Search results for: One degree of freedom vibration system

Authors: Thomas Jin-Chee Liu, Yu-Shen Chen

Abstract:

Using the numerical and experimental methods, this paper discusses some primary studies on the vibration and cooling performances of the piezoelectric cooling fan with the rectangular blade. When the fan works at its natural frequency, the vibrating displacement is largest and the cooling performance is best. Due to the vibration behavior, the cooling performance is affected by the geometry, material property, and working frequency of the piezoelectric cooling fan. 

Keywords: Piezoelectric cooling fan, finite element, vibration, natural frequency.

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Authors: Susana Sousa Machado

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The present article seeks to carry out along the lines of interpretation of the recent Portuguese Constitutional Court case law on the possibility of an employee to observe a worship day imposed by religious beliefs. In this approach to the question, considerations on the subject of the relationship between religious freedom and labour relations will inevitably arise. We intend to draw conclusions of practical application from the court decisions on the matter of freedom of religion.

Keywords: Freedom of Religion, Religion Beliefs, Workplace, Worship Day.

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Authors: Kejun Zhuang, Zhaohui Wen

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The main purpose of this paper is to investigate a discrete time three–species food chain system with ratio dependence. By employing coincidence degree theory and analysis techniques, sufficient conditions for existence of periodic solutions are established.

Keywords: Food chain, ratio–dependent, coincidence degree, periodic solutions.

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Authors: Kejun Zhuang

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In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Semi–ratio–dependent, predator–prey system, coincidence degree, time scales.

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Authors: G. Sakar, F. Ç. Bolat

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In this study free vibration analysis of aluminum honeycomb sandwich structures were carried out experimentally and numerically. The natural frequencies and mode shapes of sandwich structures fabricated with different configurations for clamped-free boundary condition were determined. The effects of lower and upper face sheet thickness, the core material thickness, cell diameter, cell angle and foil thickness on the vibration characteristics were examined. The numerical studies were performed with ANSYS package. While the sandwich structures were modeled in ANSYS the continuum model was used. Later, the numerical results were compared with the experimental findings.

Keywords: Sandwich structure, free vibration, numeric analysis, 3D model, continuum model.

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Authors: Youngkuen Cho, Seonhong Hwang, Jinyoung Min, Youngho Kim, Dohyung Lim, Hansung Kim

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Many studies have emphasized the importance of resistive exercise to maintain a healthy human body, particular in prevention of weakening of physical strength. Recently, some studies advocated that an application of vibration as a supplementary means in a regular training was effective in encouraging physical strength. Aim of the current study was, therefore, to identify if an application of vibration in a resistive exercise was effective in encouraging physical strength as that in a regular training. A 3-dimensional virtual lower extremity model for a healthy male and virtual leg-press model were generated and synchronized. Dynamic leg-press exercises on a slide machine with/without extra load and on a footboard with vibration as well as on a slide machine with extra load were analyzed. The results of the current indicated that the application of the vibration on the dynamic leg-press exercise might be not greatly effective in encouraging physical strength, compared with the dynamic leg press exercise with extra load. It was, however, thought that the application of the vibration might be helpful to elderly individuals because the reduced maximum muscle strength appeared by the effect of the vibration may avoid a muscular spasm, which can be driven from a high muscle strength sometimes produced during the leg-press exercise with extra load.

Keywords: Resistive exercise, leg-press exercise, muscle strength.

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Authors: Fengshuo Zhang, Zhouhong Li

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In this paper, we obtain sufficient conditions for the existence of at least four positive almost periodic solutions to an impulsive delayed periodic plankton allelopathy system with multiple exploited (or harvesting) terms. This result is obtained through the use of Mawhins continuation theorem of coincidence degree theory along with some properties relating to inequalities.

Keywords: Almost periodic solutions, plankton allelopathy system, coincidence degree, impulse.

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Authors: A. Shamsi, N. Choupani

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Active vibration isolation systems are less commonly used than passive systems due to their associated cost and power requirements. In principle, semi-active isolation systems can deliver the versatility, adaptability and higher performance of fully active systems for a fraction of the power consumption. Various semi-active control algorithms have been suggested in the past. This paper studies the 4DOF model of semi-active suspension performance controlled by on–off and continuous skyhook damping control strategy. The frequency and transient responses of model are evaluated in terms of body acceleration, roll angle and tire deflection and are compared with that of a passive damper. The results show that the semi-active system controlled by skyhook strategy always provides better isolation than a conventional passively damped system except at tire natural frequencies.

Keywords: Semi-active suspension system, Skyhook, Vibration isolation, 4DOF model.

