Rigid Cap Research Articles

Oscillations of captured spherical drop of viscous liquid

The complex frequencies of a viscous spherical drop where part of the free surface is embedded in a rigid spherical cap of the same radius have been determined as a function of the cap angle and the free surface tension parameter. With increasing cap angle α , the oscillation frequencies and decay magnitudes increase. This is also true for liquid drops of larger surface tension parameters. It also could be found, as has been found previously for a free floating sphere of viscous liquid, that the oscillations may cease to exist for certain diameters and low surface tension parameters, a fact not present in the treatment of frictionless liquid. In such cases, the captured liquid globule performs just an aperiodic motion. Three different liquid systems have been considered. In addition, the response of a captured spherical drop due to harmonically forced vertical translational excitation of the cap has been determined. Only a liquid sphere embedded in a spherical cap of the same radius has been evaluated numerically. The results reveal that for the mode n = 1 the geometry of a liquid sphere in a spherical cap of equal radius represents—depending on the magnitude α of the cap—for small surface tension parameters σ * ≡ σ a ρ / η 2 , a stable configuration, while for large σ * -values the spherical geometry is unstable, indicating that for those large cases the free liquid surface assumes a different geometry.

Constant Force Shaking of a Group of Four Drilled Shafts

A foundation system comprising a group of four drilled shafts, each 750 mm in diameter by 5.5 m long, constructed in silt/sand/gravel with a rigid pile cap, was subjected to constant force shaking by a servo-hydraulic actuator reacting against a heavy anchor block. Forces of up to 150 kN peak to peak were achieved with resulting displacements of up to 2 mm and accelerations of up to 0.5g. The displacement response of the pile cap was measured over a range of frequencies from 2 to 12 Hz and the resonant frequency and damping ratio were determined for three different levels of excitation. The foundation behaved much like a simple harmonic oscillator with a natural frequency of approximately 10 Hz. This resonant frequency was found to decrease slightly with increasing excitation while the damping ratio decreased slightly. Values for generalized stiffness, mass, and damping for an equivalent simple harmonic oscillator were back-calculated from the test data. The results of this study suggest that it may be possible to predict values for generalized mass and damping a priori by using simple empirical methods.

Oscillations of captured spherical drop of frictionless liquid

The natural frequencies and mode shapes have been investigated for a frictionless spherical liquid globule where part of the free surface is embedded in a spherical cap of the same radius. Five different liquid systems have been considered. With increasing cap angle α and higher modes n, the natural frequencies increase. The different mode shapes exhibit a drastic change of frequencies. In addition, the response of the captured spherical drop due to harmonically forced translational excitation of the rigid cap has been determined for the two major directions.

Subunit γ-Green Fluorescent Protein Fusions Are Functionally Incorporated into Mitochondrial F1F0-ATP Synthase, Arguing Against a Rigid Cap Structure at the Top of F1

We have investigated the question of the presence of a cap structure located at the top of the F(1) alpha(3)beta(3) hexamer of the yeast mitochondrial F(1)F(0)-ATP synthase complex. Specifically, we sought to determine whether the putative cap has a rigid structure and occludes the central shaft space formed by the alpha(3)beta(3) hexamer or alternatively whether the cap is more flexible permitting access to the central shaft space under certain conditions. Thus, we sought to establish whether subunit gamma, an essential component of the F(1) central stalk housed within the central shaft space and whose N and C termini would both lie beneath a putative cap, could be fused at its C terminus to green fluorescent protein (GFP) without loss of enzyme function. The GFP moiety serves to report on the integrity and location of fusion proteins containing different length polypeptide linkers between GFP and subunit gamma, as well as being a potential occluding structure in itself. Functional incorporation of subunit gamma-GFP fusions into ATP synthase of yeast cells lacking native subunit gamma was demonstrated by the ability of intact complexes to hydrolyze ATP and retain sensitivity to oligomycin. Our conclusion is that the putative cap structure cannot be an inflexible structure, but must be of a more flexible nature consistent with the accommodation of subunit gamma-GFP fusions within functional ATP synthase complexes.

