Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body

In the present paper a method is proposed to investigate the effects of a rigid internal body on the coupled vibration of a partially fluid-filled cylindrical container. The internal body is a thin-walled and open-ended cylindrical shell. The internal body is concentrically and partially submerged inside a container. The radial and axial distances between the internal body and the container are filled with fluid. Along the contact surface between the container and the fluid, the compatibility requirement for the fluid–structure interactions is applied and the Rayleigh–Ritz method is used to calculate the natural frequencies and modes of a partially fluid-filled cylindrical container. The fluid domain is continuous, simply connected, and non-convex. The fluid is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions for two distinct fluid regions. The resulting equations are solved by using the Galerkin method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature for the partially water-filled cylindrical container without internal body. A finite element analysis is also used to check the validity of the present method for the partially water-filled cylindrical container with internal body. The effects of the fluid level, internal body radius, and internal body length on the natural frequencies of the coupled system are also investigated.     

Pattern formation on a stretchable substrate

We propose a theoretical exploration on phase separation of a binary monolayer of molecules on a uniformly stretched substrate. By extending the previous phase-field model to involve the effect of such a finite pre-stretch, the stability of the monolayer is analyzed, and the temporal evolution of the compositional domains is simulated. Our results indicate that the pre-stretch provides an efficient way to order the phase separation patterns. Therefore, by properly adjusting the principal stretch of the substrate and the composition of the monolayer, the resulting surface pattern may be well tailored.     

Shear flow over cylindrical rods attached to a substrate

Shear flow over a periodic array of cylindrical rods attached to a substrate is studied as a model of flow over a nanomat consisting of aligned carbon nanotubes. The objectives are to evaluate the macroscopic slip velocity, compute the hydrodynamic load exerted at the rod side surface and tip, and estimate the flow-induced deflection. The hydrodynamic traction and macroscopic slip velocity are computed by solving the equations of Stokes flow for a doubly periodic square or hexagonal arrangement using a boundary-element method. The results illustrate the dependence of the slip velocity on the surface coverage expressed by the ratio of the rod radius to separation, and confirm the occurrence of hydrodynamic screening due to surrounding rods confining the traction near the exposed tip of each rod. An estimate for the flexural stiffness of nanotubes is made using available information on the flow-induced deflection. Computations for shear flow past an isolated attached rod are carried out using a highly accurate boundary-element method coupled with a finite-element method for solving the Euler–Bernoulli beam equation, and an iterative procedure involving a boundary-element implementation coupled with a boundary-value formulation involving ordinary differential equations for describing large beam deformation. The results illustrate the precise shape of deflected rods.     

Coupled thermoelasticity of functionally graded cylindrical shells

The coupled thermoelastic response of a functionally graded circular cylindrical shell is studied. The coupled thermoelastic and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. A second-order shear deformation shell theory that accounts for the transverse shear strains and rotations is considered. Including the thermo-mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain are used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The results are validated with the known data in the literature.     

Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.     

Three-dimensional elastic deformation of a functionally graded coating/substrate system

The concept of functionally graded material (FGM) is actively explored in coating design for the purpose of eliminating the mismatch of material properties at the coating/substrate interface, typical for conventional coatings, which can lead to cracking, debonding and eventual functional failure of the coating. In this paper, an FGM coating/substrate system of finite thickness subjected to transverse loading is analysed within the context of three-dimensional elasticity theory. The Young’s modulus of the coating is assumed to vary exponentially through the thickness, and the Poisson’s ratio is assumed to be constant. A comparative study of FGM versus homogeneous coating is conducted, and the dependence of stress and displacement fields in the coating substrate/system on the type of coating, geometry and loading is examined and discussed.     

Anti-plane problem of periodic cracks in a functionally graded coating–substrate structure

The static and dynamic anti-plane problem for a functionally graded coating–substrate structure containing a periodic array of parallel cracks, which are perpendicular to the boundary, is considered. Integral-transform techniques are employed to reduce the problem to the solution of an integral equation with hypersingular kernels. Numerical results are presented to show the influence of geometry, material properties and material gradient parameter on the fracture behavior.     

