Sandwich Ring Research Articles

Low-Cost Method and Biochip for Measuring the Trans-Epithelial Electrical Resistance (TEER) of Esophageal Epithelium

Trans-epithelial electrical resistance (TEER) is a good indicator of the barrier integrity of epithelial tissues and is often employed in biomedical research as an effective tool to assess ion transport and permeability of tight junctions. The Ussing chamber is the gold standard for measuring TEER of tissue specimens, but it has major drawbacks: it is a macroscopic method that requires a careful and labor intensive sample mounting protocol, allows a very limited viability for the mounted sample, has large parasitic components and low throughput as it cannot perform multiple simultaneous measurements, and this sophisticated and delicate apparatus has a relatively high cost. This paper demonstrates a low-cost home-made “sandwich ring” method which was used to measure the TEER of tissue specimens effectively. This method inspired the subsequent design of a biochip fabricated using standard soft lithography and laser engraving technologies, with which the TEER of pig epithelial tissues was measured. Moreover, it was possible to temporarily preserve the tissue specimens for days in the biochip and monitor the TEER continuously. Tissue responses after exposure tests to media of various pH values were also successfully recorded using the biochip. All these demonstrate that this biochip could be an effective, cheaper, and easier to use Ussing chamber substitute that may have relevant applications in clinical practice.

Non-linear vibrations of sandwich viscoelastic shells

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.

Vibro-acoustic study of a viscoelastic sandwich ring immersed in water

This work deals with the reduction of the system composed of a sandwich structure with a viscoelastic core coupled to fluids. Two reduction methods are proposed in this paper to solve this problem in the frequency domain. The first one consists in developing added mass operators to take into account the fluid. The second one is the use of iterative methods to calculate the coupled complex modes of the dissipative problem. This numerical strategy is applied to the response of a bidimensional sandwich ring coupled to internal and external fluids.

Non-iron [n]Metalloarenophanes

The past 15 years have witnessed the creation of a wealth of fascinating applications for strained [n]ferrocenophanes, in which the aromatic sandwich rings of ferrocene are covalently tethered (n denotes the number of bridging elements). By contrast, the related [n]metalloarenophanes, that is, ansa-complexes not derived from ferrocene, have been neglected for a long time. In this Account, we present the tremendous progress that has been achieved in this field, mostly over the last five years. We focus on systems that have been developed in our laboratories, namely, those based on [M(eta(6)-C(6)H(6))(2)] (where M is V, Cr, or Mo), [Mn(eta(5)-C(5)H(5))(eta(6)-C(6)H(6))], and [M(eta(5)-C(5)H(5))(eta(7)-C(7)H(7))] (where M is V or Cr). We begin by examining the synthetic precursors to [n]metalloarenophanes, the selectively 1,1'-dilithiated sandwich complexes. These species can be isolated and characterized both in the solid state and in solution, and an appreciation of their structural properties is essential for the controlled synthesis of strained [n]metalloarenophanes. About 25 different [n]metalloarenophanes (n = 1, 2) have been obtained from 1,1'-dilithiated sandwich complexes by their stoichiometric reaction with appropriate element dihalides, and most have been fully characterized. X-ray diffraction data confirm the presence of tilted structures, with the extent of the tilt depending on the number of bridging elements, their covalent radii, and the nature of the metal center. The tilt angle, alpha, between the planes of the two carbocyclic ligands represents a good measure of the amount of ring strain present in these species, ranging from 31.23 degrees for a highly strained [1]boravanadoarenophane to 2.60 degrees for the almost unstrained [2]silatrochrocenophane. The strained character of [n]metalloarenophanes is reflected in their rich and unusual reactivity. The thermodynamic driving force for most of the observed transformations is a significant reduction of molecular ring strain, as evidenced by smaller tilt angles in the products. For example, the [1]sila derivatives undergo facile oxidative addition of the strained Si-(arene)C bond to low-valent transition metal complexes. Catalytic reaction with Karstedt's catalyst results in the transition-metal-catalyzed ring-opening polymerization (ROP) of a [1]silatrochrocenophane, yielding a polymeric species (M(W) = 6.4 x 10(3) g mol(-1)). The transition-metal-catalyzed ROP of a paramagnetic [1]silavandoarenophane provides a rare example of a well-characterized macromolecule (M(W) > or = 2.8 x 10(4) g mol(-1)) containing spin-active metal centers in the main chain. The B-B bond of the [2]borametalloarenophanes was found to be particularly susceptible to further functionalizations. Facile oxidative addition was observed, and the resulting [3]diboraplatina derivatives could be successfully employed in the diboration of alkynes to form ansa-bis(boryl)alkenes. This transformation was also accomplished directly from the [2]borametalloarenophanes, that is, a diboration of alkynes under both homogeneous and heterogeneous catalysis conditions. Similarly, the stoichiometric diboration of the N=N double bond of azobenzene by a [3]diboraplatinachromoarenophane is possible. The Si-Si bond in [2]silachromoarenophanes can also be used in further derivatizations, although higher temperatures are required. The bis-silylation of propyne proceeded via palladium mediation under homogeneous conditions to yield ansa-bis(silyl)alkenes. Finally, we discuss the electronic properties of [n]metalloarenophanes developed in our laboratories, revealing correlations between selected NMR, EPR, and UV-visible parameters and molecular distortion.

