Deflection Slope Research Articles

Limits of agreement method for comparing TSD and FWD measurements

This article uses the limits of agreement (LOA) method to compare the falling weight deflectometer (FWD) and the traffic speed deflectometer (TSD), two pavement structural evaluation devices. The TSD measures deflection slope, whereas the FWD measures deflection. For this reason, measurements were converted to the surface curvature index (SCI) and the base damage index (BDI), which can be obtained from each device. The SCI and BDI agreement between the two devices was then evaluated. Although the relationship between the calculated SCI and BDI using both equipments is reasonably close to the line of equality, there is a significant variation and a bias in this relationship. For example, for an average SCI or BDI value of 300 μm, the bias was 30 μm (FWD values lower than TSD values), and the LOA was 380 μm.

Optimal Averaging and Localized Weak Spot Identification of Traffic Speed Deflectometer Measurements

One of the main difficulties that arise during the analysis of continuous deflection measurements is the reduction of measurement variability (noise) without smoothing out important features or adversely affecting the true spatial variability, and no objective method has been available. The use of the smoothing spline determined through minimization of the generalized cross-validation criteria is proposed for denoising traffic speed deflectometer (TSD) deflection slope measurements. The generalized cross-validation criteria find the optimal trade-off between variance and bias so that the estimated smoothing spline gives the best smoothing fit (weighted moving average fit) for minimum mean square error with respect to the true deflection slope values. The smoothing spline fit allows the construction of a confidence interval for the true deflection slope as well as the use of outlier detection methods for identifying localized weak spots, such as those caused by cracks or weak joints in jointed concrete sections. In each case, the distribution and standard deviation of the measurement error is needed. It is shown that TSD measurement error distribution is well represented by a normal distribution, and an outlier robust method is used to evaluate the standard deviation. Example data analysis uses computer-generated data to simulate a smoothly varying deflection slope profile as well as a homogeneous profile with localized weak spots and uses actual TSD deflection slope measurements. The results show that smoothing spline denoising can significantly improve the interpretation of TSD deflection slope measurements.

Slope of the Out‐of‐Plane Deflection Measurement of Composite Sandwich Plate With a Fully Potted Insert by Using Digital Phase‐Shifting Shearography

Abstract: A digital shearographic (DS) technique is a tool well‐suited for precision strain measurement and is a non‐destructive testing technology. But the fringe patterns of DS have not so high sensitivity due to the limitation of CCD camera resolution. Therefore a phase‐shifting technique is incorporated into DS and demonstrated to yield fringe patterns with good quality. The main purpose of this study is to set‐up a measuring system of digital phase‐shifting shearography (DPSS) to measure slope of the out‐of‐plane deflection of sandwich plate with a fully potted insert. The present system includes piezoelectric transducer, servo controller, Michelson shearing mechanism, image processing system and loading system. The four‐step phase shifting method is used to obtain phase map and then the phase expansion is proceeded by Macy algorithm to obtain the slope of the out‐of‐plane deflection of honeycomb sandwich plate with insert/potting material. Finally, comparing the slope of the out‐of‐plane deflection of DPSS with that of DS shows 2 to 7% difference of slope of deflection exhibiting.

A parametric study on the dynamics of urban transit maglev vehicle running on flexible guideway bridges

The purpose of this study is to develop a numerical model for a dynamic interaction analysis of an actively controlled maglev vehicle and flexible guideway structure. In addition, an investigation is performed of the effect of vehicle and guideway characteristics on dynamic responses of low and medium speed maglev systems. Dynamic governing equations are derived by combining the 5-dof maglev vehicle model, the modal properties of guideway structures and a LQG controller for electromagnetic suspension. An investigation is then carried out on the effect of vehicle models, vehicle speed, irregularity, guideway deflection ratio, span length, span continuity and damping ratio on dynamic responses of the relatively low speed maglev vehicle and guideway structures. From the numerical simulation, it is found that the air gap of the vehicle is strongly affected by vehicle speed, tract roughness and guideway deflection ratio. In particular, the guideway deflection ratio is the most influential parameter which governs the air gap. Continuous span girders are found to be effective in reducing the air gap because of its smooth curvature and small deflection slope near the support. However, the span length and damping ratio of the guideway structure do not affect the air gap. The overall dynamic magnification factor of the guideway girder is not severe compared to the traditional wheel type vehicle.

