Stable Deflection Research Articles

Elastoplastic plate shakes down under repeated impulsive loadings

When subjected to repeated dynamic impacts at identical load level, a metallic monolithic beam/plate may reach a stable state wherein measurable deformation ceases (i.e., shakedown in elastic state) after undergoing a sequence of elastoplastic deformations, which has been termed as “pseudo-shakedown” (P-S) (Jones, 1973, Shen and Jones, 1992). While the response of a single beam/plate under repeated low-velocity impacts has been thoroughly studied, its dynamic behavior under high-velocity impacts, such as explosive or alternating impulsive loads, is difficult to measure experimentally, due mainly to high costs and setup challenges. In the current study, the method of metallic foam projectile impact was employed to produce repeated impulsive loadings on a fully-clamped elastoplastic monolithic plate made of L907A (a Chinese standard shipbuilding steel). Its dynamic responses, including mid-point deflection versus time histories, final deflections, and deformation modes after each impact, were systematically measured. The phenomenon of dynamic shakedown was observed. To further explore this phenomenon, the method of finite elements (FE) was employed to simulate the repeated impulsive impact test, and its prediction accuracy was validated against experimental results. Unlike an elastoplastic (e.g., steel) monolithic plate subjected to repeated low-velocity impacts, which exhibits zero plastic energy dissipation in the P-S (pseudo-shakedown) state, the same plate under repeated high-velocity impacts shows a small level of plastic energy dissipation in the P-S state, mainly due to more extreme loading conditions. The initial impact momentum, yield strength, and tangent modulus of the material the plate is made of significantly affect both the stable deflection in the P-S state and the number of impacts needed to reach it, while the elastic modulus has limited influence. A modified dimensionless impulse loading number, accounting for the strain-hardening effect, is proposed. An approximately linear relationship between stable deflection in the P-S state and impulsive loading is found in dimensionless form.

A Laser-Induced TIG Arc Narrow-Gap Welding Technique for TC4 Titanium Alloy Thick Plates Based on the Spatial Position Control of Laser, Arc and Filler Wire

In this paper, a novel laser-induced TIG arc narrow-gap welding technology is proposed for thick plates of TC4 titanium alloy. The feasibility of achieving high-performance welding joints is investigated by adjusting the spatial deviation position of the laser, arc, and filler wire. The results exhibited remarkable capabilities. By augmenting the laser-arc malposition, a stable deflection of the arc can be achieved, resulting in enhanced heat input to the sidewall adjacent to the laser side and improved fusion capability. Moreover, an inclined weld can be obtained through increased malposition between the filler wire and arc, which helps to improve interlayer fusion and suppress porosity defects. This method, involving alternating bilateral offsets between passes, successfully achieved narrow-gap welding of 24 mm-thick TC4 titanium alloy with an average tensile strength of 880.68 MPa (equivalent to 95.05% of base material strength). Therefore, this technology exhibits promising potential as an automated welding technique for achieving high-quality narrow-gap welding in titanium alloys.

Half-wavelength-crystal channeling of relativistic ions and its possible application for a beam deflection

The simulation of both angular distributions and trajectories of relativistic ions at channeling in the system of fan-oriented half-wavelength Si and W crystals is performed. The results of our calculations have revealed a stable deflection efficiency with respect to the change of the ion energy, A/Z ion ratio, or crystal type.

Large eddy simulation of flow around two side-by-side circular cylinders at Reynolds number 3900