Three-dimensional asymptotic stress field in the vicinity of the circumferential line of intersection of an inclusion and plate surface

A heretofore unavailable asymptotic solution pertaining to the stress field in the neighborhood of the circumferential line of intersection of an inclusion and one of the bounding (top or bottom) surfaces of a plate, subjected to far-field extension/bending (mode I), inplane shear-twisting (mode II) and torsional (mode III) loadings, is presented. A local orthogonal curvilinear coordinate system (ρ,φ,θ), is selected to describe the local deformation behavior of the afore-mentioned plate in the vicinity of the afore-mentioned circumferential line of intersection. One of the components of the Euclidean metric tensor, namely g33, is approximated (ρ/a<<1) in the derivation of the kinematic relations and the ensuing governing system of three partial differential equations. Four different combinations of boundary conditions are considered: (i) free bounding surface of the plate and uncapped inclusion (free-free), (ii) bounding surface of the plate clamped by an infinitely rigid washer and inclusion covered with an infinitely rigid cap (clamped-clamped), (iii) free bounding surface of the plate and inclusion covered with an infinitely rigid cap (free-clamped), and (iv) bounding surface of the plate clamped by an infinitely rigid washer and uncapped inclusion (clamped-free). For dissimilar inclusion and plate (matrix) materials, the asymptotic stress fields in the vicinity of the line of intersection of an inclusion and the bottom (or top) surface of a plate, subjected to far-field mode I and mode II loadings, are singular, in all cases of the above described boundary conditions. In the case of the mode III (torsional) loading, the asymptotic stress fields are singular only for the free-clamped (or clamped-free) boundary condition. Numerical results presented include the effect of the ratio of the shear moduli of plate and inclusion materials, and also Poisson's ratios on the computed lowest eigenvalues.

Pile foundation in karstic limestone terrain: a geotechnical constraint and its solution

ABSTRACT&#x0D; The karstic limestone terrain poses complex geotechnical problems, as there are many uncertainties in terms of position and dimension of cavities, sinkholes, pinnacles, and overhangs developed in it. The study deals with the 6.5 km long Ampang­ Kuala Lumpur Elevated Highway over the rivers Kelang and Ampang in Malaysia. The large-diameter bored piles and cast in-place piles were constructed for this purpose.&#x0D; The toll plaza area is underlain by karstic limestone. In that area, the piles were located in rows extended as columns connected by crosshead whereas they were provided in pile groups of 2, 3, 4, or 5 connected by a rigid pile cap elsewhere. An instrumented test pile was load tested using static method and calibrated with site investigation results. To design the friction piles and end bearing piles, direct methods (viz. exploratory drilling and rock probes) and indirect methods (viz. resistivity survey and transient electromagnetic survey) were adopted. Based on lithologs, the piles were designed using the safety factor of 2 and 3. The rock probe results were used for designing the rock socket length of the end bearing piles.&#x0D; There was much variation between the designed and encountered rock head levels as revealed during the time of excavation. In such cases, the geotechnical design of end bearing piles was reviewed. As in most of the cases, rock probe holes were inclined (as they slid over a rock cliff, overhang, or pinnacle) giving rise to wrong information of rock head levels. To solve this problem at site, a new integrated approach was evolved considering the 3D subsurface topography of rock head level of the area, position and dimension of karstic features, rock mass classifications, and bearing capacity calculation. Based on the above parameters and other measures (underpinning, micropiling, grouting etc.), the piles were designed and load tested.

A simplified nonlinear approach for pile group settlement analysis in multilayered soils

A simplified analytical method is presented for nonlinear analysis of the behaviour of pile groups under vertical loads. A hyperbolic approach is adopted to describe the nonlinear relationship between the shaft shear stresses and the relative shaft displacements along a confined disturbed soil zone around a pile-soil interface. Outside the disturbed zone, the soils are assumed to behave in a linearly elastic state. By adopting the elastic closed-form analytical solution to approximate the displacement fields around a single vertically loaded pile, and the principle of superposition, a new transfer function is presented for analysis of the behaviour of pile groups in multilayered soils. Furthermore, with a simplified assumption of separating the shaft from the base interaction factors for individual piles in a pile group, a highly effective iterative procedure is developed to examine the nonlinear load–displacement behaviour of a pile group up to the failure state. Comparisons of the load–settlement responses for a number of well-instrumented field pile group test results are given to demonstrate the effectiveness and accuracy of the proposed analytical method. The computed nonlinear responses of the pile group compare favourably with measured field test results under both rigid and flexible pile cap conditions.Key words: pile groups, interface, transfer function, settlement analysis, nonlinear behaviour.

