact region. Together with the tangential load, this rocking motion causes incremental sliding processes and a macroscopic rigid body motion. In case that the oscillation amplitude is sufficiently small, the slip ceases after the first few periods and a safe shakedown occurs: the residual force in the contact withstands the tangential load. Otherwise ratcheting occurs: one side of the contact alternately sticks, while the other slips. This leads to a continuing rigid body motion. By derivation of the tangential stress distribution and use of the Boussinesq and Cerruti potential functions, we find approximations for the shakedown limits for the tangential load and the oscillation amplitude. This allows the accurate prediction of the displacement and the reduced tangential load capacity in the shakedown state. The results show strong agreement with numerical and experimental data. [ABSTRACT FROM AUTHOR]

We discuss the solution of Saint-Venant's problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension-torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters. [ABSTRACT FROM AUTHOR]

The classical Resonance Scattering Theory (RST) for plane waves in acoustics is generalized for the case of a 2D arbitrarily-shaped beam incident upon an elastic cylinder with arbitrary location that is immersed in a nonviscous fluid. The formulation is valid for an elastic (or viscoelastic) cylinder (or a cylindrical shell, a layered cylinder/shell, or a multilayered cylindrical shell, etc.) of any size and material. Partial-wave series expansions (PWSEs) for the incident, internal and scattered fields are derived, and numerical examples illustrate the theory. The wave-fields are expressed using a generalized PWSE involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. When the beam is shifted off the center of the cylinder, the off-axial BSCs are evaluated by performing standard numerical integration. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. The properties related to the arbitrary scattering of a zeroth-order quasi-Gaussian cylindrical beam (chosen as an example) by an elastic brass cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed. Moreover, the total and resonance backscattering form function moduli are numerically computed, and the results discussed with emphasis on the contribution of the surface waves circumnavigating the cylinder circular surface to the resonance backscattering. Furthermore, the analysis is extended to derive general expressions for the axial and transverse acoustic radiation force functions for the cylinder in any 2D beam of arbitrary shape. Examples are provided for a zeroth-order quasi Gaussian cylindrical beam with different waist. Potential applications are in underwater and physical acoustics, however, ongoing research in biomedical ultrasound, non-destructive evaluation, imaging, manufacturing, instrumentation, and acoustic holography to name a few, would benefit from the results of this analysis. [ABSTRACT FROM AUTHOR]

An adaptive fuzzy sliding mode control (AFSMC) scheme is applied to actively suppress the two-dimensional vortex-induced vibrations (VIV) of an elastically mounted circular cylinder, free to move in in-line and cross-flow directions. Laminar flow regime at Re=90, low non-dimensional mass with equal natural frequencies in both directions, and zero structural damping coefficients, are considered. The natural oscillator frequency is matched with the vortex shedding frequency of a stationary cylinder at Re=100. The strongly coupled unsteady fluid/cylinder interactions are captured by implementing the moving mesh technology through integration of an in-house developed User Define Function (UDF) into the main code of the commercial CFD solver Fluent. The AFSMC approach comprises of a fuzzy system designed to mimic an ideal sliding-mode controller, and a robust controller intended to compensate for the difference between the fuzzy controller and the ideal one. The fuzzy system parameters as well as the uncertainty bound of the robust controller are adaptively tuned online. A collaborative simulation scheme is realized by coupling the control model implemented in Matlab/Simulink to the plant model constructed in Fluent, aiming at determination of the transverse control force required for complete suppression of the cylinder streamwise and cross-flow oscillations. The simulation results demonstrate the high performance and effectiveness of the adopted control algorithm in attenuating the 2D-VIV of the elastic cylinder over a certain flow velocity range. Also, the enhanced transient performance of the AFSM control strategy in comparison with a conventional PID control law is demonstrated. Furthermore, the effect of control action on the time evolution of vortex shedding from the cylinder is discussed. In particular, it is observed that the coalesced vortices in the far wake region of the uncontrolled cylinder, featuring the C(2S)-type vortex shedding characteristic mode, are ultimately forced to switch to the classical von Kármán vortex street of 2S-type mode, displaying wake vortices of moderately weaker strengths very similar to those of the stationary cylinder. Lastly, robustness of AFSMC is verified against relatively large structural uncertainties as well as with respect to a moderate deviation in the uniform inlet flow velocity. [ABSTRACT FROM AUTHOR]

Abstract: Considering the possible effect of the thin protein-rich sheath on the indentation deformation of an enamel rod, we analyzed the indentation response of an elastic cylinder with a compliant layer between the cylinder and rigid-surrounding material. For the film thickness much less than the characteristic dimension of the cylinder, closed-form solutions were obtained between the indentation load and the indentation depth, which depends on the film thickness and the ratio of the Young's modulus of the cylinder to the Young's modulus of the film. The finite element results supported the relationships for the ratio of the film thickness to the characteristic dimension of the cylinder less than or equal to 1/3. The indentation load required to produce the same indentation displacement decreases with increasing the ratio of the Young's modulus of the cylinder to the Young's modulus of the film for compressible-elastic films. Incompressible-elastic films have no significant effect on the indentation response of the elastic cylinder. [Copyright &y& Elsevier]

In this paper we study the deformation of right cylinders filled with an anisotropic, inhomogeneous, microstretch elastic material. We assume it is subjected to a prescribed thermal field which is linear in the axial coordinate. In order to construct the solution, we study first the problem of extension-bending-torsion, when the thermal field does not depend of the axial coordinate. Then, we study the problem of extension-bending- torsion-flexure for a the thermal field which is linear in the axial coordinate. We reduce the three-dimensional problem to the study of four plane problems. The influence of thermal field on the deformation of the microstretch cylinder is outlined. [ABSTRACT FROM AUTHOR]

The effect of the free edge of a semi-infinite elastic cylinder with circular cross section is considered. It is shown that there exists a complex resonance frequency associated with an axially symmetric localized vibration near the free edge for every value of the Poisson ratio v. For two particular values of v, v = 0 and v = 0.1267, the imaginary part of the complex resonance frequency is zero which corresponds to a trapped mode of the semi-infinite rod. This resonance is also shown to be associated with two eigenfrequencies of the finite length cylinder. [ABSTRACT FROM PUBLISHER]

Abstract: The torsional problem of a finite elastic cylinder with a circumferential edge crack is studied in this paper. An efficient solution to the problem is achieved by using a new form of regularization applied to dual Dini series equations. Unlike the Srivastav approach, this regularization transforms dual equations into a Fredholm integral equation of the second kind given on the crack surface. Hence, exact asymptotic expansions of the Fredholm equation solution, the stress intensity factor and the torque are derived for the case of a shallow crack. The asymptotic expansions are certain power-logarithmic series of the normalized crack depth. Coefficients of these series are found from recurrent relations. Calculations for a shallow crack manifest that the stress intensity factor exhibits the rather weak dependence upon the cylinder length when the torque is fixed and the triple length is larger than the diameter. [Copyright &y& Elsevier]

The problem on large deformations of round cylinders made of homogeneous and fiber-reinforced elastomeric materials under the action of inertia forces caused by rotatory motion is solved. The solution is given in a plane axisymmetric statement, where the deformation parameters of the cylinders depend only on the radial coordinate. Based on the mathematical model presented, the deformation of revolving cylinders made of homogeneous elastomeric materials and reinforced with fibers in the axial, circumferential, and radial directions is investigated. The ultimate rotational speeds for cylinders with different reinforcement schemes and tight and loose fits are found at which their limiting configurations are reached. [ABSTRACT FROM AUTHOR]