This paper investigates the flow dynamics around two circular cylinders in a side-by-side arrangement with different spacing ratios (T/D, T is the center-to-center cylinder spacing and D is the diameter) under a subcritical Reynolds number condition (Re = 3900). A three-dimensional (3D) numerical model was developed with Large Eddy Simulation (LES) technique. The model was well validated against published data of flow around a single cylinder at Re = 3900. Numerical simulations were conducted for flow around two side-by-side circular cylinders with T/D = 1.2, 1.5, 1.75, 2, 2.5, 3, 3.5, and 4. Based on the LES results, three wake regimes were identified: single bluff body regime (T/D = 1.2), biased flow regime (T/D = 1.5–2), and parallel vortex streets regime (T/D = 2.5–4). In the single bluff body regime with T/D = 1.2, the stable deflection of gap flow is also observed which indicates that there may exist a transition state from the single bluff body regime to the biased flow regime. In biased flow regime, the pairing and merging process of the outer vortices with the inner vortices are analyzed. The occurrence of the flip-flopping phenomenon is found to be related to the merging tendency between gap-side vortices in narrow wake region and free-flow-side vortices in wide wake region, and the relative phase of gap side vortices in transient state. In the parallel vortex streets regime, the phase relation of the vortex shedding process was analyzed. The time proportions of the in-phase mode and anti-phase mode are found to be varied with spacing ratio. As the spacing ratio increases, the wakes behind the cylinders lose their dependency on the anti-phase mode. The results of the present study were compared with the existing results at other Reynolds numbers. It is found that vortex shedding manner during the flip-over transitions is closely related to the spacing ratios and is independent of the Reynolds number.

Performance Evaluation of Traffic Speed Deflectometer Based on Virtual Standard Test Road

It is challenging to find actual standard test roads (ASTRs) to evaluate the measuring performance of the Traffic Speed Deflectometer (TSD), leading to misjudgment of its evaluation results. To address this issue, a method to construct virtual standard test roads (VSTRs) using in-service roads is proposed. Firstly, the principle of TSD based on the Laser-Doppler effect to measure pavement deflection is introduced, and the shortcomings of traditional evaluation methods are reviewed and summarized. Secondly, an adaptive construction method for VSTRs is proposed based on the K-means clustering algorithm. It layers the Falling Weight Deflectometer (FWD) measurements on in-service roads and reconstructs them as virtual roads with stable deflections but different ranges. Thirdly, two new indexes, the coefficient of variation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$CV_{k}$ </tex-math></inline-formula> and the influence coefficient of speed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ICS_{k}$ </tex-math></inline-formula> , are proposed to replace the traditional indexes, such as repeatability and correlation coefficient. Finally, the feasibility of evaluating TSD performance based on VSTRs and the new indexes is verified by experiments. Results show that the newly constructed VSTRs solve the problem that the ASTRs are challenging to obtain, reducing the experimental requirements for evaluating TSD, and the new indexes achieve an efficient and scientific evaluation of TSD.

Generation of buckling and wrinkling in elastic films: The effect of initial imperfection.

The symmetry breaking that is induced by initial imperfection (e.g., geometry or material inhomogeneity and out-of-plane disturbance) is a necessary condition for film buckling. However, the effect of initial imperfection on the buckling behavior is still not clear cut. Herein, given an elastic substrate-free circular film subjected to in-plane compressive stress and arbitrary initial imperfection, evolution of the deflection morphology is numerically studied and theoretically analyzed. Specifically, a two-dimensional spatial spectrum analysis is adopted to acquire the deflection morphology's dominant wavelength, which is combined with the maximum absolute deflection to characterize the deflection patterns. Before the so-called critical instability, the film under compression is found to go through a transition stage. Overall, the deflection increment in this stage is negligible except approaching the critical state. However, the dominant wavelength is found to be continuously growing (or decreasing) rather than suddenly appears upon reaching the so-called critical state, and, interestingly, such growth is found to be independent of the intensity and pattern of the initial imperfection if the same initial dominant wavelength is guaranteed. In the discussion, for both the transition and buckling stages, evolution laws of the deflection amplitude and wavelength are established analytically and found to agree well with the numerical results. This research clearly presents the actual evolution process of wrinkling morphology from linear in-plane deformation with small stable deflection to out-of-plane instability with large deflection, which deepens the cognition of instability behavior of films and provides a basis for related applications such as high-precision mechanical characterization.

