Search results for: Free cantilever method

Authors: E. H. N. Gashti, J. Razzaghi, K. Kujala

Abstract:

In general, codes and regulations consider seismic loads only for completed structures of the bridges while, evaluation of incomplete structure of bridges, especially those constructed by free cantilever method, under these loads is also of great importance. Hence, this research tried to study the behavior of incomplete structure of common bridge type (box girder bridge), in construction phase under vertical seismic loads. Subsequently, the paper provided suitable guidelines and solutions to resist this destructive phenomenon. Research results proved that use of preventive methods can significantly reduce the stresses resulted from vertical seismic loads in box cross sections to an acceptable range recommended by design codes.

Keywords: Box girder bridges, Prestress loads, Free cantilever method, Seismic loads, Construction phase.

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

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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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Authors: H. Ozbasaran

Abstract:

Lateral torsional buckling is a global buckling mode which should be considered in design of slender structural members under flexure about their strong axis. It is possible to compute the load which causes lateral torsional buckling of a beam by finite element analysis, however, closed form equations are needed in engineering practice for calculation ease which can be obtained by using energy method. In lateral torsional buckling applications of energy method, a proper function for the critical lateral torsional buckling mode should be chosen which can be thought as the variation of twisting angle along the buckled beam. Accuracy of the results depends on how close is the chosen function to the exact mode. Since critical lateral torsional buckling mode of the cantilever I-beams varies due to material properties, section properties and loading case, the hardest step is to determine a proper mode function in application of energy method. This paper presents an approximate function for critical lateral torsional buckling mode of doubly symmetric cantilever I-beams. Coefficient matrices are calculated for concentrated load at free end, uniformly distributed load and constant moment along the beam cases. Critical lateral torsional buckling modes obtained by presented function and exact solutions are compared. It is found that the modes obtained by presented function coincide with differential equation solutions for considered loading cases.

Keywords: Buckling mode, cantilever, lateral-torsional buckling, I-beam.

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Authors: Amin Eslami, Jafar Bolouri Bazaz

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Under active stress conditions, a rigid cantilever retaining wall tends to rotate about a pivot point located within the embedded depth of the wall. For purely granular and cohesive soils, a methodology was previously reported called minimization of moment ratio to determine the location of the pivot point of rotation. The usage of this new methodology is to estimate the rotational stability safety factor. Moreover, the degree of improvement required in a backfill to get a desired safety factor can be estimated by the concept of the shear strength demand. In this article, the accuracy of this method for another type of cantilever walls called Contiguous Bored Pile (CBP) retaining wall is evaluated by using physical modeling technique. Based on observations, the results of moment ratio minimization method are in good agreement with the results of the carried out physical modeling.

Keywords: Cantilever Retaining Wall, Physical Modeling, Minimization of Moment Ratio Method, Pivot Point.

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Authors: B. G. Sheeparamatti, Prashant Hanasi, Vanita Abbigeri

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The objective of this work is to carryout critical comparison of different actuation mechanisms like electrostatic, thermal, piezoelectric, and magnetic with reference to a micro cantilever. The relevant parameters like force generated, displacement are compared in actuation methods. With these results, helps in choosing the best actuation method for a particular application. In this study, Comsol/Multiphysics software is used. Modeling and simulation is done by considering the micro cantilever of same dimensions as an actuator using all the above mentioned actuation techniques. In addition to their small size, micro actuators consume very little power and are capable of accurate results. In this work, a comparison of actuation mechanisms is done to decide the efficient system in micro domain.

Keywords: Actuation techniques, microswitch, micro actuator, microsystems.

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Authors: S.H. Mirtalaie, M. Mohammadi, M.A. Hajabasi, F.Hejripour

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In this paper the Differential Quadrature Method (DQM) is employed to study the coupled lateral-torsional free vibration behavior of the laminated composite beams. In such structures due to the fiber orientations in various layers, the lateral displacement leads to a twisting moment. The coupling of lateral and torsional vibrations is modeled by the bending-twisting material coupling rigidity. In the present study, in addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies of the beam. The governing differential equations of motion which form a system of three coupled PDEs are solved numerically using DQ procedure under different boundary conditions consist of the combinations of simply, clamped, free and other end conditions. The resulting natural frequencies and mode shapes for cantilever beam are compared with similar results in the literature and good agreement is achieved.

Keywords: Differential Quadrature Method, Free vibration, Laminated composite beam, Material coupling.

