Search results for: Non-contact displacement measurement

Authors: Giorgi Bregadze

Abstract:

Tourism is the most viable and sustainable economic development option for Georgia and one of the main sources of foreign exchange earnings. Events are considered as one of the most effective ways to attract foreign visitors to the country, and, recently, the government of Georgia has begun investing in this sector very actively. This article stresses the necessity of research based economic policy in the tourism sector. In this regard, it is of paramount importance to measure the economic effects of the events which are subsidized by taxpayers’ money. The economic effect of events can be analyzed from two perspectives; financial perspective of the government and perspective of economic effects of the tourism administration. The article emphasizes more realistic and all-inclusive focus of the economic effect analysis of the tourism administration as it concentrates on the income of residents and local businesses, part of which generate tax revenues for the government. The public would like to know what the economic returns to investment are. In this article, the methodology used to describe the economic effects of UEFA Super Cup held in Tbilisi, will help to answer this question. Methodology is based on three main principles and covers three stages. Using the suggested methodology article estimates the direct economic effect of UEFA Super cup on Georgian economy. Although the attempt to make an economic effect analysis of the event was successful in Georgia, some obstacles and insufficiencies were identified during the survey. The article offers several recommendations that will help to refine methodology and improve the accuracy of the data. Furthermore, it is very important to receive the correct standard of measurement of events in Georgia. In this caseü non-ethical acts of measurement which are widely utilized by different research companies will not trigger others to show overestimated effects. It is worth mentioning that to author’s best knowledge, this is the first attempt to measure the economic effect of an event held in Georgia.

Keywords: Biased economic effect analysis, expenditure of local citizens, time switchers and casuals, UEFA super cup.

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Authors: Omar.S. Qaftan, T. T. Sabbagh

Abstract:

This paper studies the free-field response by adopting a flexible membrane container as soil boundary for experimental shaking table tests. The influence of the soil container boundary on the soil behaviour and the dynamic soil properties under seismic effect were examined. A flexible container with 1/50 scale factor was adopted in the experimental tests, including construction, instrumentation, and determination of the results of dynamic tests on a shaking table. Horizontal face displacements and accelerations were analysed to determine the influence of the container boundary on the performance of the soil. The outputs results show that the flexible boundary container allows more displacement and larger accelerations. The soil in a rigid wall container cannot deform as similar as the soil in the real field does. Therefore, the response of flexible container tested is believed to be more reliable for soil boundary than that in the rigid container.

Keywords: Soil, boundary, seismic, earthquake, ground motion.

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Authors: Tariq T. Darabseh

Abstract:

The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.

Keywords: Finite element method, thermal stresses, Green-Lindsay theory, functionally graded material.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Functionally Graded Beam, Free Vibration, Elastic Foundation, Engesser-Timoshenko Beam Theory.

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Authors: T. Strobl, D. Raps, M. Hornung

Abstract:

In this study, the adhesion of ice to solid substrates with different surface properties is compared. Clear ice, similar to atmospheric in-flight icing encounters, is accreted on the different substrates under controlled conditions. The ice adhesion behavior is investigated by means of a dynamic vibration testing technique with an electromagnetic shaker initiating ice de-bonding in the interface between the substrate and the ice. The results of the experiments reveal that the affinity for ice accretion is significantly influenced by the water contact angle of the respective sample.

Keywords: Contact angle, dynamic vibration measurement, ice adhesion, interfacial shear stress.

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Authors: Ahmad Z., Othman S. Z., Md Yunus B., Mohamed A.

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According to the masonry standard the compressive strength is basically dependent on factors such as the mortar strength and the relative values of unit and mortar strength. However interlocking brick has none or less use of mortar. Therefore there is a need to investigate the behavior of masonry walls using interlocking bricks. In this study a series of tests have been conducted; physical properties and compressive strength of brick units and masonry walls were constructed from interlocking bricks and tested under constant vertical load at different eccentricities. The purpose of the experimental investigations is to obtain the force displacement curves, analyze the behavior of masonry walls. The results showed that the brick is categorized as common brick (BS 3921:1985) and severe weathering grade (ASTM C62). The maximum compressive stress of interlocking brick wall is 3.6 N/mm2 and fulfilled the requirement of standard for residential building.