A New 3D Finite Element for Sandwich Beams With a Viscoelastic Core

A sandwich finite element for laminated steels is presented. It is based on a discrete displacement approach and allows for both symmetrical and unsymmetrical configurations. The three-layer sandwich model is built assuming a Timoshenko hypothesis for the viscoelastic core and Euler–Bernoulli hypotheses for the elastic faces, but the latter is modified to account for the rotational influence of the transversal shearing in the core. The validity and accuracy of the presented element are assessed through comparisons with numerical results of sandwich beams and sandwich rings with a variety of geometrical and mechanical properties and various boundary conditions. The present results are also compared with analytical, finite element, and experimental solutions for various boundary conditions.

Thermoelastic bending of a sandwich ring plate on an elastic foundation

The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical results for a sandwich ring plate in a temperature field are presented

Stability of a Circular Sandwich Ring under an Axially Symmetric Temperature Field Inhomogeneous across the Thickness

The linearized problems on the stability of a circular sandwich ring of symmetric structure under an axially symmetric temperature field inhomogeneous across the core thickness are stated and analytical solutions to them are given. The first problem deals with the mixed flexural buckling form (BF) of the ring as a whole, realized as a result of buckling in one of the load-carrying layers due to formation of precritical pressure stresses in the layer. The second problem considers purely shear BFs when one load-carrying layer is rotated relative to the other. The deformation processes for the load-carrying layers are described by the Kirchhoff-Love model, and for the core of arbitrary thickness - by two models, namely by the equations of the plane problem of elasticity theory and by the model of a transversely soft layer of arbitrary thickness (the same equations simplified by the assumption of zero circumferential normal stresses). Within the frames of the first model adopted for the core, the shear BF is theoretically possible but practically unrealizable, since the mixed flexural BF arises earlier than the shear BF.

Shear Buckling Form of a Circular Sandwich Ring under Uniform External Pressure

The problem on the stability of a circular sandwich ring under uniform external pressure is considered. It is shown that, along with a mixed flexural-shear buckling form (BF), a pure shear BF can be realized in the core. This form is accompanied by rotation of the load-carrying layers at the cost of the transverse shear strain (constant in the circumferential direction) in the core. It is found that the simplified equations of the theory of shallow shells cannot describe this nonclassical BF. The critical loads corresponding to the shear BF may prove to be smaller than the critical load of the classical mixed flexural BF for a circular sandwich ring of medium thickness at a low shear modulus of the core. The results obtained contribute greatly to the understanding of buckling mechanisms of sandwich structures and supplement the existing classification of BFs.

Stability problem of a circular sandwich ring under uniform external pressure

The solution of the stability problem of a circular sandwich ring under uniform external pressure is given in a refined statement. The need to determinate the precritical stresses in load-bearing layers in the refined statement with regard to the transverse compression of the core is established, which is the basis for the detection of the mixed flexural buckling forms (BFs) with more than two half-waves along the circumferential coordinate (n>2). It is found that sandwich structures with a determining parameter of transverse compression corresponding to the limit of transition from the mixed BFs to synphasic ones are the most efficient from the weight viewpoint.

Solution of Circular Sandwich Ring under Two Forces Acting along Diameter

In perhaps the first nontrivial application of an alternative interfacial compatibility condition, the elasticity solution of a circular three-layer sandwich ring under two forces acting along a diameter is obtained. Within each layer, the material property is linearly elastic and isotropic. The difficulty in treating the concentrated load at the outer boundary is overcome by using a solid disk solution in combination with a general series solution. A parametric study is carried out to quantitatively establish the beneficial effects in the mechanical sense of adding the cover layers to the core layer. The solution is applicable to sandwich pipes used in wastewater systems. The solution is also useful in providing a benchmark for numerical methods to compare with.