Intraplate deformation in western Europe deduced from an analysis of the International Terrestrial Reference Frame 1997 (ITRF97) velocity field

Although tectonic deformation in western Europe is essentially concentrated in the Appenines and Alpine (Alps, Pyrenees) mountain ranges, several large historical and instrumentally recorded earthquakes (M&gt;6) are known in the supposedly “stable” part of Europe. Because of its accuracy and internal consistency at a global scale, the International Terrestrial Reference Frame 1997 (ITRF97) velocity field allows testing of intraplate rigidity in western Europe at a millimeter per year level. Using the full statistical information available on the ITRF97 velocities, we identify a subset of sites located in central Europe that satisfies a rigid cap rotation with residual velocities &lt;1 mm/yr and therefore provide a stable Europe reference frame (SERF). In this reference frame we find residual velocities at European ITRF sites that are consistent with known active tectonic features. We identify a northward motion at sites located in Italy, with internal deformation of the Adriatic block rather than rigid plate motion and a westward motion of the westernmost part of Europe of the order of 1–2 mm/yr relative to central Europe. The relative motion of the Adriatic block and western Europe agrees with the current extension known in the Tyrrhenian sea and the Apennines. In central Europe, we find active deformation &lt;1 mm/yr in the eastern Alps and western Carpathians. In the Alpine range our results indicate E‐W extension across the western Alps and N‐S compression across the central and eastern Alps, in agreement with the strain regime deduced from seismotectonic observations. In Belgium and the Netherlands we find residual velocities of 1–1.5 mm/yr to the northwest at all the sites, most likely accommodated along the Upper and Lower Rhine Graben structures. An important outcome of this study is the identification of internal deformation of the order of 1–2 mm/yr in an area usually interpreted as “stable” Europe. This result should be further checked as new, denser, and more accurate space geodetic data sets with longer observation time spans, become available for Europe.

Seismic Behavior of Micropiles: Used as Foundation Support Elements: Three-Dimensional Finite Element Analysis

Presented is a three-dimensional finite element analysis of the seismic behavior of micropiles used in engineering applications, such as construction in earthquake areas, and seismic retrofitting of structure foundation and retaining systems. It is composed of two parts. The first is concerned with analysis of the seismic behavior of a single micropile supporting a superstructure; results obtained with three-dimensional finite element modeling are compared to those obtained from a simplified model based on the Winkler approach. The second part includes a study of the seismic behavior of groups of micropiles. Numerical simulations are conducted to study the variation of the group effect with the variation of micropile spacing, number of micropiles, and the position of the micropile in the group. Analysis of results of numerical simulations shows that the presence of the superstructure induces significant inertial effect, which causes a high increase in the bending moment in the upper part of micropiles; the inertial effect depends mainly on the loading frequency with respect to the fundamental frequency of the soil layer and that of the superstructure. A group effect is observed in groups of micropiles connected by a rigid cap. The group effect depends mainly on micropile spacing, number of micropiles, and position of micropiles in the group. Results show an increase in moment at the head of micropiles with the increase of the micropile spacing (presence of inertial effect) and a concentration of seismic loading on corner micropiles.

A variational approach for the analysis of pile group–pile cap interaction

This paper presents a variational approach for the analysis of pile groups having rigid pile caps in contact with the ground. The pile groups are assumed to be embedded in an isotropic elastic half-space. Both the deformations and shear stresses of group piles are each represented by a finite series with a set of undetermined constants, and Mindlin's solution is applied to evaluate the interaction among the piles, pile cap and soil. The response of the pile group–pile cap system is determined by the use of the principle of minimum potential energy. Comparison of the present solutions with other numerical methods has shown good agreement. The computed results are also shown to be in favourable agreement with field measurements.

Rigid Calix[4]arene as a Building Block for the Synthesis of New Quaternary Ammonium Cation Receptors

The synthesis of a new series of neutral hosts derived from the head-to-head linkage of two calix[4]arene-bis(crown-3) units fixed in the rigid cone conformation with bridges of different nature and length is described. The binding abilities of the new receptors towards tetraalkylammonium and N-methylpyridinium cations of different size and shape in CDCl3 solution have been extensively investigated by 1H NMR spectroscopy. In this solvent, ion-pairing is found to have a strong effect on the binding efficiency. In the more polar CDCl3/CD3CN solvent mixture, a substantial decrease in the Kass values is observed, which can be attributed, in part, to CD3CN competing for the binding sites of the host. In all cases, the double calixarenes 2, 7, 8, and 9 have been found to exhibit efficiencies much higher than that of the corresponding rigid calix[4]arene-bis(crown-3) 1. The bridge present in these double calix[4]arenes dictates the orientation and distance between the two rigid caps and thus represents a new control element in determining the efficiency and selectivity of binding. The orientation and span imposed by the different bridges to the two calixarene subunits is responsible for the different binding modes observed with N-methylpyridinium and isomeric N-methylpicolinium cations.