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: Stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: Valbona Metaj

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The relationship between the state and the religion is different based on the fact that how powerful is the religion faith in a state and of the influences that affected the views of the constitution drafters according to the constitutional system they were based to draft their constitution. This paper aims at providing, through a comparative methodology, how it is regulated by the constitution the relationship between the state and the religion. The object of this study are the constitutions of Italy as a nation with catholic religious tradition, Greece as a nation with orthodox religion tradition, and Turkey as a nation which represents Muslim religion, while Albania as a nation known for its religious plurality. In particular, the analysis will be focused on the secular or religious principle provided in the constitution of each respective state. This comparative overview intends to discern which of the states analyzed is more tolerant and fully respects the freedom of religion. It results that most of the states subject of this study, despite their religious tradition have chosen the secular principle in their constitutions, but the religious freedom is differently guaranteed.

Keywords: Constitution, religion, religious freedom, secular.

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Authors: V. K. Nelson, S. Karthikeyan

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Axisymmetric vibration of an infinite Pyrocomposite circular hollow cylinder made of inner and outer pyroelectric layer of 6mm-class bonded together by a Linear Elastic Material with Voids (LEMV) layer is studied. The exact frequency equation is obtained for the traction free surfaces with continuity condition at the interfaces. Numerical results in the form of data and dispersion curves for the first and second mode of the axisymmetric vibration of the cylinder BaTio3 / Adhesive / BaTio3 by taking the Adhesive layer as an existing Carbon Fibre Reinforced Polymer (CFRP) are compared with a hypothetical LEMV layer with and without voids and as well with a pyroelectric hollow cylinder. The damping is analyzed through the imaginary parts of the complex frequencies.

Keywords: Axisymmetric vibration, CFRP, hollow cylinders, LEMV, pyrocomposite

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Authors: Hongmao Zhu, Jun Chu, Lei Shen, Zhihua Luo

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The principle of frequency and amplitude measurement of a vibrating object in water using ultrasonic speckle technique is presented in this paper. Compared with other traditional techniques, the ultrasonic speckle technique can be applied to vibration measurement of a nonmetal object with rough surface in water in a noncontact way. The relationship between speckle movement and object movement was analyzed. Based on this study, an ultrasonic speckle measurement system was set up. With this system the frequency and amplitude of an underwater vibrating cantilever beam was detected. The result shows that the experimental data is in good agreement with the calibrating data.

Keywords: Frequency, Amplitude, Vibration measurement, Ultrasonic speckle

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Authors: Azin Shakibabarough, Mojtaba Valinejadshoubi, Ashutosh Bagchi

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Structural vibration means repetitive motion that causes fatigue and reduction of the performance of a structure. An earthquake may release high amount of energy that can have adverse effect on all components of a structure. Therefore, decreasing of vibration or maintaining performance of structures such as bridges, dams, roads and buildings is important for life safety and reducing economic loss. When earthquake or any vibration happens, investigation on parts of a structure which sustain the seismic loads is mandatory to provide a safe condition for the occupants. One of the solutions for reducing the earthquake vibration in a structure is using of vibration control devices such as dampers and base isolators. The objective of this study is to investigate the optimal positions of friction dampers and base isolators for better seismic response of 2D frame. For this purpose, a two bay and six story frame with different distribution formats was modeled and some of their responses to earthquake such as inter-story drift, max joint displacement, max axial force and max bending moment were determined and compared using non-linear dynamic analysis.

Keywords: Fast nonlinear analysis, friction damper, base isolator, seismic vibration control, seismic response.

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Authors: Emiliano Matta

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Passive resonant vibration absorbers are among the most widely used dynamic control systems in civil engineering. They typically consist in a single-degree-of-freedom mechanical appendage of the main structure, tuned to one structural target mode through frequency and damping optimization. One classical scheme is the pendulum absorber, whose mass is constrained to move along a curved trajectory and is damped by viscous dashpots. Even though the principle is well known, the search for improved arrangements is still under way. In recent years this investigation inspired a type of bidirectional pendulum absorber (BPA), consisting of a mass constrained to move along an optimal three-dimensional (3D) concave surface. For such a BPA, the surface principal curvatures are designed to ensure a bidirectional tuning of the absorber to both principal modes of the main structure, while damping is produced either by horizontal viscous dashpots or by vertical friction dashpots, connecting the BPA to the main structure. In this paper, a variant of BPA is proposed, where damping originates from the variable tangential friction force which develops between the pendulum mass and the 3D surface as a result of a spatially-varying friction coefficient pattern. Namely, a friction coefficient is proposed that varies along the pendulum surface in proportion to the modulus of the 3D surface gradient. With such an assumption, the dissipative model of the absorber can be proven to be nonlinear homogeneous in the small displacement domain. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, because its equivalent damping ratio results independent on the amplitude of oscillations, and therefore its optimal performance does not depend on the excitation level. On the other hand, the HBPA is more compact than viscously damped BPAs because it does not need the installation of dampers. This paper presents the analytical model of the HBPA and an optimal methodology for its design. Numerical simulations of single- and multi-story building structures under wind and earthquake loads are presented to compare the HBPA with classical viscously damped BPAs. It is shown that the HBPA is a promising alternative to existing BPA types and that homogeneous tangential friction is an effective means to realize systems provided with amplitude-independent damping.