Forced response of sandwich ring with viscoelastic core subjected to traveling loads

The forced vibrations of a three-layer sandwich ring with viscoelastic material (VEM) core subjected to traveling loads are investigated. The VEM layer is added to provide damping, and subsequently to reduce vibration. The derived differential equations contain three displacements, which are one transverse displacement and two tangential displacements of the two face layers. The modal expansion technique then yields the forced solution being characterized of six generalized coordinates for each circumferential wave number n. The closed form solutions to the harmonic traveling point loads are solved and discussed. Examples for various cases are illustrated as well and the influences of the viscoelastic core and the face layers on dynamic response and damping effects are particularly discussed. The results show that a very thin VEM can suppress the vibration very effectively.

The buckling of honeycomb sandwich circular rings

A theoretical solution is given for the overall buckling and wrinkling of sandwich circular rings when subjected to a uniform radial pressure loading. The core is in the form of a honeycomb material, and the faces can be made from laminated fibre reinforced plastics, which exhibit coupling between bending and stretching. The elasticity equations for both the orthotropic core and faces are satisfied, and it is found that the problem is governed by four simultaneous differential equations for the displacements of the faces. A solution is obtained by assuming simple sine and cosine functions for these displacements. Minimum critical pressures are found numerically and results are given which show the dependence on face thickness, core thickness and mean radius. A procedure is suggested for finding approximate solutions for sandwich rings subjected to more general loading conditions.

Finite Elements for Curved Sandwich Beams

SummaryThe formulation of curved finite elements to represent a two-dimensional circular sandwich ring with honeycomb core and laminated faces is investigated. Assumed stress hybrid and equilibrium methods are found to be easier to employ in this case than the displacement approach. Using these methods, an element stiffness matrix is developed. The approximations of membrane faces and an infinite core normal stiffness are then used to develop simpler elements. Test cases show that these assumptions may become invalid, but that they are adequate for most practical cases where the core thickness to radius ratio and the face thickness to core thickness ratio are both low.

Mechanical impedance of damped three-layered sandwich rings.

Experimental and theoretical results of the radial driving point mechanical impedance of three-layered sandwich rings are presented and discussed. The composite sandwich rings, subjected to a time-harmonic radially-concentrated load, are made up of two thin elastic layers with a thin viscoelastic damping core between them. The effects of the operational temperature and frequency ranges concerned on the viscoelastic material properties are taken into account. Experimental data are compared well with the theoretical predictions over a wide frequency range of interest. Resonant conditions for lobar bending modes are also given.

In-Plane Transient Response of a Sandwich Ring to Radial Impact

The transient response of sandwich rings to concentrated radial impulsive loads is studied on the basis of a Timoshenko-type theory. Solutions are obtained by integral transform techniques and also by representation in series of normal modes. Numerical results show that the ring's response is predominantly flexural and is highly dependent on the ratio of the extensional stiffness to the shear stiffness. It is also found that as the core stiffness decreases relative to the facing-sheet stiffnesses, the influence of the thickness-to-radius ratio becomes more important.

Transient Response of a Sandwich Ring to Radial Impact

The transient response of sandwich rings to concentrated radial impulsive loads is studied on the basis of a Timoshenko-type theory. Solutions are obtained by integral transform techniques and also by representation in a series of normal modes. Numerical and experimental results show that the ring's response is predominantly flexural and is highly dependent on the ratio of the extensional stiffness to the shear stiffness. It is also found that, as the core stiffness decreases relative to the facing-sheet stiffnesses, the influence of the thickness-to-radius ratio becomes more important.

Wave Propagation in a Sandwich Ring

The propagation of small-amplitude free harmonic waves in an elastic sandwich ring is studied by using a Timoshenko-type theory, which takes into account the effects of radial shear deformation, rotatory inertia, and extension of the neutral axis. The form of the equations of motion is the same for both homogeneous and sandwich rings, but the range of values for the parameters involved in the latter case can lead to qualitative changes in the wave propagation characteristics of the system. It is shown that the ratio of the ring's extensional stiffness to its shear stiffness has an important influence on the frequencies and group velocities of sandwich rings. When this ratio becomes large, two of the three modes of wave propagation become less dispersive. Numerical examples are presented and discussed.

Wave Propagation in a Sandwich Ring

Using a Timoshenko-type theory for a sandwich ring, an equation is developed giving the phase velocities for the different types of wavemotion present. Approximations to the theory are given when the neutral axis is inextensible. A further approximation is given when the wavelength of the motion is long and the curvature is slight, by neglecting the rotatory inertia term in the Timoshenko theory. Taking typical values for sandwich materials, curves are drawn showing the effects of these approximations. Curves showing group velocity versus wavenumber are also given. The transient response of a ring to concentrated loads representing a delta function and a step function in time is studied using this theory. Three different wave-propagation speeds are noted for the wavefronts and an asymptotic expression valid near each wavefront is given.