Keywords: Interlocking brick, soil-cement brick, masonry wall, compressive strength, eccentricities

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Authors: H.K. Abd El-Maksoud, H.H. Keyser

Abstract:

Competitive relationships among Bradyrhizobium japonicum USDA serogroup 123, 122 and 138 were screened versus the standard commercial soybean variety Williams and two introductions P1 377578 "671" in a field trial. Displacement of strain 123 by an effective strain should improved N2 fixation. Root nodules were collected and strain occupancy percentage was determined using strain specific fluorescent antibodies technique. As anticipated the strain USDA 123 dominated 92% of nodules due to the high affinity between the host and the symbiont. This dominance was consistent and not changed materially either by inoculation practice or by introducing new strainan. The interrelationship between the genotype Williams and serogroup 122 & 138 was found very weak although the cell density of the strain in the rhizosphere area was equal. On the other hand, the nodule occupancy of genotypes 671 and 166 with rhizobia serogroup 123 was almost diminished to zero. . The data further exhibited that the genotypes P1 671 and P1 166 have high affinity to colonize with strains 122 and 138 whereas Williams was highly promiscuous to strain 123.

Keywords: B. japonicum serogroups, Competition, Host restriction, Soybean genotype.

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Authors: Z. Haddad, C. Abid, O. Rahli, O. Margeat, W. Dachraoui, A. Mataoui

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The present study aims to measure the volumetric mass density of NiPd-heptane nanofluids synthesized using a one step method known as thermal decomposition of metal-surfactant complexes. The particle concentration is up to 7.55g/l and the temperature range of the experiment is from 20°C to 50°C. The measured values were compared with the mixture theory and good agreement between the theoretical equation and measurement were obtained. Moreover, the available nanofluids volumetric mass density data in the literature is reviewed.

Keywords: NiPd nanoparticles, nanofluids, volumetric mass density, stability.

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Authors: Iliana Marinova, Valentin Mateev

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In this paper a computer system for electromagnetic properties measurements is designed. The system employs Agilent 4294A precision impedance analyzer to measure the amplitude and the phase of a signal applied over a tested biological tissue sample. Measured by the developed computer system data could be used for tissue characterization in wide frequency range from 40Hz to 110MHz. The computer system can interface with output devices acquiring flexible testing process.

Keywords: Electromagnetic properties, human tissue, bioimpedance, measurement system.

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Authors: K. Kamalanand, S. Srinivasan

Abstract:

Analysis of blood vessel mechanics in normal and diseased conditions is essential for disease research, medical device design and treatment planning. In this work, 3D finite element models of normal vessel and atherosclerotic vessel with 50% plaque deposition were developed. The developed models were meshed using finite number of tetrahedral elements. The developed models were simulated using actual blood pressure signals. Based on the transient analysis performed on the developed models, the parameters such as total displacement, strain energy density and entropy per unit volume were obtained. Further, the obtained parameters were used to develop artificial neural network models for analyzing normal and atherosclerotic blood vessels. In this paper, the objectives of the study, methodology and significant observations are presented.

Keywords: Blood vessel, atherosclerosis, finite element model, artificial neural networks

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Authors: Jae-Neung Lee, Sung-Bum Pan, Keun-Chang Kwak

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This paper describes an analysis of Yacht Simulator international trends and also explains about Yacht. The results are summarized as follows. Attached to the cockpit are sensors that feed -back information on rudder angle, boat heel angle and mainsheet tension to the computer. Energy expenditure of the sailor measure indirectly using expired gas analysis for the measurement of VO2 and VCO2. At sea course configurations and wind conditions can be preset to suit any level of sailor from complete beginner to advanced sailor.

Keywords: Trends Analysis, Yacht Simulator, Sailing.