Critical stretch for formation of a cylindrical void in a compressible hyperelastic material

Formation of a cylindrical void in an infinitely long compressible hyperelastic cylinder under axial and radial stretches is examined. The cavitation phenomenon is viewed here as a bifurcation of a solution with a cavity from the homogeneously deformed configuration, taking place when the applied radial stretch reaches a certain critical value. This amounts to modeling the underlying phenomenon as a kind of elastic instability. A formulation of shooting-method type is presented to derive an equation which gives the critical radial stretch for a prescribed axial stretch. For a special class of hyperelastic solids, called modified Blatz-Ko material, the obtained equation leads to an explicit expression for the critical stretches and stresses. Some analytical as well as numerical calculations are carried out to explicitly obtain the critical values for cavitation. The results are summarized in the form of cavitation curves in the two-dimensional space of axial and radial stretches or stresses. Influence of the axial stretch on the critical radial stretch is discussed. Throughout the paper, the corresponding results for a spherically symmetric void formation are referred to when appropriate and compared with the cylindrical case of the present interest. It is then indicated that in the state of equitriaxial stretch, cavitation into a cylindrical shape is likely to occur at lower stretch than into a spherical one.     

On the cyclic bending behaviour of a hard coating on a ductile substrate with periodic surface hardened regions

A cyclic bending experiment is designed to investigate the interface fracture behaviour of a hard chromium coating on a ductile substrate with periodic surface hardened regions. The unique deflection pattern of the vertical cracks after they run through the coating and impinge at the interface is revealed experimentally. A simple double-layer elastic beam model is adopted to investigate the interfacial shear stresses analytically. A FE model is employed to compute the stresses of the tri-phase structure under a single round of bending, and to investigate the effect of the loading conditions on the deflection pattern of the vertical cracks at the interface.     

The spectrum of a linear magnetohydrodynamic model with cylindrical symmetry

Communicated by K. R. Rajagopal     

Filtration model of longitudinal flow in a finned cylindrical channel

The problem of laminar flow of a viscous incompressible fluid in a finned circular tube is considered. A solution is obtained in the form of series in eigenfunctions of the Laplace operator; the coefficients in the series are found numerically. For the same problem, a simpler filtration approximation is proposed in which the system of fins is modeled by a radially inhomogeneous porous layer, and fluid flow in it is described by the Brinkman equation. A formula for the effective permeability of the porous medium is obtained by varying the number and height of fins. The formula provides an accurate evaluation of the mean flow velocity and viscous drag coefficient in finned channels.     

Dynamic interaction of a spherical radiator in a fluid-filled cylindrical borehole within a poroelastic formation

Harmonic acoustic radiation from a modally oscillating spherical source positioned at the center of a fluid-filled cylindrical cavity embedded within a fluid-saturated porous elastic formation is studied in an exact manner. The formulation utilizes the Biot theory of dynamic poroelasticity along with the cylindrical to spherical wave-field transformations, and the pertinent boundary conditions to obtain a closed-form series solution. The analytical results are illustrated with a numerical example in which the spherical source, with its polar axis oriented along the main axis of a water-filled borehole and embedded within a water-saturated Ridgefield sandstone formation, is excited in vibrational modes of various orders. The magnitude of the reflected component of acoustic pressure along the axis of the borehole for a pulsating (n = 0), an oscillating (n = 1), and also a multipole (n = 0–3) spherical source as a function of the excitation frequency is calculated and discussed for representative values of the parameters characterizing the system. Special attention is paid to the effects of source excitation frequency, size, surface velocity profile, and internal impedance as well as borehole interface permeability condition on the reflected pressure magnitudes. Limiting cases are considered and fair agreements with well-known solutions are obtained.     

