Search results for: flexible beam

Authors: M. Sadighi, H. Pouriayevali, M. Saadati

Abstract:

This paper deals with analysis of flexural stiffness, indentation and their energies in three point loading of sandwich beams with composite faces from Eglass/epoxy and cores from Polyurethane or PVC. Energy is consumed in three stages of indentation in laminated beam, indentation of sandwich beam and bending of sandwich beam. Theory of elasticity is chosen to present equations for indentation of laminated beam, then these equations have been corrected to offer better results. An analytical model has been used assuming an elastic-perfectly plastic compressive behavior of the foam core. Classical theory of beam is used to describe three point bending. Finite element (FE) analysis of static indentation sandwich beams is performed using the FE code ABAQUS. The foam core is modeled using the crushable foam material model and response of the foam core is experimentally characterized in uniaxial compression. Three point bending and indentation have been done experimentally in two cases of low velocity and higher velocity (quasi-impact) of loading. Results can describe response of beam in terms of core and faces thicknesses, core material, indentor diameter, energy absorbed, and length of plastic area in the testing. The experimental results are in good agreement with the analytical and FE analyses. These results can be used as an introduction for impact loading and energy absorbing of sandwich structures.

Keywords: Three point Bending, Indentation, Foams, Composite laminated beam, Sandwich beams, Finite element

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Authors: Omar M. Ben-Sasi

Abstract:

A total of fourteen slab-edge beam-column connection specimens were tested gradually to failure under the effect of simultaneous action of shear force and moment. The objective was to investigate the influence of some parameters thought to be important on the behavior and strength of slab-column connections with edge beams encountered in flat slab flooring and roofing systems. The parameters included the existence and strength of edge beam, depth and width of edge beam, steel reinforcement ratio of slab, ratio of moment to shear force, and the existence of openings in the region next to the column.

Results obtained demonstrated the importance of the studied parameters on the strength and behavior of slab-column connections with edge beams.

Keywords: Strength, flat slab, slab-column connections, shear force, moment, behavior.

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Authors: Karim Kemih, Yacine Yaiche, Malek Benslama

Abstract:

To establish optical communication between any two satellites, the transmitter satellite must track the beacon of the receiver satellite and point the information optical beam in its direction. Optical tracking and pointing systems for free space suffer during tracking from high-amplitude vibration because of background radiation from interstellar objects such as the Sun, Moon, Earth, and stars in the tracking field of view or the mechanical impact from satellite internal and external sources. The vibrations of beam pointing increase the bit error rate and jam communication between the two satellites. One way to overcome this problem is the use of very small transmitter beam divergence angles of too narrow divergence angle is that the transmitter beam may sometimes miss the receiver satellite, due to pointing vibrations. In this paper we propose the use of genetic algorithm to optimize the BER as function of transmitter optics aperture.

Keywords: Optical Satellite Communication, Genetic Algorithm, Transmitter Optics Aperture

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Authors: Naser Ojaroudi Parchin, Atta Ullah, Haleh Jahanbakhsh Basherlou, Raed A. Abd-Alhameed, Peter S. Excell

Abstract:

A design of beam-steerable antenna array for the future cellular communication (5G) is presented. The proposed design contains eight elements of compact end-fire antennas arranged on the top edge of smartphone printed circuit board (PCB). Configuration of the antenna element consists of the conductive patterns on the top and bottom copper foil layers and a substrate layer with a via-hole. The simulated results including input-impedance and also fundamental radiation properties have been presented and discussed. The impedance bandwidth (S₁₁ ≤ -10 dB) of the antenna spans from 17.5 to 21 GHz (more than 3 GHz bandwidth) with a resonance at 19 GHz. The antenna exhibits end-fire (directional) radiation beams with wide-angle scanning property and could be used for the future 5G beam-forming. Furthermore, the characteristics of the array design in the vicinity of user-hand are studied.

Keywords: Beam-steering, end-fire radiation mode, mobile-phone antenna, phased array.