A model for red blood cell motion in bifurcating microvessels

A theoretical model is developed for red blood cell motion in a diverging microvessel bifurcation, where the downstream branches are equal in size but receive different flows. The model is used to study migration of red cells across streamlines of the underlying flow, due to particle shape and flow asymmetry. Effects of cell–cell interactions are neglected. Shapes of flowing red cells are approximated by rigid spherical caps. In uniform shear flows, such particles rotate periodically and oscillate about fluid streamlines with no net migration. However, net migration can occur in non-uniform flows due to the particles’ lack of fore-aft symmetry. A nonuniform flow field representative of a bifurcation is developed: flow bounded by two parallel plates, and divided by a cylindrical post. Significant migration is found to occur only with a nonuniform and asymmetric distribution of upstream orientations. The model suggests that the assumption made in previous models of bifurcations, that red cells follow fluid streamlines, is justified if cells approach the bifurcations with random orientations.

The molecular basis of CD 1 ‐mediated presentation of Iipid antigens

The CD1 family of proteins mediates a newly described pathway for presentation of lipids and glycolipids for specific recognition by T cells. All four of the known human CD1 proteins (CD1a, CD1b, CD1c and CD1d) as well as murine CD1d have now been shown to mediate T-cell recognition of lipid or glycolipid antigens. These antigens include naturally occurring foreign glycolipids from intracellular pathogens or synthetic glycolipids that are related in structure to mammalian glycolipids. The CD1b and CD1d-presented antigens differ in their fine structures but reveal a general motif in which a rigid hydrophilic cap is bound to two aliphatic hydrocarbon chains. Different T-cell populations recognize individual antigens without cross-reactivity to closely related antigen structures or CD1 isoforms, documenting the complexity and fine specificity of CD1-mediated T-cell responses. Mapping of the molecular determinants of recognition for CD1b and CD1d-presented antigens reveals that T cells discriminate the fine structure of the hydrophilic cap of the antigen, but both the length and structure of the lipid chains may be altered without loss of recognition. This pattern of lipid antigen recognition may be accounted for by a simple molecular mechanism of presentation that parallels the known mechanism for presentation of peptides, but solves the special problems related to the hydrophobic chemical nature of the lipid antigens. We propose that CD1 binds antigen by accommodating the two lipid tails within the hydrophobic groove of its two membrane distal domains, positioning the rigid hydrophilic cap of the antigen on the solvent-exposed surface of the CD1 protein, where it can directly contact the T-cell antigen receptor. This model provides a molecular basis for recognition of a new and diverse set of T-cell antigens contained within the lipid bilayers of cellular membranes.

Boundary element analysis of capped and uncapped pile groups

A conventional application of the Boundary Element Method (BEM) to the elastic analysis of sizeable capped pile groups rapidly leads to large computational execution time. This paper develops a BEM formulation for solving such problems more efficiently, and with adequate precision, in which the traction along each pile in a group is represented by a polynomial function. With this approach the tractions need only a few nodes along the shaft to be represented and all the integrals involved can be analytically evaluated. The pile is supposed to be rigid but the formulation can be easily extended to the inclusion of its flexibility. Only vertical displacement compatibility between the soil, the piles and the smooth, rigid cap is enforced. The cap–soil interface is divided into triangular elements, each with three nodes, across which contact pressures vary linearly. Numerical results are presented for single piles and for pile groups, with and without ground-contacting caps. In all these examples the pile loads and group stiffnesses are close to those obtained from other formulations.

Numerical and experimental study of finite-amplitude standing waves in a tube at high sonic frequencies

Finite-amplitude standing waves in an air-filled tube are studied numerically and experimentally. The standing wave is excited at one end of the rigid-walled tube and a rigid cap is assumed at the other end. The one-dimensional nonlinear second order wave equation is solved numerically using a finite element algorithm based on the Bubnov–Galerkin method. Viscous and thermal losses at the walls of the tube are taken into account. An experimental setup is developed for the study of standing waves at high sonic frequencies. The acoustic field is measured along the tube axis with a fine calibrated probe. Experimental data of pressure distributions for the fundamental frequency (9.5 kHz) and the second harmonic (19 kHz) are compared with the numerical results, as a function of the tube length.

Resonance interactions of waves in an ice channel

The properties of low-amplitude surface waves propagating in an ice channel are investigated in the shallow-water approximation. The ice cover is modelled either by a rigid cap or by a thin elastic plate floating on a liquid surface. It is shown that an ice channel is a waveguide for surface waves. The dispersive properties of the natural oscillations of the liquid in the channel are investigated. The resonance velocities of the motion of the load on the channel surface, at which the amplitude of the forced oscillations of the liquid increases without limit in time, are determined. The decay instability of the natural oscillations of high harmonics with respect to waves of the first mode is demonstrated. The process is described by the standard equations for non-linear three-wave interaction. The investigations lead to the conclusion that critical modes of motion of a boat are realizable in an ice channel.