High Speed Microactuators for Low Aspect Ratio High Speed Micro Aircraft Surfaces

This paper covers a class of actuators for modern high speed, high performance subscale aircraft. The paper starts with an explanation of the challenges faced by micro aircraft, including low power, extremely tight volume constraints, and high actuator bandwidth requirements. A survey of suitable actuators and actuator materials demonstrates that several classes of piezoceramic actuators are ideally matched to the operational environment. While conventional, linear actuation of piezoelectric actuators can achieve some results, dramatic improvements via reverse-biased spring mechanisms can boost performance and actuator envelopes by nearly an order of magnitude. Among the highest performance, low weight configurations are post-buckled precompressed (PBP) actuator arrangements. Analytical models display large deflections at bandwidths compatible with micro aircraft flight control speed requirements. Bench testing of an example PBP micro actuator powered low aspect ratio flight control surface displays +/−11° deflections through 40 Hz, with no occupation of volume within the aircraft fuselage and good correlation between theory and experiment. A wind tunnel model of an example high speed micro aircraft was fabricated along with low aspect ratio PBP flight control surfaces, demonstrating stable deflection characteristics with increasing speed and actuator bandwidths so high that all major aeromechanical modes could be easily controlled. A new way to control such a PBP stabilator with a Limit Dynamic Driver is found to greatly expand the dynamic range of the stabilator, boosting the dynamic response of the stabilator by more than a factor of four with position feedback system engaged.

A Handheld Haptic Robot for Large-Format Touchscreens

This paper presents a handheld surface robot built around a single steerable wheel that can direct the user's motion or modulate the interaction forces with the touchscreen. Steering control is used to render spatial constraints on a touchscreen surface in coordination with the displayed visual objects. A force sensor using flexures and Hall effect sensors is integrated into the device design for economic two-dimensional force sensing. The flexure array and device frame are built a single part out of nylon using the selective laser sintering additive manufacturing process. The position and orientation of the device are supplied by touchscreen eliminating the need for a grounded external frame and resulting in a more compact form. Potential applications include upper limb stroke therapy, gaming, and touchscreen accessibility for disabled individuals. The device exerts up to 10.6 ± 1.0 N of friction force and has a 90° peak-to-peak sine tracking bandwidth of 7.0 Hz. The embedded force sensor has a 6.5% full-scale force magnitude error with an average 4.0° load angle error. The device tracks force-sensitive compliant haptic boundaries with a stiffness range between 0.1 N/mm and 2.0 N/mm. Also demonstrated is stiffness tracking of a 0.175 N/mm boundary (near maximum stable deflections) with mean error 9.4% of the maximum desired deflection.

Study on dynamic actuation in double microcantilever-based electrostatic microactuators with an in-house experimental set-up

This paper investigates the effect of dynamic excitation and its utility for enhancement of stable displacement range for a double cantilever-based electrostatic microactuator. A coupled electromechanical problem has been formulated using Galerkin method and solved considering dynamic actuation. The effect of excitation frequency is analyzed thoroughly to estimate the maximum stable displacement range of the actuator. Extensive studies illustrate that for suitable ac voltage–frequency combination, the maximum stable tip deflection for the cantilevers can be obtained even in the range of 50% to 90% of initial gap under specific damping. Such inherent dynamic characteristic of the actuator has been exploited here to achieve larger travel range. Furthermore, the theoretical observation has been experimentally demonstrated with a double microcantilever-based structure fabricated using silicon-on-insulator based process. The experimentation has been carried out using a developed in-house set-up. The major advantage in the present study is that unlike reported literature, the extended range has been achieved here without any additional complex circuits or design modifications. The proposed concept can be extended further to improve the displacement range of other microstructures toward different applications.