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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: Muhammad Naseem Baig, Abdul Qudoos Khan, Jamal Ali

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Ground deformations in deep excavations are affected by wall stiffness and pile embedment ratio. This paper presents the findings of a parametric study of a 64-ft deep excavation in mixed stiff soil conditions supported by cantilever pile wall. A series of finite element analysis has been carried out in Plaxis 2D by varying the pile embedment ratio and wall stiffness. It has been observed that maximum wall deflections decrease by increasing the embedment ratio up to 1.50; however, any further increase in pile length does not improve the performance of the wall. Similarly, increasing wall stiffness reduces the wall deformations and affects the deflection patterns of the wall. The finite element analysis results are compared with the field data of 25 case studies of cantilever walls. Analysis results fall within the range of normalized wall deflections of the 25 case studies. It has been concluded that deep excavations can be supported by cantilever walls provided the system stiffness is increased significantly.

Keywords: Excavations, support systems, wall stiffness, cantilever walls.

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Authors: Anas M. Fares

Abstract:

Reinforced concrete shear walls are the most frequently used forms of lateral resisting structural elements. These walls may take many forms due to their functions and locations in the building. In Palestine, the most lateral resisting forces construction forms is the cantilever shear walls system. It is thus of prime importance to study the rigidity of these walls. The virtual work theorem is used to derive the total lateral deflection of cantilever shear walls due to flexural and shear deformation. The case of neglecting the shear deformation in the walls is also studied, and it is found that the wall height to length aspect ratio (H/B) plays a major role in calculating the lateral deflection and the rigidity of such walls. When the H/B is more than or equal to 3.7, the shear deformation may be neglected from the calculation of the lateral deflection. Moreover, the walls with the same material properties, same lateral load value, and same aspect ratio, shall have the same of both the lateral deflection and the rigidity. Finally, an equation to calculate the total rigidity and total deflection of such walls is derived by using the virtual work theorem for a cantilever beam.

Keywords: Cantilever shear walls, flexural deformation, lateral deflection, lateral loads, reinforced concrete shear walls, rigidity, shear deformation, virtual work theorem.

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Authors: Chih-Jer Lin, Chun-Ying Lee, Chiang-Ho Cheng, Geng-Fung Chen

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This paper investigates experimental studies on vibration suppression for a cantilever beam using an Electro-Rheological (ER) sandwich shock absorber. ER fluid (ERF) is a class of smart materials that can undergo significant reversible changes immediately in its rheological and mechanical properties under the influence of an applied electric field. Firstly, an ER sandwich beam is fabricated by inserting a starch-based ERF into a hollow composite beam. At the same time, experimental investigations are focused on the frequency response of the ERF sandwich beam. Second, the ERF sandwich beam is attached to a cantilever beam to become as a shock absorber. Finally, a fuzzy semi-active vibration control is designed to suppress the vibration of the cantilever beam via the ERF sandwich shock absorber. To check the consistency of the proposed fuzzy controller, the real-time implementation validated the performance of the controller.

Keywords: Electro-Rheological Fluid, Semi-active vibration control, shock absorber, fuzzy control, Real-time control.

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Authors: R. I. Liban, N. Tayşi

Abstract:

This paper deals with a nonlinear finite element analysis to examine the behavior up to failure of cantilever composite steel-concrete beams which are prestressed externally. 'Pre-' means stressing the high strength external tendons in the steel beam section before the concrete slab is added. The composite beam contains a concrete slab which is connected together with steel I-beam by means of perfect shear connectors between the concrete slab and the steel beam which is subjected to static loading. A finite element analysis will be done to study the effects of external prestressed tendons on the composite steel-concrete beams by locating the tendons in different locations (profiles). ANSYS version 12.1 computer program is being used to analyze the represented three-dimensional model of the cantilever composite beam. This model gives all these outputs, mainly load-displacement behavior of the cantilever end and in the middle span of the simple support part.

Keywords: Composite steel-concrete beams, external prestressing, finite element analysis, ANSYS.

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Authors: Mevlüt Burak Dalmış, Kemal Yaman

Abstract:

In this study, flutter characteristics of cantilever rectangular plate structure under incompressible flow regime are investigated by comparing the results of commercial flutter analysis program ZAERO^© with wind tunnel tests conducted in Ankara Wind Tunnel (ART). A rectangular polycarbonate (PC) plate, 5x125x1000 mm in dimensions, is used for both numerical and experimental investigations. Analysis and test results are very compatible with each other. A comparison between two different solution methods (g and k-method) of ZAERO^© is also done. It is seen that, k-method gives closer result than the other one. However, g-method results are on conservative side and it is better to use conservative results namely g-method results. Even if the modal analysis results are used for the flutter analysis for this simple structure, a modal test should be conducted in order to validate the modal analysis results to have accurate flutter analysis results for more complicated structures.

Keywords: Flutter, plate, subsonic flow, wind tunnel.