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Authors: S. A. Naeini, A. Khalili

Abstract:

Nowadays, tunnels with different applications are developed, and most of them are related to subway tunnels. The excavation of shallow tunnels that pass under municipal utilities is very important, and the surface settlement control is an important factor in the design. The study sought to analyze the settlement and also to find an appropriate model in order to predict the behavior of the tunnel in Tehran subway line-3. The displacement in these sections is also determined by using numerical analyses and numerical modeling. In addition, the Adaptive Neuro-Fuzzy Inference System (ANFIS) method is utilized by Hybrid training algorithm. The database pertinent to the optimum network was obtained from 46 subway tunnels in Iran and Turkey which have been constructed by the new Austrian tunneling method (NATM) with similar parameters based on type of their soil. The surface settlement was measured, and the acquired results were compared to the predicted values. The results disclosed that computing intelligence is a good substitute for numerical modeling.

Keywords: Settlement, subway line, FLAC3D, ANFIS method.

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Authors: Paras Ram, Vikas Kumar

Abstract:

An attempt has been made to study the effect of rotation on incompressible, electrically non-conducting ferrofluid in porous medium on Axi-symmetric steady flow over a rotating disk excluding thermal effects. Here, we solved the boundary layer equations with boundary conditions using Neuringer-Rosensweig model considering the z-axis as the axis of rotation. The non linear boundary layer equations involved in the problem are transformed to the non linear coupled ordinary differential equations by Karman's transformation and solved by power series approximations. Besides numerically calculating the velocity components and pressure for different values of porosity parameter with the variation of Karman's parameter we have also calculated the displacement thickness of boundary layer, the total volume flowing outward the z-axis and angle between wall and ferrofluid. The results for all above variables are obtained numerically and discussed graphically.

Keywords: Ferrofluid, magnetic field porous medium, rotating disk.

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Authors: M. Amelsakhi, A. Sohrabi-Bidar, A. Shareghi

Abstract:

One of the most important issues about the structural damages caused by earthquake is the evaluating of the spectral response of the site on which the construction is built. This fact has demonstrated during many earlier earthquakes and many researchers’ reports have concerned with it. According to these reports, features of the site materials and geometry of the ground surface are considered the main factors. This study concentrates on the specific form of topographies like hills. Assessing of spectral responses of different points on the hills and beside demonstrates considerable differences between 1D and 2D methods of geotechnical analyses. A general trend of amplifications on the top of the hills and de-amplifications near the toe of the hills has been appeared within the acceleration, velocity and displacement response spectrums of horizontal motion. Evaluating of spectral responses of different sizes of the hills revealed that as much as the hill-size enlarges differences between spectral responses of 1D and 2D analyses transfers to longer range of periods and becomes wider.

Keywords: Topography effect, Amplification ratio, Response spectrum.

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Authors: Ayudhia P. Gusti, Semin

Abstract:

It is known that total operating cost of a vessel is dominated by the cost of fuel consumption. How to reduce the fuel cost of ship so that the operational costs of fuel can be minimized is the question that arises. As the basis of these kinds of problem, sailing speed determination is an important factor to be considered by a shipping company. Optimal speed determination will give a significant influence on the route and berth schedule of ships, which also affect vessel operating costs. The purpose of this paper is to clarify some important issues about ship speed optimization. Sailing speed, displacement, sailing time, and specific fuel consumption were obtained from shipping log data to be further analyzed for modeling the speed optimization. The presented speed optimization model is expected to affect the fuel consumption and to reduce the cost of fuel consumption.

Keywords: Maritime transportation, reducing fuel, shipping log data, speed optimization.

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Authors: Jer-Rong Chang

Abstract:

The flexible follower response of a translating cam with four different profiles for rise-dwell-fall-dwell (RDFD) motion is investigated. The cycloidal displacement motion, the modified sinusoidal acceleration motion, the modified trapezoidal acceleration motion, and the 3-4-5 polynomial motion are employed to describe the rise and the fall motions of the follower and the associated four kinds of cam profiles are studied. Since the follower flexibility is considered, the contact point of the roller and the cam is an unknown. Two geometric constraints formulated to restrain the unknown position are substituted into Hamilton-s principle with Lagrange multipliers. Applying the assumed mode method, one can obtain the governing equations of motion as non-linear differential-algebraic equations. The equations are solved using Runge-Kutta method. Then, the responses of the flexible follower undergoing the four different motions are investigated in time domain and in frequency domain.