Mechanical properties of ambient cured high strength hybrid steel and synthetic fibers reinforced geopolymer composites

Ambient cured geopolymer offers significant promise to the construction world as a possible alternative to ordinary Portland cement (OPC). However, as a member of the ceramic family, geopolymers exhibit extremely brittle behaviour. The inclusion of short discrete fibers is an effective way to enhance their ductility. In this research, a series of fiber combinations and volume fractions between steel fibers with end-hooked or spiraled and synthetic fibers (made of high strength polyethylene (HSPE)) were incorporated in a high strength ambient cured geopolymer matrix. The performance of synthesized geopolymer composites was compared in terms of fresh and hardened state properties, such as workability, uniaxial compressive strength, modulus of elasticity, Poisson's ratio, flexural tensile strength, energy absorption capacity and post-peak residual strength etc. The interfacial bond between the spiral steel fiber and the geopolymer matrix as well as fiber distribution in the composites were assessed through individual fiber-pull out tests and physical examination of the cast samples, respectively. The test results show that the addition of fibers significantly improved the load carrying capacity of the composites under flexure load, i.e. increased from 3.89 MPa to 11.30 MPa together with an improved behaviour in compression. In general, all fiber reinforced composites displayed a stable deflection hardening response and multiple-cracking failure mode. Moreover, among composites with different fiber volume fractions, the composite having 1.60% steel+0.40% HSPE showed the highest ultimate flexure strength, correspondingly the highest energy absorption capacity. The individual fiber pull-out test curves ascertained a strong bonding between the geopolymer mortar and spiral-steel fiber.

Study of synergistic toughening in a bimodal epoxy nanocomposite

Toughening of epoxy with different types of modifiers produces a bimodal blend that might show better fracture resistance in comparison with single-modified ones. In this research, bimodal epoxy formulations including mixtures of glass microsphere and silica nanoparticles are explored for possible synergistic toughening. The influence of composition on the glass transition temperature ( Tg), tensile characteristics, and fracture toughness ( KIC) is investigated. Interestingly, a synergism in fracture toughness is observed when mixtures of modifiers were incorporated. For the fixed overall modifier content, KIC is higher when the volume fraction of glass microsphere is lesser than the volume fraction of nanosilica. Fractographs reveal that glass microsphere increases the toughness of epoxy matrix by crack pinning/bridging mechanisms. On the other hand, nanosilica enhances the toughness by increase in plastic deformation via shear banding/particle debonding. Interestingly, the origin of synergistic toughness in bimodal epoxies is the interaction between the glass microsphere and crack-tip damage zone which provides comprehensive stable crack deflection within the nanosilica-toughened epoxy. This mechanism results in a mixed-mode crack growth that reduces the strain energy release rate in bimodal formulations.

Nonlinear nonlocal analysis of electrostatic nanoactuators

This study investigates the small scale effect on the nonlinear static and dynamic response of a capacitive nanoactuator subjected to a DC voltage. The nanoactuator is modeled as a Euler–Bernoulli beam cantilever beam and beam clamped at its both ends. The model accounts for residual stresses, initial deflection, the von Kármán nonlinear strains, and the electrostatic forcing. The intermolecular forces, such as the Casimir and von der Waals forces, are also included in the model. Hamilton’s principle is used to derive the governing equations and boundary conditions for the nonlinear Euler–Bernoulli beam with Eringen’s nonlocal elasticity model. The differential quadrature method (DQM) is used to solve the governing equations. First, the static response to an applied DC voltage is determined to investigate the influence of scale effect on the maximum stable deflection and pull-in voltage of the device. Next, the dynamic response is investigated by examining the small scale effect on the natural frequencies of the system.

Nonlinear analysis of microstructure-dependent functionally graded piezoelectric material actuators

In the present work, a nonlinear thermo-electro-mechanical response of functionally graded piezoelectric material (FGPM) actuators is investigated. The theoretical formulation is based on the Timoshenko beam theory with the von Kármán nonlinearity (in the form of midplane stretching), and a microstructural length scale is incorporated by means of the modified couple stress theory. A power-law distribution of thermal, electrical, and mechanical properties through beam thickness (or height) is assumed. The governing equations are derived using the principle of virtual displacements. A displacement finite element model of the theory is developed, and the resulting system of nonlinear algebraic equations is solved with the help of Newton's iteration method. Numerical results are presented for transverse deflection as a function of load parameters and out-of-plane boundary conditions. The parametric effects of microstructural length scale parameter, power-law index of the material distribution across the thickness, boundary conditions, beam geometry, and applied actuator voltage on the beam response are investigated through various numerical examples. The results reveal the existence of bifurcation (or critical states) for certain types of in-plane loads. For other load types, including out-of-plane loads, the beam undergoes a unique and stable deflection path that does not contain any critical point.