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Authors: Kapse Swapnil, K. Shankar

Abstract:

Aiming at optimizing the weight and deflection of cantilever beam subjected to maximum stress and maximum deflection, Multi-objective Particle Swarm Optimization (MOPSO) with Utopia Point based local search is implemented. Utopia point is used to govern the search towards the Pareto Optimal set. The elite candidates obtained during the iterations are stored in an archive according to non-dominated sorting and also the archive is truncated based on least crowding distance. Local search is also performed on elite candidates and the most diverse particle is selected as the global best. This method is implemented on standard test functions and it is observed that the improved algorithm gives better convergence and diversity as compared to NSGA-II in fewer iterations. Implementation on practical structural problem shows that in 5 to 6 iterations, the improved algorithm converges with better diversity as evident by the improvement of cantilever beam on an average of 0.78% and 9.28% in the weight and deflection respectively compared to NSGA-II.

Keywords: Utopia point, multi-objective particle swarm optimization, local search, cantilever beam.

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Authors: Minghui Wang, Juntao Zhang

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An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: Yuwaraj M. Ghugal, Ajay G. Dahake

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A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick cantilever isotropic beams are considered for the numerical studies to demonstrate the efficiency of the. Results obtained are discussed critically with those of other theories.

Keywords: Trigonometric shear deformation, thick beam, flexure, principle of virtual work, equilibrium equations, stress.

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Authors: Thomas Jin-Chee Liu, Yu-Shen Chen, Hsi-Yang Ho, Jyun-Ting Liu, Chih-Chun Lee

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This paper discusses some notes on the vibration design for the piezoelectric cooling fan. After reviewing the fundamental formulas of the cantilever Euler beam, it is not easy to find the optimal design of the piezoelectric fan. The experiments also show the complicated results of the vibration behavior and air flow.

Keywords: Piezoelectric cooling fan, vibration, cantilever Euler beam, air flow.

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Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

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Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

Abstract:

The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: Smart material, on-line differential artificial neural network, active control, finite element method.

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Authors: Ali Mutlu, Berrin Mutlu

Abstract:

In this paper we use the definition of CW basis of a free simplicial algebra. Using the free simplicial algebra, it is shown to construct free or totally free 2−crossed modules on suitable construction data with given a CW−basis of the free simplicial algebra. We give applications free crossed squares, free squared complexes and free 2−crossed complexes by using of 1(one) skeleton resolution of a step by step construction of the free simplicial algebra with a given CW−basis.

Keywords: Free crossed square, Free 2−crossed modules, Free simplicial algebra, Free square complexes, Free 2−crossed complexes CW−basis, 1−skeleton. A. M. S.Classification:[2000] 18D35, 18G30, 18G50, 18G55, 55Q05, 55Q20.

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Authors: Giho Jeong, Sooin Jeong, Kuisoon Kim

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It is very important to determine reference temperature when convective temperature because it should be used to calculate the temperature potential. This paper deals with the development of a new method that can determine heat transfer coefficient and reference free stream temperature simultaneously, based on transient heat transfer experiments with using two narrow band thermo-tropic liquid crystals (TLC's). The method is validated through error analysis in terms of the random uncertainties in the measured temperatures. It is shown how the uncertainties in heat transfer coefficient and free stream temperature can be reduced. The general method described in this paper is applicable to many heat transfer models with unknown free stream temperature.

Keywords: Heat transfer coefficient, Thermo-tropic LiquidCrystal (TLC), Free stream temperature.

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Authors: Vinod B. Suryawanshi, Ajit D. Kelkar

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Composite materials, due to their unique properties such as high strength to weight ratio, corrosion resistance, and impact resistance have huge potential as structural materials in automotive, construction and transportation applications. However, these properties often come at higher cost owing to complex design methods, difficult manufacturing processes and raw material cost. Traditionally, tapered laminated composite structures are manufactured using autoclave manufacturing process by ply drop off technique. Autoclave manufacturing though very powerful suffers from high capital investment and higher energy consumption. As per the current trends in composite manufacturing, Out of Autoclave (OoA) processes are looked as emerging technologies for manufacturing the structural composite components for aerospace and defense applications. However, there is a need for improvement among these processes to make them reliable and consistent. In this paper, feasibility of using out of autoclave process to manufacture the variable thickness cantilever beam is discussed. The minimum weight design for the composite beam is obtained using constant stress beam concept by tailoring the thickness of the beam. Ply drop off techniques was used to fabricate the variable thickness beam from glass/epoxy prepregs. Experiments were conducted to measure bending stresses along the span of the cantilever beam at different intervals by applying the concentrated load at the free end. Experimental results showed that the stresses in the bean at different intervals were constant. This proves the ability of OoA process to manufacture the constant stress beam. Finite element model for the constant stress beam was developed using commercial finite element simulation software. It was observed that the simulation results agreed very well with the experimental results and thus validated design and manufacturing approach used.