Piezoelectric response of a three coaxial cylinder model

Abstract The response of a 1-1-3 transducer is modeled as three coaxial cylinders with the center cylinder as the piezoelectric element. Different combinations of properties for the outer two cylinders have been used to determine the maximum hydrostatic response. For a 20v/o PZT-5H composite with a 25v/o soft filler in a 55v/o hard tube the maximum predicted effective dh° is 110 pC/N. The maximum dh° for a 1–3 composite modeled by two coaxial cylinders is 90 pC/N while the base ceramic is 45 pC/N. A maximum effective gh° of 20 mVm/N is also predicted for the same combination of materials. The d33° and d31° moduli are maximized for soft fillers and tubes, but have values of 380 and 135 pC/N respectively for the combination of materials that maximize the dh° value. A rigid end cap attached to the ceramic, which bears the axial load, gives a five fold predicted increase in the dh° response. The d33° and d31° moduli are again maximized for soft fillers and tubes, but have values of 590 and 210 pC/N, respectively, for the combination of materials that maximize the dh° value in the above case.

Active Control of Structurally Radiated Sound from an Enclosed Finite Cylinder

A long, thin aluminum cylinder was configured with two rigid end caps and in strumented with piezoceramic actuators and either microphone or polyvinylidene fluoride (PVDF) structural sensors for narrow-band active structural acoustic control. The input disturbance to the cylinder was generated with a shaker attached by a stinger, and all tests were performed in an anechoic chamber. In the first series of tests, the cylinder was driven with a shaker attached to the end cap, exciting the "accordion mode" of the structure. Upon applying control and using PVDF sen sors, significant levels of global sound attenuation, approximately 25 dB on-resonance and 15 dB off- resonance, were observed in the acoustic field. In both the on-resonance and off-resonance test cases, three control actuators were required to achieve the stated levels of sound attenuation due to interaction between the accordion modes and the cylinder modes. In the second series of tests, the cylinder was driven radially with a shaker to excite higher order cylinder modes. Control was ap plied with six piezoelectric actuators wired to control selected circumferential modes in the first test case, and the actuators were chosen in a helical pattern about the cylinder in the second test case. In the latter case, approximately 10 dB of global sound attenuation was observed in the acoustic field when using microphone error sensors, while results obtained when implementing the PVDF error sensors yielded little sound attenuation in controlling the cylinder modes.

Piezoelectric composites of the 1–3 type used as underwater sound sources

Piezoelectric composites with 1–3 connectivity used in the thickness mode have traditionally used a relatively rigid polymer as the matrix encapsulant to force uniform surface motion. Finite element analyses are employed to show that these rigid polymers constrain the piezoelectric rod motion sufficiently to reduce rod displacements by 50% or more. The magnitude of the reduction depends upon the ceramic volume fraction, the rod aspect ratio, rod spacing, and of course the stiffness of the matrix. Further, it has been shown [W. A. Smith, ONR Tech Note (31 May 1991)] that the hydrostatic response, rather than the thickness mode alone, controls the performance of 1–3 composites used as underwater sound sources. It is shown in this paper that efficient lightweight underwater sound sources can be produced by: (1) using lightweight rigid cap plates and a very compliant matrix polymer to produce uniform surface motion comparable to the motion of the unconstrained rod, and (2) using rigid edge strips bonded to the cap plates to prevent edge motion, thereby effectively limiting the transmitting response to the thickness mode. [Work supported by ONR.]

Active structural acoustic control of cylinder radiation with piezoelectric actuators and PVDF sensors

An aluminum cylinder, measuring 1.22 m long with a wall thickness of 2.77 mm and a diameter of 0.254 m, was configured with two rigid end caps and instrumented with piezoceramic actuators and polyvinylidene fluoride (PVDF) sensors for narrow-band active structural acoustic control. All tests were performed in an anechoic environment. In the first test case, the cylinder was driven with a shaker on one end cap, exciting the ‘‘accordion mode’’ of the structure. Significant levels of sound radiation (90 dB) from the end caps were observed in this mode of vibration and the piezoceramic actuators were more than sufficient for controlling the structural acoustic response, yielding 35 dB of global attenuation. In the second test case, the cylinder was driven radially to excite the (0,1) mode of the cylinder as well as higher-order modes to demonstrate the capability of the piezoceramic actuators for controlling the structural acoustic response of the ‘‘breathing mode’’ as well as higher-order cylinder modes. Results from this preliminary study suggest that piezoceramic actuators and PVDF sensors are viable transducers for creating an adaptive/sensory structure for active structural acoustic control on cylinders. [Work supported by ONR.]