Keywords: translating cam, flexible follower, rise-dwell-falldwell, response

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Authors: Devdutt, M. L. Aggarwal

Abstract:

In this paper, passenger ride comfort issues are studied taking active quarter car model with three degrees of freedom. A hybrid fuzzy – PID controller with coupled rules (HFPIDCR) is designed for vibration control of passenger seat. Three different control strategies are considered. In first case, main suspension is controlled. In second case, passenger seat suspension is controlled. In third case, both main suspension and passenger seat suspensions are controlled. Passenger seat acceleration and displacement results are obtained using bump and sinusoidal type road disturbances. Finally, obtained simulation results of designed uncontrolled and controlled quarter car models are compared and discussed to select best control strategy for achieving high level of passenger ride comfort.

Keywords: Active suspension system, HFPIDCR controller, passenger ride comfort, quarter car model.

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Authors: Yue Hu, Xilu Zhao, Takao Yamaguchi, Manabu Sasajima, Yoshio Koike, Akira Hara

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This study optimized the design parameters of a cone loudspeaker as an example of high flexibility of the product design. We developed an acoustic analysis software program that considers the impact of damping caused by air viscosity. In sound reproduction, it is difficult to optimize each parameter of the loudspeaker design. To overcome the limitation of the design problem in practice, this study presents an acoustic analysis algorithm to optimize the design parameters of the loudspeaker. The material character of cone paper and the loudspeaker edge were the design parameters, and the vibration displacement of the cone paper was the objective function. The results of the analysis showed that the design had high accuracy as compared to the predicted value. These results suggested that although the parameter design is difficult, with experience and intuition, the design can be performed easily using the optimized design found with the acoustic analysis software.

Keywords: Air viscosity, design parameters, loudspeaker, optimization.

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Authors: Tamás Mankovits, Dávid Huri, Imre Kállai, Imre Kocsis, Tamás Szabó

Abstract:

Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. Rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. In this paper a comprehensive investigation is introduced including laboratory measurements, mesh density analysis and complex finite element simulations to obtain the load-displacement curve of the chosen rubber bumper. Contact and friction effects are also taken into consideration. The aim of this research is to elaborate a FEM model which is accurate and competitive for a future shape optimization task.

Keywords: Rubber bumper, finite element analysis, compression test, Mooney-Rivlin material model.

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Authors: Laurent Pitteloud, Jörg Meier

Abstract:

Piled raft foundations represent an efficient and reliable technique for transferring high vertical and horizontal loads to the subsoil. Piled raft foundations were success­fully implemented for several high-rise buildings world­wide over the last decades. For the structural design of this foundation type the stiffnesses of both the piles and the raft have to be deter­mined for the static (e.g. dead load, live load) and the dynamic load cases (e.g. earthquake). In this context the question often arises, to which proportion wind loads are to be considered as dynamic loads. Usually a piled raft foundation has to be monitored in order to verify the design hypotheses. As an additional benefit, the analysis of this monitoring data may lead to a better under­standing of the behaviour of this foundation type for future projects in similar subsoil conditions. In case the measurement frequency is high enough, one may also draw conclusions on the effect of wind loading on the piled raft foundation. For a 41-storey office building in Basel, Switzerland, the preliminary design showed that a piled raft foundation was the best solution to satisfy both design requirements, as well as economic aspects. A high-frequency monitoring of the foundation including pile loads, vertical stresses under the raft, as well as pore water pressures was performed over 5 years. In windy situations the analysis of the measure­ments shows that the pile load increment due to wind consists of a static and a cyclic load term. As piles and raft react with different stiffnesses under static and dynamic loading, these measure­ments are useful for the correct definition of stiffnesses of future piled raft foundations. This paper outlines the design strategy and the numerical modelling of the aforementioned piled raft foundation. The measurement results are presented and analysed. Based on the findings, comments and conclusions on the definition of pile and raft stiffnesses for vertical and wind loading are proposed.