Keywords: Amplitude-independent damping, Homogeneous friction, Pendulum nonlinear dynamics, Structural control, Vibration resonant absorbers.

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Authors: M. Z Md Zain, M. O. Tokhi, M. S. Alam

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This paper describes a practical approach to design and develop a hybrid learning with acceleration feedback control (HLC) scheme for input tracking and end-point vibration suppression of flexible manipulator systems. Initially, a collocated proportionalderivative (PD) control scheme using hub-angle and hub-velocity feedback is developed for control of rigid-body motion of the system. This is then extended to incorporate a further hybrid control scheme of the collocated PD control and iterative learning control with acceleration feedback using genetic algorithms (GAs) to optimize the learning parameters. Experimental results of the response of the manipulator with the control schemes are presented in the time and frequency domains. The performance of the HLC is assessed in terms of input tracking, level of vibration reduction at resonance modes and robustness with various payloads.

Keywords: Flexible manipulator, iterative learning control, vibration suppression.

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Authors: Dong Wook Lee, Seung Hyun Kim

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Trial blasting is conducted to identify the characteristics of the blasting of the applicable ground before production blasting and to investigate various problems posed by blasting. The methods and pattern of production blasting are determined based on an analysis of the results of trial blasting. The bedrock in Jeju Island, South Korea is formed through the volcanic activities unlike the inland areas, composed of porous basalt. Trial blasting showed that the blast vibration frequency of sedimentary and metamorphic rocks in the inland areas is in a high frequency band of about 80 Hz while the blast vibration frequency of Jeju Island is in a low frequency band of 10~25 Hz. The frequency band is analyzed to be low due to the large cycle of blasting pattern as blast vibration passes through the layered structured ground layer where the rock formation and clickers irregularly repeat. In addition, the blast vibration equation derived from trial blasting was R: 0.885, S.E: 0.216 when applying the square root scaled distance (SRSD) relatively suitable for long distance, estimated at the confidence level of 95%.

Keywords: Attenuation index, basaltic ground, blasting vibration constant, blast vibration equation, clinker layer.

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Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

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An analytical 4-DOF nonlinear model of a de Laval rotor-stator system based on Energy Principles has been used theoretically and experimentally to investigate fault symptoms in a rotating system. The faults, namely rotor-stator-rub, crack and unbalance are modeled as excitations on the rotor shaft. Mayes steering function is used to simulate the breathing behaviour of the crack. The fault analysis technique is based on waveform signal, orbits and Fast Fourier Transform (FFT) derived from simulated and real measured signals. Simulated and experimental results manifest considerable mutual resemblance of elliptic-shaped orbits and FFT for a same range of test data.

Keywords: A breathing crack, fault, FFT, nonlinear, orbit, rotorstator rub, vibration analysis.

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Authors: Seongmin Yim, Hyun-Kyu Kang

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As a part of evaluation system for R&D program, the Korean government has applied feasibility analysis since 2008. Various professionals put forth a great effort in order to catch up the high degree of freedom of R&D programs, and make contributions to evolving the feasibility analysis. We analyze diverse R&D programs from various viewpoints, such as technology, policy, and Economics, integrate the separate analysis, and finally arrive at a definite result; whether a program is feasible or unfeasible. This paper describes the concept and method of the feasibility analysis as a decision making tool. The analysis unit and content of each criterion, which are key elements in a comprehensive decision making structure, are examined

Keywords: Decision Making of New Government R&D Program, Feasibility Analysis Study

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Authors: Emad Askar, Eldesoky Elsoaly, Mohamed Kamel, Hisham Kamel

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The objective of this article is to improve the passive vibration damping of solar array (SA) used in space structures, by the effective application of numerical optimization. A case study of a SA is used for demonstration. A finite element (FE) model was created and verified by experimental testing. Optimization was then conducted by implementing the FE model with the genetic algorithm, to find the optimal placement of aluminum circular patches, to suppress the first two bending mode shapes. The results were verified using experimental testing. Finally, a parametric study was conducted using the FE model where patch locations, material type, and shape were varied one at a time, and the results were compared with the optimal ones. The results clearly show that through the proper application of FE modeling and numerical optimization, passive vibration damping of space structures has been successfully achieved.