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Authors: Mojtaba Ghodsi, Hamidreza Ziaifar, Morteza Mohammadzaheri, Payam Soltani

Abstract:

This article presents an analytical model to estimate the harvested power from a Magnetostrictive cantilevered beam with tip excitation. Furthermore, the effects of internal and external damping on harvested power are investigated. The magnetostrictive material in this harvester is Galfenol. In comparison to other popular smart materials like Terfenol-D, Galfenol has higher strength and machinability. In this article, first, a mechanical model of the Euler-Bernoulli beam is employed to calculate the deflection of the harvester. Then, the magneto-mechanical equation of Galfenol is combined with Faraday's law to calculate the generated voltage of the Magnetostrictive cantilevered beam harvester. Finally, the beam model is incorporated in the aforementioned combination. The results show that a 30×8.5×1 mm Galfenol cantilever beam harvester with 80 turn pickup coil can generate up to 3.7 mV and 9 mW. Furthermore, sensitivity analysis made by Response Surface Method (RSM) shows that the harvested power is only sensitive to the internal damping coefficient.

Keywords: Internal damping coefficient, external damping coefficient, Euler-Bernoulli, energy harvester, Galfenol, magnetostrictive, response surface method.

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Authors: Andras Szekrenyes

Abstract:

This work presents the mixed-mode II/III prestressed split-cantilever beam specimen for the fracture testing of composite materials. In accordance with the concept of prestressed composite beams one of the two fracture modes is provided by the prestressed state of the specimen, and the other one is increased up to fracture initiation by using a testing machine. The novel beam-like specimen is able to provide any combination of the mode-II and mode-III energy release rates. A simple closed-form solution is developed using beam theory as a data reduction scheme and for the calculation of the energy release rates in the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode beam specimen can be used to obtain the fracture criterion of transparent composite materials in the GII - GIII plane in a relatively simple way.

Keywords: Composite, fracture mechanics, toughness testing, mixed-mode II/III fracture.

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Authors: V. Přivřelová

Abstract:

Well-designed composite steel and concrete structures highlight the good material properties and lower the deficiencies of steel and concrete, in particular they make use of high tensile strength of steel and high stiffness of concrete. The most common composite steel and concrete structure is a simply supported beam, which concrete slab transferring the slab load to a beam is connected to the steel cross-section. The aim of this paper is to find the most adequate numerical model of a simply supported composite beam with the cross-sectional and material parameters based on the results of a processed parametric study and numerical analysis. The paper also evaluates the suitability of using compact concrete with the lightweight aggregates for composite steel and concrete beams. The most adequate numerical model will be used in the resent future to compare the results of laboratory tests.

Keywords: Composite beams, high-performance concrete, highstrength steel, lightweight concrete slab, modeling.

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Authors: Talebi Aliasghar, Ebrahimpour Komeleh Hooman, Maghsoudi Ali Akbar

Abstract:

In reinforced concrete (RC) structures, beam-column connection region has a considerable effect on the behavior of structures. Using fiber reinforcement polymer (FRP) for the strengthening of connections in RC structures can be one of the solutions to retrofitting this zone which result in the enhanced behavior of structure. In this paper, these changes in behavior by using FRP for high strength concrete beam-column connection have been studied by finite element modeling. The concrete damage plasticity (CDP) model has been used to analyze the RC. The results illustrated a considerable development in load-bearing capacity but also a noticeable reduction in ductility. The study also assesses these qualities for several modes of strengthening and suggests the most effective mode of strengthening. Using FRP in flexural zone and FRP with 45-degree oriented fibers in shear zone of joint showed the most significant change in behavior.

Keywords: High strength concrete, beam-column connection, FRP, FEM.

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Authors: Jebari Chaker, Ounelli Habib

Abstract:

In this paper we propose a new approach for flexible document categorization according to the document type or genre instead of topic. Our approach implements two homogenous classifiers: contextual classifier and logical classifier. The contextual classifier is based on the document URL, whereas, the logical classifier use the logical structure of the document to perform the categorization. The final categorization is obtained by combining contextual and logical categorizations. In our approach, each document is assigned to all predefined categories with different membership degrees. Our experiments demonstrate that our approach is best than other genre categorization approaches.