Buckling analysis of a composite shell with multiple delaminations based on a higher order zig-zag theory

A new three-node triangular shell element based on a higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The baseline higher order zig-zag composite shell theory for multiple delaminations has been developed in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of the surface including twisting curvatures can be described in an exact manner since the developed shell finite element is based on the geometrically exact surface representation. It is therefore possible to apply the present finite element formulation to the composite structures with arbitrary shaped multiple delaminations, general layup configurations and arbitrary boundary conditions. The slopes of deflections are included as independent degrees of freedom, which require the normal slope continuities between element interfaces. The nonconforming shape functions of Specht's three-node triangular plate bending element are employed to interpolate out-of-plane displacements. The developed element passes the bending and twisting patch tests for flat surface configurations. The element is then used to analyze the linear buckling problem of composite cylindrical shells with multiple delaminations. Throughout the numerical examples, it is demonstrated that the developed shell finite element is numerically efficient because it has minimal nodal degrees of freedom to describe the composite shells having multiple delaminations. The finite element realization of a higher order zig-zag shell theory with multiple delaminations can be served as a powerful numerical tool to analyze the complicated shell structures for the critical buckling loads as well as the corresponding mode shapes.

Dynamics of a hollow rubber-metal laminate structure

Transverse frequencies of vibration of a hollow cylindrical rubber‐metal laminate structure, subject to a mean pressure difference across the cylinder wall will be presented. Extending Timoshenko beam theory to model such a structure, we use two independent observations most often credited to J. A. Haringx: First, an analogy exists between an axially loaded Euler beam and a pipe without axial loading but subject to internal pressure, and second, for this type of rubber‐metal laminate structure, the transverse component of the axial load acts perpendicular to the bending slope, rather than the deflection slope. When dynamics of the pressurized laminate are considered, theory predicts somewhat unexpected changes in the resonance frequency of transverse bending modes as a function of mean pressure difference across the structure. Experimental results illustrating static buckling behavior will be shown for both positive and negative pressure differentials, corresponding to the analogous axial loading cases of buckling in both compression and tension. In applications where oscillatory pressures are present across the structure, the unusual tuning curve has implications for prediction of parametric instabilities.

Value of Noncontact Mapping for Identifying Left Ventricular Scar in an Ovine Model

We assessed the hypothesis that "virtual electrograms" from a noncontact mapping system (EnSite 3000) could be used to localize myocardial scar. Myocardial infarctions were induced in sheep by inflating an angioplasty balloon in the left anterior descending coronary artery for 3 hours. Scar mapping was performed on 8 sheep without inducible ventricular tachycardia by use of the noncontact mapping system and a 256-channel contact mapping system. Transmural mapping needles were inserted into myocardial regions that were (1) scarred, (2) peripheral to the scar, and (3) distant from the scar. Unipolar electrograms were exported from both systems and analyzed on a personal computer workstation. The percentage of myocardial scarring at each needle site was assessed histologically. Pearson's correlation was used to assess the degree of association between various electrogram characteristics and the presence of myocardial scarring. The only noncontact electrogram characteristic that showed any association with the presence of myocardial scarring was the negative slope duration (contact, r=0.62, P<0.001; noncontact, r=0.23, P=0.004). The other electrogram characteristics studied were electrogram maximal deflection (contact, r=0.38, P<0.001; noncontact, r=0.03, P=0.75) and minimal slope (contact, r=0.42, P<0.001; noncontact, r=0.05, P=0.54). Noncontact electrograms do not reliably identify ventricular scar. Alternative strategies such as importing computed tomography images into the geometry should be used when scar localization is important.

Spatiotemporal dynamics of reentrant ventricular tachycardias in canine myocardial infarction: pharmacological modulation.

During the transition from a slow to rapid depolarization rhythm, rate-dependent sodium channel blockade develops progressively and increases from beat to beat under procainamide but more abruptly under lidocaine. We investigated the consequences of such differences on the dynamic course and stability of reentrant tachycardias at their onset. Procainamide and lidocaine were infused to equipotent plasma concentrations in canines with three-day-old myocardial infarction. We measured the activation times (ms) and maximum slopes of negative deflections in activation complexes (absolute value: /-dV/dt(max)/ in mV/ms) in 191 unipolar electrograms recorded from ischemically damaged subepicardial muscle during programmed stimulation inducing reentrant tachycardias. Procainamide caused a greater reduction in /-dV/dt(max)/ than did lidocaine in the responses to basic stimulation, and it favored the occurrence of cycle length prolongation at tachycardia onset as the /-dV/dt(max)/ decreased progressively in successive beats. This resulted in conduction block and tachycardia termination in three of eight preparations. In contrast, lidocaine caused a greater depression in /-dV/dt(max)/ in response to closely coupled extrastimuli, but /-dV/dt(max)/ remained constant or even improved thereafter, and none of the tachycardias terminated spontaneously under lidocaine (n = 9). However, the reentrant circuits remained spatially unstable, and lidocaine favored the occurrence of cycle length dynamics displaying constant or decreasing trends. This study supports the notion that cycle length dynamics at tachycardia onset are determined by the properties of the reentrant substrate and their pharmacological modulation.

