Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.

A thermal-elastic analysis on laser-induced reverse bulging and plugging in circular brass foil

A new failure mode is observed in circular brass foils induced by laser beam. The new failure is based on the following experimental facts : (1) the peripheries of the circular brass foils are fixed and the surfaces of the foils are radiated by laser beam ; (2) the laser beam used is considered to be non-Gaussian spatially, actually an approximately uniform distribution limited in a certain size spot ; (3) the pulse on time of laser beam should be 250 μs, i.e. so called long duration pulse laser. The failure process consists of three stages ; i.e. thermal bulging, localized shear deformation and perforation by plugging. The word reverse in reverse bulging and plugging mode means that bulging and plugging occur in the direction of incident laser beam. To study the newly-discovered type of failure quantitatively, analytical solutions for the axisymmetric temperature field and deflection curve are derived. The calculated results show that the newly discovered failure mode is attributed to the spatial structure effect of laser beam indeed.

Non-slipping Adhesive Contact between Mismatched Elastic Cylinders

要: We have recently proposed a generalized JKR model for non-slipping adhesive contact between two elastic spheres subjected to a pair of pulling forces and a mismatch strain (Chen, S., Gao, H., 2006c. Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation sensor. J. Mech. Phys. Solids 54, 1548-1567). Here we extend this model to adhesion between two mismatched elastic cylinders. The attention is focused on how the mismatch strain affects the contact area and the pull-off force. It is found that there exists a critical mismatch strain at which the contact spontaneously dissociates. The analysis suggests possible mechanisms by which mechanical deformation can affect binding between cells and molecules in biology.

Effective elastic properties of piezoelectric composites with radially polarized cylinders

Effective elastic properties of piezoelectric composites containing an infinitely long, radially polarized cylinder embedded in an isotropic non-piezoelectric matrix are theoretically investigated under an external strain field. Analytical solutions of elastic displacement and electric potentials are exactly derived, and the effective elastic responses are formulated in the dilute limit. Meanwhile, a vanishing piezoelectric response mechanism is revealed in the piezoelectric composite containing radially polarized cylinders. Furthermore, it is shown that the effective elastic properties can be enhanced (or reduced) due to the increase of the piezoelectric (or dielectric) constants of the cylinders. (C) 2009 Elsevier B.V. All rights reserved.

Elastic fields of interacting elliptic inhomogeneities

This paper presents a method for the calculation of two-dimensional elastic fields in a solid containing any number of inhomogeneities under arbitrary far field loadings. The method called 'pseudo-dislocations method', is illustrated for the solution of interacting elliptic inhomogeneities. It reduces the interacting inhomogeneities problem to a set of linear algebraic equations. Numerical results are presented for a variety of elliptic inhomogeneity arrangements, including the special cases of elliptic holes, cracks and circular inhomogeneities. All these complicated problems can be solved with high accuracy and efficiency.

Stress-distribution at the rigid circular-arc inclusion end

The elastic plane problem of a rigid co-circular arc inclusion under arbitrary loads is dealt with. Applying Schwarz's reflection principle integrated with the analysis of the singularity of complex stress functions, the general solution of the problem is found and several closed-form solutions to some problems of practical importance are given. Finally, the stress distribution at the arc inclusion end is examined and a comparison is made with that of the rigid line inclusion end to show the effect of curvature.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

Finite element analysis on a circular wedge prism with 400 mm diameter

The paper comprehensively analyzes the distortions of a circular wedge prism with 400 mm diameter in a scanner by method of optical-mechanical-thermal integrating analysis. The structure and intensity of the prism assembly is verified and checked, and the surface deformations of the prism under gravity load, as well as the thermo-elastic distortions of the prism, are analyzed in detail and evaluated, which is finally contrasted with the measured values of Zygo Mark interferometer. The results show: the maximal distortion of the prism assembly is 10 nm magnitude and the maximal stress is 0.441 Mpa, which has much tolerance to the precision requirement of structure and the admissible stress of material; the influence of heat effect on the surface deformations of prism is proved to be far greater than the influence of gravity load, so some strict temperature-controlled measures are to be considered when the scanner is used. (c) 2006 Elsevier GmbH. All rights reserved.

Scaling relationships in conical indentation of elastic perfectly plastic solids

Using dimensional analysis and finite element calculations we derive several scaling relationships for conical indentation into elastic-perfectly plastic solids. These scaling relationships provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They are also helpful as a guide to numerical and finite element calculations of conical indentation problems. Finally, the scaling relationships are used to reveal the general relationships between hardness, contact area, initial unloading slope, and mechanical properties of solids.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Saturated duration for dynamic structural plastic response and fundamental periods of elastic vibration

The relationship is determined between saturated duration of rectangular pressure pulses applied to rigid, perfectly plastic structures and their fundamental periods of elastic vibration. It is shown that the ratio between the saturated duration and the fundamental period of elastic vibration of a structure is dependent upon two factors: the first one is the slenderness or thinness ratio of the structure; and the second one is the square root of ratio between the Young's elastic modulus and the yield stress of the structural material. Dimensional analysis shows that the aforementioned ratio is one of the basic similarity parameters for elastic-plastic modeling under dynamic loading.

Dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading

In this paper the problem of a cylindrical crack located in a functionally graded material (FGM) interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered. The shear modulus and the mass density of the FGM interlayer are assumed to vary continuously between those of the two coaxial cylinders. This mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) is also obtained by a numerical Laplace inversion technique. The DSIF is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation. The influences of the crack location, the FGM interlayer thickness and the relative magnitudes of the adjoining material properties are examined. It is found among others that, by increasing the FGM gradient, the DSIF can be greatly reduced.

Influences of Hydration Force and Elastic Strain Energy on the Stability of Solid Film in a Very Thin Solid-on-Liquid Structure

Since hydration forces become very strong at short range and are particularly important for determining the magnitude of the adhesion between two surfaces or interaction energy, the influences of the hydration force and elastic strain energy due to hydration-induced layering of liquid molecules close to a solid film surface on the stability of a solid film in a solid-on-liquid (SOL) nanostructure are studied in this paper. The liquid of this thin SOL structure is a kind of water solution. Since the surface forces play an important role in the structure, the total free energy change of SOL structures consists of the changes in the bulk elastic energy within the solid film, the surface energy at the solid-liquid interface and the solid-air interface, and highly nonlinear volumetric component associated with interfacial forces. The critical wavelength of one-dimensional undulation, the critical thickness of the solid film, and the critical thickness of the liquid layer are studied, and the stability regions of the solid film have been determined. Emphasis is placed on calculation of critical values, which are the basis of analyzing the stability of the very thin solid film.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.