Keywords: Categorization, combination, flexible, logicalstructure, genre, category, URL.

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Authors: Sandhya Dixit, Tilak Raj

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Flexible Manufacturing System (FMS) is seen as an option for industries which want to boost productivity as well as respond quickly to an increasingly changing marketplace. FMS produces in mid variety, mid volume range and can meet the changing market demands very quickly. But still the impact of adoption of FMS on the productivity of any industry is not very clear. In this paper an attempt has been made to model the various factors affecting the productivity of FMS installation using Total Interpretive Structural Modelling (TISM) Technique.

Keywords: Flexible manufacturing system, productivity, total interpretive structural modelling.

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Authors: T. Zalabsky, P. Bezousek, T. Shejbal

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The paper describes new concept of the ribbon beam antenna for RFID technology. Antenna is located near to railway lines to monitor tags situated on trains. Antenna works at 2.45 GHz and it is fabricated by microstrip technology. Antenna contains two same mirrored parts having the same radiation patterns. Each part consists of three dielectric layers. The first layer has on one side radiation elements. The second layer is only for mechanical construction and it sets optimal electromagnetic field for each radiating elements. The third layer has on its top side a ground plane and on the bottom side a microstrip circuit used for individual radiation elements feeding.

Keywords: RFID, cosecant radiation pattern, ribbon beam, patch antenna, microstrip.

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Authors: Iman Badr

Abstract:

The concept of flexible manufacturing is highly appealing in gaining a competitive edge in the market by quickly adapting to the changing customer needs. Scheduling jobs on flexible manufacturing systems (FMSs) is a challenging task of managing the available flexibility on the shop floor to react to the dynamics of the environment in real-time. In this paper, an agent-oriented scheduling framework that can be integrated with a real or a simulated FMS is proposed. This framework works in stochastic environments with a dynamic model of job arrival. It supports a hierarchical cooperative scheduling that builds on the available flexibility of the shop floor. Testing the framework on a model of a real FMS showed the capability of the proposed approach to overcome the drawbacks of the conventional approaches and maintain a near optimal solution despite the dynamics of the operational environment.

Keywords: Autonomous agents, Flexible manufacturing systems(FMS), Manufacturing scheduling, Real-time systems.

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

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This paper studies dynamic stability of homogeneous beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Bernoulli-Euler beam theory. Applying the Hamilton's principle, the governing dynamic equation is established. The influences of applied voltage, foundation coefficient and piezoelectric thickness on the unstable regions are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Dynamic stability, Homogeneous graded beam-Piezoelectric layer, Harmonic balance method.

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Authors: Martha C. Orazulume, Jibril D. Jiya

Abstract:

Flexible satellites are equipped with various appendages which vibrate under the influence of any excitation and make the attitude of the satellite to be unstable. Therefore, the system must be able to adjust to balance the effect of these appendages in order to point accurately and satisfactorily which is one of the most important problems in satellite design. Proportional Integral Derivative (PID) Controller is simple to design and computationally efficient to implement which is used to stabilize the effect of these flexible appendages. However, manual turning of the PID is time consuming, waste energy and money. Particle Swarm Optimization (PSO) is used to tune the parameters of PID Controller. Simulation results obtained show that PSO tuned PID Controller is able to re-orient the spacecraft attitude as well as dampen the effect of mechanical resonance and yields better performance when compared with manually tuned PID Controller.

Keywords: Attitude control, flexible satellite, particle swarm optimization, PID controller.