Feedback-stabilized deformable membrane mirrors for focus control

This paper describes a method to extend the range of motion of a deformable, continuous membrane mirror beyond the limit of open-loop electrostatic instability through feedback control. The feedback scheme employs capacitive sensing directly at the mirror actuation electrodes and is based on frequency modulation of a coupled ring oscillator using a differential measurement technique. Analysis of the system shows that the range of stable deflection depends on the relative dynamics of the device and the feedback control circuitry. Experimental results demonstrate stable closed-loop deflection of our silicon nitride membrane test device to 69% of the air gap and confirm the dependence of the maximum stable displacement on overall loop dynamics.

Nonlinear large deflection of nanopillars fabricated by focused ion-beam induced chemical vapor deposition using double-cantilever testing

Nanopillars with nanosized diameter and microsized length can be constructed by chemical vapor deposition using a focused ion beam. For a pillar consisting of an outer amorphous carbon ring and an inner gallium core, we performed the bending tests using the unique double-cantilever specimen joining two pillars together by an electron-beam deposition technique in a scanning electron microscope. The precise load-deflection curves indicate that the pillars have a nonlinear softening region after the linear response as the diameter increases. However, pillars finally become extremely hardened at the large deformation. Thus, the pillar intrinsically possesses much more flexibility and stable deflection for bending than expected, in contrast to tensile deformation. The bending rigidity obtained by the infinitesimal deflection corresponds well to that by the resonance vibration tests reported so far. It also certifies that the proposed double-cantilever bending method can maintain high accuracy for the nanoscaled materials testing.

The pull-in behavior of electrostatically actuated bistable microstructures

The results of theoretical and experimental investigation of an initially curved clamped–clamped microbeam actuated by a distributed electrostatic force are presented. Reduced-order Galerkin and consistently constructed lumped models of the shallow Euler–Bernoulli arch were built and verified by numerical analysis, and the influence of various parameters on the stability was investigated. Due to the unique combination of generic mechanical and electrostatic nonlinearities, the voltage–deflection characteristic of the device may have two maxima implying the existence of sequential snap-through buckling and pull-in instability and of bistability of the beam. The first critical voltage can be higher or lower than the second one, while the stable deflections are significantly larger than in a straight beam. The minimal initial elevation required for the appearance of the snap-through in the electrostatically actuated beam is smaller than in the case of uniform deflection-independent loading; a closed-form approximation of this elevation was evaluated. The devices were fabricated from silicon on insulator (SOI) wafer using deep reactive ion etching and in-plane responses were characterized by means of optical and scanning electron microscopy. Model results obtained for the actual dimensions of the device were in good agreement with the experimental data.

Amorphous &lt;inline-formula&gt;&lt;math display="inline" overflow="scroll"&gt;&lt;mrow&gt;&lt;mi&gt;TiAl&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/inline-formula&gt; films for micromirror arrays with stable analog deflection integrated on complementary metal oxide semiconductors

Large micromechanical mirror arrays (MMA) with analog pixel deflection integrated onto active CMOS address circuitry require both high-quality planar reflective optical surfaces and a stable deflection versus voltage characteristic. However, for implementing a CMOS-compatible surface-micromachining process, certain obstacles such as a restricted thermal budget and a limited selection of suitable materials must be overcome. Amorphous TiAl is presented as a new actuator material for monolithical MEMS integration onto CMOS circuitry. TiAl films may be sputter deposited at room temperature, have an x-ray amorphous structure, and a low stress gradient. The glassy structure and high melting point make TiAl less vulnerable to stress relaxation, which makes TiAl an ideal spring material. One-level actuators with TiAl or Al-TiAl-Al structural layers and two-level actuators with separate TiAl spring and Al-alloy mirror layers were fabricated and tested with respect to their drift stability. The stability of TiAl-based actuators was found to be superior in comparison to one-level Al-alloy actuators. Two-level actuators with TiAl hinges emerge as the most promising design.