Keywords: Beams, Composites, Constant Stress, Structures.

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Authors: Faruk Fırat Çalım, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: Circular rod, Out-of-plane free vibration analysis, Transfer Matrix Method.

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Authors: M.H. Djavareshkian, A. Esmaeli

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A pressure-based implicit procedure to solve Navier- Stokes equations on a nonorthogonal mesh with collocated finite volume formulation is used to simulate flow around the smart and conventional flaps of spoiler under the ground effect. Cantilever beam with uniformly varying load with roller support at the free end is considered for smart flaps. The boundedness criteria for this procedure are determined from a Normalized Variable diagram (NVD) scheme. The procedure incorporates es the k -ε eddyviscosity turbulence model. The method is first validated against experimental data. Then, the algorithm is applied for turbulent aerodynamic flows around a spoiler section with smart and conventional flaps for different attack angle, flap angle and ground clearance where the results of two flaps are compared.

Keywords: Smart spoiler, Ground Effect, Flap, Aerodynamic coefficients, Race car.

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Authors: Pakorn Uttayopas, Chawalit Kittichaikarn

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This paper presents an experimental investigation for the characteristics of an energy harvesting device exploiting flow-induced vibration in a wind tunnel. A stationary bluff body is connected with a downstream tip body via an aluminium cantilever beam. Various lengths of aluminium cantilever beam and different shapes of downstream tip body are considered. The results show that the characteristics of the energy harvester’s vibration depend on both the length of the aluminium cantilever beam and the shape of the downstream tip body. The highest ratio between vibration amplitude and bluff body diameter was found to be 1.39 for an energy harvester with a symmetrical triangular tip body and L/D₁ = 5 at 9.8 m/s of flow speed (Re = 20077). Using this configuration, the electrical energy was extracted with a polyvinylidene fluoride (PVDF) piezoelectric beam with different load resistances, of which the optimal value could be found on each Reynolds number. The highest power output was found to be 3.19 µW, at 9.8 m/s of flow speed (Re = 20077) and 27 MΩ of load resistance.

Keywords: Downstream structures, energy harvesting, flow-induced vibration, piezoelectric material, wind tunnel.

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Authors: U. Mutman, S. B. Coskun

Abstract:

In this study Homotopy Perturbation Method (HPM) is employed to investigate free vibration of an Euler beam with variable stiffness resting on an elastic foundation. HPM is an easy-to-use and very efficient technique for the solution of linear or nonlinear problems. HPM produces analytical approximate expression which is continuous in the solution domain. This work shows that HPM is a promising method for free vibration analysis of nonuniform Euler beams on elastic foundation. Several case problems have been solved by using the technique and solutions have been compared with those available in the literature.

Keywords: Homotopy Perturbation Method, Elastic Foundation, Vibration, Beam

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Authors: F. Soleymani, M. Sharifi

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Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: H. Ozbasaran

Abstract:

IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: Cantilever, IPN, IPE, lateral torsional buckling

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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: Meisam Omidi, M. Mirijalili, Mohammadmehdi Choolaei, Z. Sharifi, F. Haghiralsadat, F. Yazdian

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In this work, we have used arrays of micromechanical piezoresistive cantilever with different geometries to detect carcinoembryonic antigen (CEA), which is known as an important biomarker associated with various cancers such as colorectal, lung, breast, pancreatic, and bladder cancer. The sensing principle is based on the surface stress changes induced by antigen–antibody interaction on the microcantilevers surfaces. Different concentrations of CEA in a human serum albumin (HSA) solution were detected as a function of deflection of the beams. According to the experiments, it was revealed that microcantilevers have surface stress sensitivities in the order of 8 (mJ/m). This matter allows them to detect CEA concentrations as low as 3 ng/mL or 18 pM. This indicates the fact that the self-sensing microcantilevers approach is beneficial for pathological tests.

Keywords: Micromechanical biosensors, Carcinoembryonic antigen (CEA), surface stress.

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Authors: Nilson Barbieri, Renato Barbieri

Abstract:

–In this paper the damage in clamped-free, clampedclamped and free-free beam are analyzed considering samples without and with structural modifications. The damage location is investigated by the use of the bispectrum and wavelet analysis. The mathematical models are obtained using 2D elasticity theory and the Finite Element Method (FEM). The numerical and experimental data are approximated using the Particle Swarm Optimizer (PSO) method and this way is possible to adjust the localization and the severity of the damage. The experimental data are obtained through accelerometers placed along the sample. The system is excited using impact hammer.

Keywords: Damage, beam, PSO, bispectrum, wavelet transform

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