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Authors: Parviz Fattahi

Abstract:

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it quit difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. The combining of several optimization criteria induces additional complexity and new problems. In this paper, a Pareto approach to solve the multi objective flexible job shop scheduling problems is proposed. The objectives considered are to minimize the overall completion time (makespan) and total weighted tardiness (TWT). An effective simulated annealing algorithm based on the proposed approach is presented to solve multi objective flexible job shop scheduling problem. An external memory of non-dominated solutions is considered to save and update the non-dominated solutions during the solution process. Numerical examples are used to evaluate and study the performance of the proposed algorithm. The proposed algorithm can be applied easily in real factory conditions and for large size problems. It should thus be useful to both practitioners and researchers.

Keywords: Flexible job shop, Scheduling, Hierarchical approach, simulated annealing, tabu search, multi objective.

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Authors: Lee Yih Rou, Hishammuddin Asmuni

Abstract:

Flexible Job Shop Problem (FJSP) is an extension of classical Job Shop Problem (JSP). The FJSP extends the routing flexibility of the JSP, i.e assigning machine to an operation. Thus it makes it more difficult than the JSP. In this study, Cooperative Coevolutionary Genetic Algorithm (CCGA) is presented to solve the FJSP. Makespan (time needed to complete all jobs) is used as the performance evaluation for CCGA. In order to test performance and efficiency of our CCGA the benchmark problems are solved. Computational result shows that the proposed CCGA is comparable with other approaches.

Keywords: Co-evolution, Genetic Algorithm (GA), Flexible JobShop Problem(FJSP)

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Authors: A. Badalyan, R. Hovsepyan, V. Mekhitaryan, P. Mantashyan, R. Drampyan

Abstract:

In this paper we report the technique of optical induction of 2 and 3-dimensional (2D and 3D) photonic lattices in photorefractive materials based on diffraction grating self replication -Talbot effect. 1D and 2D different rotational symmery diffraction masks with the periods of few tens micrometers and 532 nm cw laser beam were used in the experiments to form an intensity modulated light beam profile. A few hundred micrometric scale replications of mask generated intensity structures along the beam propagation axis were observed. Up to 20 high contrast replications were detected for 1D annular mask with 30

Keywords: Diffraction gratings, laser, photonic lattice, Talbot effect.

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Authors: Adla Bentellis, Zizette Boufaïda

Abstract:

Nowadays, the pace of business change is such that, increasingly, new functionality has to be realized and reliably installed in a matter of days, or even hours. Consequently, more and more business processes are prone to a continuous change. The objective of the research in progress is to use the MAP model, in a conceptual modeling method for flexible and adaptive business process. This method can be used to capture the flexibility dimensions of a business process; it takes inspiration from modularity concept in the object oriented paradigm to establish a hierarchical construction of the BP modeling. Its intent is to provide a flexible modeling that allows companies to quickly adapt their business processes.

Keywords: Business Process, Business process modeling, flexibility, MAP Model.

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Authors: Mustafa Kaya

Abstract:

Since, it is essential to provide homeless people by the earthquake with safe, habitable accommodation repairing medium and slight levels of damage at the connection parts should be undertaken. In order to prove that a repaired connection was sufficiently strong, a precast beam to column post tensioned connection was tested in three phases. In phase one, the middle level damage was observed at 6% drift at these connections. As a result of the extra loads applied, little damage was observed. In the last phase, the four connections tested in the first phase were repaired using epoxy resin and then retested. The results from the tests on the repaired precast and the undamaged specimens showed that the repaired specimens were sufficiently strong, thus proving that repair to damaged precast beam to column post tensioned connections can be undertaken.

Keywords: Precast beam to column connection, momentresisting connection, post-tensioned connections, repair of precast connections.

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Authors: Sophia Fry, Mahir Irtiza, Alexa Hoffman, Yousef Sardahi

Abstract:

This study presents an intelligent control algorithm for a flexible robotic arm. Fuzzy control is used to control the motion of the arm to maintain the arm tip at the desired position while reducing vibration and increasing the system speed of response. The Fuzzy controller (FC) is based on adding the tip angular position to the arm deflection angle and using their sum as a feedback signal to the control algorithm. This reduces the complexity of the FC in terms of the input variables, number of membership functions, fuzzy rules, and control structure. Also, the design of the fuzzy controller is model-free and uses only our knowledge about the system. To show the efficacy of the FC, the control algorithm is implemented on the flexible joint manipulator (FJM) developed by Quanser. The results show that the proposed control method is effective in terms of response time, overshoot, and vibration amplitude.