How many ECG leads are required for in vivo studies in safety pharmacology?

This article explains the principles of electrocardiography, and explains how it is used by Safety Pharmacology, with a focus on the requirement for multiple leads in Safety Pharmacology assessment. Electrocardiography as used in different disciplines (e.g., medicine, anesthesiology, physiology, and pharmacology/toxicology/safety pharmacology) has different requirements for the number of electrodes applied. Electrodes may be placed at an infinite number of points on the body, and voltages (electrocardiograms) may be registered between/among them. However in safety pharmacology there is little evidence that more than 1—or at most 3—lead(s) is (are) required to provide all of the information that might be present using an infinite number. This is based upon (1) the biophysics of the heart as a generator of electrical potential/voltage, (2) the fact that most properties of electrophysiology affected adversely by drugs are expressed as changes in durations, and (3) experience. A single, unipolar lead (V 3) recorded from the left sternal border at the 5th intercostal space possesses minimal artifact and large, stable deflections. This lead allows for accurate measurement of heart rate and rhythm, durations of component deflections (e.g., PQ, QRS, QT), and J-point deviation. A greater number of leads seldom or never yield additional information that detects liabilities. Commonly voltages recorded between the right thoracic and left pelvic limbs (lead II) provides information similar to lead V 3, and lead II is easier to apply, and produces voltages with less artifact and similar to those in lead V 3. A lead measuring the voltage between the left and right thoracic limbs (lead I) along with lead II allows for estimating orientation of vectors in the frontal plane, but knowledge of these vectors seldom or never indicates liability of a test article.

Charge control of parallel-plate, electrostatic actuators and the tip-in instability

Controlling the charge, rather than the voltage, on a parallel-plate, electrostatic actuator theoretically permits stable operation for all deflections. Practically, we show that, using charge control, the maximum stable deflection is limited by 1) charge pull-in, in which the actuator snaps due to the presence of parasitic capacitance and 2) tip-in, in which the rotation mode becomes unstable. This work presents a circuit that controls the amount of charge on a parallel-plate, electrostatic actuator. This circuit reduces the sensitivity to parasitic capacitance, so that tip-in is the limiting instability. A small-signal model of the actuator is developed and used to determine the circuit bandwidth and gain requirements for stable deflections. Four different parallel-plate actuators have been designed and tested to verify the charge control technique as well as to verify charge pull-in, tip-in, and the bandwidth requirements. One design travels 83% of the gap before tip-in. Another design can only travel 20% of the gap before tip-in, regardless of whether voltage control or charge control is used.

Design of large deflection electrostatic actuators

Electrostatic, comb-drive actuators have been designed for applications requiring displacements of up to 150 /spl mu/m in less than 1 ms. A nonlinear model of the actuator relates the resonant frequency and the maximum stable deflection to the actuator dimensions. A suite of experiments that were carried out on deep reactive ion etched (DRIE), single-crystal silicon, comb-drive actuators confirm the validity of the model. Four actuator design improvements were implemented. First, a folded-flexure suspension consisting of two folded beams rather than four and a U-shaped shuttle allowed the actuator area to be cut in half without degrading its performance. Second, the comb teeth were designed with linearly increasing lengths to reduce side instability by a factor of two. Third, the folded-flexure suspensions were fabricated in an initially bent configuration, improving the suspension stiffness ratio and reducing side instability by an additional factor of 30. Finally, additional actuation range was achieved using a launch and capture actuation scheme in which the actuator was allowed to swing backward after full forward deflection; the shuttle was captured and held using the backs of the comb banks as high-force, parallel-plate actuators.