Trapping of surface waves by porous and flexible structures

The trapping of surface waves by submerged vertical porous and flexible barriers near the end of a semi-infinitely long channel of finite depth is investigated. The barrier configurations include a bottom-touching barrier and a surface-piercing barrier. In the case of a bottom-touching barrier, the barrier is clamped at the bottom and is free at the upper end. While in the case of a surface-piercing barrier, the barrier is clamped by a structure above the free surface and is free at the lower end which is inside the water. By matching the velocity and pressure along the barrier and along the gap and using the edge conditions at the end points, systems of linear equations are obtained. In the case of a surface-piercing barrier, the deflection, slope of deflection, the bending moment and the shear force acting on the barrier are assumed to be continuous at the interaction point where the barrier and the free surface meet each other. The reflection coefficients are obtained and discussed for various wave conditions, geometrical settings, and barrier properties. The hydrodynamic force and the overturning moment on the barrier and the deflection of a flexible barrier are calculated and analysed for different cases.

Digital transform processing of carrier fringe patterns from speckle-shearing interferometry

The Fourier transform (FT) and the wavelet transform (WT) methods are used to process the fringe carrier pattern resulting from speckle-shearing inteferometry, in which the carrier frequency is modulated by deformation of a bending plate. Both the amount and the sign of the first derivative of the out-of-plane displacement can be obtained by these two transform techniques in the whole field. Phase distributions of the deflection slope are compared, which shows the wavelet analysis gives a better solution with noise reduction and without deficiency of filter window choice as for that in the Fourier transform. Meanwhile, the phase values in the path along the maximum WT amplitudes give a direct map of the second derivative patterns of the deflection, which presents the same image as that given by the shearing subtraction of the phase patterns from the inverse Fourier transformation but avoids the processing of unwrapping for the phase reconstruction.

Constitutive equations of symmetrical triple layer piezoelectric benders

Piezoelectric triple layer benders, with a structure of two piezoelectric top and bottom layers sandwiched by a non-piezoelectric elastic central layer, are one of the most commonly used piezoelectric devices. In this paper, we present the derivation of the constitutive equations of a symmetrical triple layer piezoelectric bender under different excitation conditions. The constitutive equations are presented by a 4x4 matrix with an external moment M, an external tip force F, a uniform load p, and an applied electric voltage V as the extensive parameters, with the generated tip angular deflection (slope) alpha, tip deflection delta, volume displacement v, and electric charge Q as the internal parameters. Further analysis on the electromechanical behavior of the triple layer piezoelectric bender can be made on the constitutive equations.

Generalized conforming triangular elements for plate bending

AbstractBased on the modified principle of potential energy, three triangular thin‐plate elements with nine degrees of freedom (LZ1, LZ2 and LZ3) are derived by using compatibility conditions for nodal deflection at each node and generalized compatibility conditions for average deflection and average normal slope along each side of the element. These generalized conforming elements are low‐order and high‐precision elements which pass the patch test. When overall considerations of accuracy, simplicity and reliability are taken into account, these new elements are the best 9‐DOF triangular thin‐plate elements currently available.

Second-order phenomena in strain measurement by speckle techniques

The contrast degradation due to tilt between exposures limits the amount of tilt, the number of fringes and the spatial resolution. The effect was derived quantitatively and verified experimentally. Mutual influences between system parameters cause ambiguity in the measurement results. The main effects are imaginary displacement resulting from combined deflection and initial slope, and imaginary strain resulting from deflection. These effects were demonstrated experimentally. Formulas were developed that enable the designer of the experiment to choose the desirable parameters of the set-up. They point out the difficulties in using the method in ‘field measurements’, primarily because of the finite dimensions of the lens and the photographic plate.