Keywords: Dynamic loading, high-frequency monitoring, piled raft foundations, wind loading.

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Authors: Chiang-Ho Cheng, An-Shik Yang, Chih-Jer Lin, Chun-Ying Lee

Abstract:

This paper aims to present the design, fabrication and test of a novel piezoelectric actuated, check-valves embedded micropump having the advantages of miniature size, light weight and low power consumption. This device is designed to pump gases and liquids with the capability of performing the self-priming and bubble-tolerant work mode by maximizing the stroke volume of the membrane as well as the compression ratio via minimization of the dead volume of the micropump chamber and channel. By experiment apparatus setup, we can get the real-time values of the flow rate of micropump, the displacement of the piezoelectric actuator and the deformation of the check valve, simultaneously. The micropump with check valve 0.4 mm in thickness obtained higher output performance under the sinusoidal waveform of 120 V_pp. The micropump achieved the maximum pumping rates of 42.2 ml/min and back pressure of 14.0 kPa at the corresponding frequency of 28 and 20 Hz. The presented micropump is able to pump gases with a pumping rate of 196 ml/min at operating frequencies of 280 Hz under the sinusoidal waveform of 120 V_pp.

Keywords: Actuator, Check-valve, Micropump, Piezoelectric.

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Authors: Zeinab A.Hussein, Manal S. Abd El-Wahab, Shorouk A. W. El-Shennawy

Abstract:

Children with hemiplgic cerebral palsy often walk with diminished reciprocal arm swing so the purpose of this study was to describe kinematic characteristics in children with hemiplegic cerebral palsy (CP) during the gait suphases, and find if there is a correlation between upper(shoulder and elbow) and lower(hip, knee, and ankle) limb joints either in involved or uninvolved.48 children with hemiplegic cerebral palsy (18boys, 30girls) with an average age of (5.1±0.87) years were selected randomly to evaluate joint angles during gait by 3D motion analysis system with 6 pro reflex cameras in a sagittal plane for both sides of the body. The results showed increased shoulder and elbow flexion, increased hip angular displacement, decreased knee and ankle arcs during gait cycle, also there is correlation between shoulder and elbow to hip, knee, and ankle joints during various subphases of gait.

Keywords: Cerebral palsy, Gait, Hemiplegia, Motion analysis.

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Authors: Huan Xiong, Ming Chen

Abstract:

In order to research Internet quantificationally and better model the performance of network, this paper proposes a novel AS level network performance model (MNPM), it takes autonomous system (AS) as basic modeling unit, measures E2E performance between any two outdegrees of an AS and organizes measurement results into matrix form which called performance matrix (PM). Inter-AS performance calculation is defined according to performance information stored in PM. Simulation has been implemented to verify the correctness of MNPM and a practical application of MNPM (network congestion detection) is given.

Keywords: AS, network performance, model, metric, congestion.

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Authors: Ihsan Al-Abboodi, Tahsin Toma-Sabbagh

Abstract:

Laboratory tests have been carried out to investigate the response of 2x2 pile group subjected to triangular soil movement. The pile group was instrumented with displacement and tilting devices at the pile cap and strain gauges on two piles of the group. In this paper, results from four model tests were presented to study the effects of axial loads and soil density on the lateral behavior of piles. The responses in terms of bending moment, shear force, soil pressure, deflection, and rotation of piles were compared. Test results indicate that increasing the soil strength could increase the measured moment, shear, soil pressure, and pile deformations. Most importantly, adding loads to the pile cap induces additional moment to the head of front-pile row unlike the back-pile row which was influenced insignificantly.

Keywords: Pile group, passive piles, lateral soil movement, soil density, axial loads.

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Authors: Chiang-Ho Cheng, Hong-Yih Cheng, An-Shik Yang, Tung-Hsun Hsu

Abstract:

This paper reports a novel actuating design that uses the shear deformation of a piezoelectric actuator to deflect a bulge-diaphragm for driving an array microdroplet ejector. In essence, we employed a circular-shaped actuator poled radial direction with remnant polarization normal to the actuating electric field for inducing the piezoelectric shear effect. The array microdroplet ejector consists of a shear type piezoelectric actuator, a vibration plate, two chamber plates, two channel plates and a nozzle plate. The vibration, chamber and nozzle plate components are fabricated using nickel electroforming technology, whereas the channel plate is fabricated by etching of stainless steel. The diaphragm displacement was measured by the laser two-dimensional scanning vibrometer. The ejected droplets of the microejector were also observed via an optic visualization system.