Boiling induced nanoparticle coating and its effect on pool boiling heat transfer on a vertical cylindrical surface using CuO nanofluids

Experiments were performed to study boiling induced nanoparticle coating and its influence on pool boiling heat transfer using low concentrations of CuO- nanofluid in distilled water at atmospheric pressure. To investigate the effect of the nanoparticle coated surface on pool boiling performance, two different concentrations of CuO nanofluids (0.1 and 0.5?g/l) were chosen and tests were conducted on a clean heater surface in nanofluid and nanoparticle coated surface in pure water. For the bare heater tested in CuO nanofluid, CHF was enhanced by 35.83 and 41.68?% respectively at 0.1 and 0.5?g/l concentration of nanofluid. For the nanoparticle coated heater surface obtained by boiling induced coating using 0.1 and 0.5?g/l concentration of nanofluid and tested in pure water, CHF was enhanced by 29.38 and 37.53?% respectively. Based on the experimental investigations it can be concluded that nanoparticle coating can also be a potential substitute for enhancing the heat transfer in pure water. Transient behaviour of nanofluid was studied by keeping heat flux constant at 1,000 and 1,500?kW/m² for 90?min in 0.5?g/l concentration. The boiling curve shifted to the right indicating degradation in boiling heat transfer due to prolonged exposure of heater surface to nanofluid. Experimental outcome indicated that pool boiling performance of nanofluid could be a strong function of time and applied heat flux. The longer the duration of exposure of the heater surface, the higher will be the degradation in heat transfer.     

Three-dimensional divergent waves on a model viscoelastic coating in a potential incompressible fluid flow

Generation of three-dimensional nonlinear waves on a model viscoelastic coating in a potential flow of an incompressible fluid is studied. Periodic nonlinear waves enhanced by the development of quasi-static instability (wave divergence) are considered. The coating is modeled by a flexible flat plate supported by a distributed nonlinearly-elastic spring foundation. Plate flexure is described on the basis of the Karman equations of the theory of thin plates. Perturbations of surface pressure in the potential flow are found in the small slope approximation to an accuracy to terms of the second order of smallness. Numerical simulation reveals a jump-like transition from two-dimensional nonlinear waves to three-dimensional wave structures, which are also observed in experiments.     

Buckling of an orthotropic graded coating with an embedded crack bonded to a homogeneous substrate

To simulate buckling of nonuniform coatings, we consider the problem of an embedded crack in a graded orthotropic coating bonded to a homogeneous substrate subjected to a compressive loading. The coating is graded in the thickness direction and the material gradient is orthogonal to the crack direction which is parallel with the free surface. The elastic properties of the material are assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the crack orientation. The loading consists of a uniform compressive strain applied away from the crack region. The graded coating is modeled as a nonhomogeneous medium with an orthotropic stress–strain law. Using a nonlinear continuum theory and a suitable perturbation technique, the plane strain problem is reduced to an eigenvalue problem describing the onset of buckling. Using integral transforms, the resulting plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the critical buckling strain. The Finite Element Method was additionally used to model the crack problem. The main objective of the paper is to study the influence of material nonhomogeneity on the buckling resistance of the graded layer for various crack positions, coating thicknesses and different orthotropic FGMs.     

涂层/基体材料界面结合强度测量方法的现状与展望

界面结合强度是涂层/基体材料体系中的一项重要力学性能指标.而表征与评价涂层/基体材料的界面结合强度又得依靠实验 方法的测定.由于涂层/基体材料体系的多样性与复杂性, 至今还没有形成适合于测量这类材料的界面结合强度的标准方法. 目前, 常用来测量涂层/基体材料的界面结合强度的方法有：拉伸法、剪切法、弯曲法、划痕法、压入法等.本文就目前表征 与评价涂层/基体材料界面结合强度的测量方法做了综述, 讨论了它们的适用范围, 比较了它们的优势与不足.