Infrared two-dimensional acoustooptic deflector using a tellurium crystal

The first single element 2-D acoustooptic (2DAO) laser beam deflector using a tellurium crystal was designed and fabricated for laser wavelength applications from 5 to 20 microm. The giant values of the figure of merit M associated with these two AO interactions equal to 285,000 x 10(-15) s(3)/kg, are between 2 and 3 orders of magnitude higher than germanium, the next best AO material for 10.6 microm. This latter value indicates that acoustic power densities inside the crystal of the order of 0.1 W/mm(2) are sufficient to diffract 100% of the incident light. The experimental data confirm the predicted 13 degrees /25 MHz deflection slope. The theoretical amplitude and frequency modulation characteristics of the 2DAO deflector are also evaluated.

Mechanical properties of endodontic broaches and effects of bead sterilization

Endodontic broaches from three manufacturers were tested in torsion and bending both as received and after hot bead sterilization. Products were found to be labeled nonuniformly as to size and handle color. Initial (as-is) testing of the same labeled size or handle color showed significant differences among manufacturers. Heating affected both torsion and bending. In most cases, torsion and angular deflection at torsional failure, slope of torsion versus angular deflection at 45 degrees, bending moment at 45 degrees, and slope of bending moment versus angular deflection at 10 degrees were increased compared to the as-is state. The need for a specification for broaches is confirmed. Endodontic broaches from three manufacturers were tested in torsion and bending both as received and after hot bead sterilization. Products were found to be labeled nonuniformly as to size and handle color. Initial (as-is) testing of the same labeled size or handle color showed significant differences among manufacturers. Heating affected both torsion and bending. In most cases, torsion and angular deflection at torsional failure, slope of torsion versus angular deflection at 45 degrees, bending moment at 45 degrees, and slope of bending moment versus angular deflection at 10 degrees were increased compared to the as-is state. The need for a specification for broaches is confirmed.

The Determination of Mechanical Parameters and Residual Stresses for Thin Films Using Micro-Cantilever Beams

AbstractA method for determining mechanical parameters and residual stresses for thin films is described. Multi-layer cantilever beams (LPCVD SiNx/thermal SiO2) are fabricated utilizing standard IC processing technologies and micromachining of silicon. The elastic response of the beams to imposed deflections is then measured using a Nanoindenter, a sub-micron hardness testing machine. The elastic constants of the nitride films are calculated from the force vs. deflection slope and known elastic constants of the thermal SiO2 and silicon. By measuring the curvature of the multi-layer cantilever beams with a scanning electron microscope after successive etching of the LPCVD nitride films, average and differential stresses in the films were calculated.

Influence of in-plane displacement in single-aperture and double-aperture speckle shearing interferometry

The difference in the information obtained by the single-aperture and the double-aperture methods in speckle shearing interferometry is discussed. It is shown theoretically and experimentally that the use of a single aperture is essential for obtaining the proper value of the deflection slope of an object: the single-aperture method enables us to obtain the proper slope distribution regardless of the direction of displacement. With the double-aperture method, however, proper distribution can be obtained only for displacement in a particular direction, and this introduces an error into the slope measurement.

The perturbation parameter in the problem of large deflection of clamped circular plates

In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads.

Continental Shelf Circulation Induced by a Moving, Localized Wind Stress

A linear, two-dimensional model of a rotating, stratified fluid is constructed to investigate the circulation induced by a moving, localized line of surface stress. This model is used to analyze the effect of moving cold fronts on continental shelf circulation. The nature of the induced circulation depends on the relative magnitude of the translation speed of the storm and the natural internal wave speed. If the surface stress moves slower than the internal wave speed. the disturbance is quasi-geostrophic and moves with the storm. If the storm moves faster than the internal wave speed, two sets of internal-inertial waves are produced. One set of waves is forced by the surface forcing and travels at the speed of the storm. Another set of waves is produced by reflection of the directly forced waves from the coastal wall. We conclude that free surface deflection (slope) is responsible for the low-frequency. quasi-geostrophic currents due to passing cold fronts. The internal response is composed of tree inertia waves which radiate away from the coast, leaving no residual circulation. Model results are compared to current meter data collected during the passage of a cold front over the South Atlantic Bight on 9 January 1978. The inertia frequency response observed at the mooring is reproduced by the model calculation.

Finite element model for dynamic analysis of Timoshenko beam

This paper presents for the first time a finite element model with nodal degrees of freedom which can satisfy all the forced and natural boundary conditions of a Timoshenko beam. The mass and stiffness matrices of the element are derived from kinetic and strain energies by assigning polynomial expressions for total deflection and bending slope. The superiority of this element is illustrated by comparing the results with those given by various investigators using other element models.