Keywords: Actuator, nozzle, microejector, piezoelectric.

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Authors: H. M. Usman Sani, Shafaat A. Bazaz, Nisar Ahmed

Abstract:

In this paper, Fabless Prototyping Methodology is introduced for the design and analysis of MEMS devices. Conventionally Finite Element Analysis (FEA) is performed before system level simulation. In our proposed methodology, system level simulation is performed earlier than FEA as it is computationally less extensive and low cost. System level simulations are based on equivalent behavioral models of MEMS device. Electrostatic actuation based MEMS Microgripper is chosen as case study to implement this methodology. This paper addresses the behavioral model development and simulation of actuator part of an electrostatically actuated Microgripper. Simulation results show that the actuator part of Microgripper works efficiently for a voltage range of 0-45V with the corresponding jaw displacement of 0-4.5425μm. With some minor changes in design, this range can be enhanced to 15μm at 85V.

Keywords: MEMS Actuator, Behavioral Model, CoventorWare, Microgripper, SOIMUMPs, System Level Simulation

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Authors: M. Zheng, V. S. Alagar

Abstract:

The paper discusses complexity of component-based development (CBD) of embedded systems. Although CBD has its merits, it must be augmented with methods to control the complexities that arise due to resource constraints, timeliness, and run-time deployment of components in embedded system development. Software component specification, system-level testing, and run-time reliability measurement are some ways to control the complexity.

Keywords: Components, embedded systems, complexity, softwaredevelopment, traffic controller system.

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Authors: Chun-Yao Lee, Siang-Ren Wang

Abstract:

The purpose of this paper is to discuss the influence of resistance characteristic on the high conductive concrete considering the various voltage and environment. The four-electrode method is applied to the tailor-made high conductive concrete with appropriate proportion. The curve of resistivity with the changes of voltage and environment is plotted and the changes of resistivity are explored. The result based on the methods reveals that resistivity is less affected by the temperature factor, and the four-electrode method would be an applicable measurement method on a site inspection.

Keywords: Conductive concrete, Resistivity.

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Authors: S. Parida, S. C. Mohanty

Abstract:

The free vibration behavior of thick pretwisted cantilevered functionally graded material (FGM) plate subjected to the thermal environment is investigated numerically in the present paper. A mathematical model is developed in the framework of higher order shear deformation theory (HOST) with C⁰ finite element formulation i.e. independent displacement and rotations. The material properties are assumed to be temperature dependent and vary continuously through the thickness based on the volume fraction exponent in simple power rule. The finite element model has been discretized into eight node quadratic serendipity elements with node wise seven degrees of freedom. The effect of plate geometry, temperature field, material composition, and the modal analysis on the vibrational characteristics is examined. Finally, the results are verified by comparing with those available in literature.

Keywords: FGM, pretwisted plate, thermal environment, HOST, simple power law.

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Authors: Juárez-Luna Gelacio, Ayala Gustavo, Retama-Velasco Jaime

Abstract:

This paper shows the advantages of the material failure process simulation by improve finite elements with embedded discontinuities, using a new definition of traction vector, dependent on the discontinuity length and the angle. Particularly, two families of this kind of elements are compared: kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The constitutive model to describe the behavior of the material in the symmetric formulation is a traction-displacement jump relationship equipped with softening after reaching the failure surface.

To show the validity of this symmetric formulation, representative numerical examples illustrating the performance of the proposed formulation are presented. It is shown that the non-symmetric family may over or underestimate the energy required to create a discontinuity, as this effect is related with the total length of the discontinuity, fact that is not noticed when the discontinuity path is a straight line.

Keywords: Variational formulation, strong discontinuity, embedded discontinuities, strain localization.

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