Keywords: Fuzzy logic control, model-free control, flexible joint manipulators, nonlinear control.

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

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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: Sam-Ang Keo, Franck Brachelet, Florin Breaban, Didier Defer

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This paper presents a NDT by infrared thermography with excitation CO2 Laser, wavelength of 10.6 μm. This excitation is the controllable heating beam, confirmed by a preliminary test on a wooden plate 1.2 m x 0.9 m x 1 cm. As the first practice, this method is applied to detecting the defect in CFRP heated by the Laser 300 W during 40 s. Two samples 40 cm x 40 cm x 4.5 cm are prepared, one with defect, another one without defect. The laser beam passes through the lens of a deviation device, and heats the samples placed at a determinate position and area. As a result, the absence of adhesive can be detected. This method displays prominently its application as NDT with the composite materials. This work gives a good perspective to characterize the laser beam, which is very useful for the next detection campaigns.

Keywords: CO2 LASER, Infrared Thermography, NDT, CFRP, Defect Detection.

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Authors: Morteza Raki, Abolghasem Zabihollah, Omid Askari

Abstract:

Cantilever beam is a simplified sample of a lot of mechanical components used in a wide range of applications, including many industries such as gas turbine blade. Due to the nature of the operating conditions, beams are subject to variety of damages especially crack propagates. Crack propagation may lead to catastrophic failure during operation. Therefore, online detection of crack presence and its propagation is very important and may reduce possible significant cost of the whole system failure. This paper aims to investigate the effect of cracks presence and crack propagation on one end fixed beam`s vibration. A finite element model will be developed for the blade in which the modal response of the structure with and without crack will be studied. 

Keywords: Blade, crack propagation, health monitoring, modal analysis.

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Authors: Yizhi Gai, Yukinori Kobayashi, Yohei Hoshino, Takanori Emaru

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Motion control of flexible arms is more difficult than that of rigid arms, however utilizing its dynamics enables improved performance such as a fast motion in short operation time. This paper investigates a ball throwing robot with one rigid link and one flexible link. This robot throws a ball at a set speed with a proper control torque. A mathematical model of this ball throwing robot is derived through Hamilton’s principle. Several patterns of torque input are designed and tested through the proposed simulation models. The parameters of each torque input pattern is optimized and determined by chaos embedded vector evaluated particle swarm optimization (CEVEPSO). Then, the residual vibration of the manipulator after throwing is suppressed with input shaping technique. Finally, a real experiment is set up for the model checking.

Keywords: Motion control, flexible robotic arm, CEVEPSO, ball throwing robot.

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Authors: Teguh Sudibyo, Cheng-Cheng Chen

Abstract:

Eight steel reinforced concrete beams (SRC), were fabricated and tested under earthquake type cyclic loading. The effectiveness of intermediate stiffeners, such as mid-span stiffener and plastic hinge zone stiffeners, in enhancing composite action and ductility of SRC beams was investigated. The effectiveness of strengthened beam-to-column (SBC) and weakened beam-to-column (WBC) connections in enhancing beam ductility was also studied. It was found that: (1) All the specimens possessed fairly high flexural ductility and were found adequate for structures in high seismic zones. (2) WBC connections induced stress concentration which caused extra damage to concrete near the flange tapering zone. This extra damage inhibited the flexural strength development and the ductility of the specimens with WBC connections to some extent. (3) Specimens with SBC connections demonstrated higher flexural strength and ductility compared to specimens with WBC connections. (4) The intermediate stiffeners, especially combination of plastic hinge zone stiffener and mid span stiffeners, have an obvious effect in enhancing the ductility of the beams with SBC connection.

Keywords: Composite beam, concrete encased steel beam, steel reinforced concrete, stiffeners.

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Authors: Naohiko Honma, Kojiro Suzuki

Abstract:

This paper proposes the concept of aerocapture with aerodynamic-environment-adaptive variable geometry flexible aeroshell that vehicle deploys. The flexible membrane is composed of thin-layer film or textile as its aeroshell in order to solve some problems obstructing realization of aerocapture technique. Multi-objective optimization study is conducted to investigate solutions and derive design guidelines. As a result, solutions which can avoid aerodynamic heating and enlarge the corridor width up to 10% are obtained successfully, so that the effectiveness of this concept can be demonstrated. The deformation-use optimum solution changes its drag coefficient from 1.6 to 1.1, along with the change in dynamic pressure. Moreover, optimization results show that deformation-use solution requires the membrane for which upper temperature limit and strain limit are more than 700 K and 120%, respectively, and elasticity (Young-s modulus) is of order of 106 Pa.

Keywords: Aerocapture, flexible aeroshell, optimization, response surface methodology.

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Authors: Hasan Hassoun, Jaafar Hallal, Denis Duhamel, Mohammad Hammoud, Ali Hage Diab

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This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-contact vibration sensor to recover the vibration modes of a vibrating structure such as a cantilever beam. A video of a vibrating beam is filmed using a smartphone camera and then processed by the motion magnification technique. Based on this method, the first two natural frequencies and their associated mode shapes are estimated experimentally and compared to the analytical ones. Results show a relative error of less than 4% between the experimental and analytical approaches for the first two natural frequencies of the beam. Also, for the first two-mode shapes, a Modal Assurance Criterion (MAC) value of above 0.9 between the two approaches is obtained. This slight error between the different techniques ensures the viability of a cheap smartphone camera as a non-contact vibration sensor, particularly for structures vibrating at relatively low natural frequencies.

Keywords: Modal Analysis, motion magnification, smartphone camera, structural vibration, vibration modes.

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Authors: Geeta Partap, Nitika Chugh

Abstract:

The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: Microstretch, deflection, exponential load, Laplace transforms, Residue theorem, simply supported.

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Authors: A. Kurşun, M. Tunay Çetin, E. Çetin, H. Aykul

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In this investigation an elastic stress analysis is carried out a woven steel fiber reinforced thermoplastic cantilever beam loaded uniformly at the upper surface. The composite beam material consists of low density polyethylene as a thermoplastic (LDFE, f.2.12) and woven steel fibers. Granules of the polyethylene are put into the moulds and they are heated up to 160°C by using electrical resistance. Subsequently, the material is held for 5min under 2.5 MPa at this temperature. The temperature is decreased to 30°C under 15 MPa pressure in 3min. Closed form solution is found satisfying both the governing differential equation and boundary conditions. We investigated orientation angle effect on stress distribution of composite cantilever beams. The results show that orientation angle play an important role in determining the responses of a woven steel fiber reinforced thermoplastic cantilever beams and an optimal design of these structures.

Keywords: Cantilever beam, elastic stress analysis, orientation angle, thermoplastic.

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Authors: Easa Ali Abbasi, Akbar Allahverdizadeh, Reza Jahangiri, Behnam Dadashzadeh

Abstract:

Electrical current measurement is a suitable method for the performance determination of electrical devices. There are two contact and noncontact methods in this measuring process. Contact method has some disadvantages like having direct connection with wire which may endamage the system. Thus, in this paper, a bimorph piezoelectric cantilever beam which has a permanent magnet on its free end is used to measure electrical current in a noncontact way. In mathematical modeling, based on Galerkin method, the governing equation of the cantilever beam is solved, and the equation presenting the relation between applied force and beam’s output voltage is presented. Magnetic force resulting from current carrying wire is considered as the external excitation force of the system. The results are compared with other references in order to demonstrate the accuracy of the mathematical model. Finally, the effects of geometric parameters on the output voltage and natural frequency are presented.

Keywords: Cantilever beam, electrical current measurement, forced excitation, piezoelectric.

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