Keywords: Damping optimization, genetic algorithm optimization, passive vibration damping, solar array vibration damping.

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Authors: Thanh-Phong Dao, Shyh-Chour Huang

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This study presents a quasi-zero stiffness (QZS) vibration isolator using flexure-based spring mechanisms which afford both negative and positive stiffness elements, which enable self-adjustment. The QZS property of the isolator is achieved at the equilibrium position. A nonlinear mathematical model is then developed, based on the pre-compression of the flexure-based spring mechanisms. The dynamics are further analyzed using the Harmonic Balance method. The vibration attention efficiency is illustrated using displacement transmissibility, which is then compared with the corresponding linear isolator. The effects of parameters on performance are also investigated by numerical solutions. The flexure-based spring mechanisms are subsequently designed using the concept of compliant mechanisms, with evaluation by ANSYS software, and simulations of the QZS isolator.

Keywords: Vibration isolator, quasi-zero stiffness, flexure-based spring mechanisms, compliant mechanism.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

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In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

Keywords: Non-linear vibrations, Annular plates, Large amplitudes, FGM.

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Authors: Omer S. Mughieda

Abstract:

Two-dimensional finite element model was created in this work to investigate the stresses distribution within rock-like samples with offset open non-persistent joints under biaxial loading. The results of this study have explained the fracture mechanisms observed in tests on rock-like material with open non-persistent offset joints [1]. Finite element code SAP2000 was used to study the stresses distribution within the specimens. Four-nodded isoperimetric plain strain element with two degree of freedom per node, and the three-nodded constant strain triangular element with two degree of freedom per node were used in the present study.The results of the present study explained the formation of wing cracks at the tip of the joints for low confining stress as well as the formation of wing cracks at the middle of the joint for the higher confining stress. High shear stresses found in the numerical study at the tip of the joints explained the formation of secondary cracks at the tip of the joints in the experimental study. The study results coincide with the experimental observations which showed that for bridge inclination of 0o, the coalescence occurred due to shear failure and for bridge inclination of 90o the coalescence occurred due to tensile failure while for the other bridge inclinations coalescence occurred due to mixed tensile and shear failure.

Keywords: Finite element, open offset rock joint, SAP2000, biaxial loading.

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Authors: Omid A. Zargar

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In this paper, some common gearboxes vibration analysis methods and condition monitoring systems are explained. In addition, an experimental gearbox vibration analysis is discussed through a critical case history for a mixer gearbox related to Iran oil industry. The case history also consists of gear manufacturing (machining) recommendations, lubrication condition of gearbox and machinery maintenance activities that caused reduction in noise and vibration of the gearbox. Besides some of the recent patents and innovations in gearboxes, lubrication and vibration monitoring systems explained. Finally micro pitting and surface fatigue in pinion and bevel of mentioned horizontal to vertical gearbox discussed in details.

Keywords: Gear box, condition monitoring, time wave form (TWF), fast Fourier transform (FFT), gear mesh frequency (GMF), Shock Pulse measurement (SPM), bearing condition unit (BCU), pinion, bevel gear, micro pitting, surface fatigue.

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

Abstract:

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: K. Jayakumar, S. Thangavel

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In this paper proposed the effective fault detection of industrial drives by using Biorthogonal Posterior Vibration Signal-Data Probabilistic Wavelet Neural Network (BPPVS-WNN) system. This system was focused to reducing the current flow and to identify faults with lesser execution time with harmonic values obtained through fifth derivative. Initially, the construction of Biorthogonal vibration signal-data based wavelet transform in BPPVS-WNN system localizes the time and frequency domain. The Biorthogonal wavelet approximates the broken bearing using double scaling and factor, identifies the transient disturbance due to fault on induction motor through approximate coefficients and detailed coefficient. Posterior Probabilistic Neural Network detects the final level of faults using the detailed coefficient till fifth derivative and the results obtained through it at a faster rate at constant frequency signal on the industrial drive. Experiment through the Simulink tool detects the healthy and unhealthy motor on measuring parametric factors such as fault detection rate based on time, current flow rate, and execution time.

Keywords: Biorthogonal Wavelet Transform, Posterior Probabilistic Neural Network, Induction Motor.

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Authors: Iman Mousavinejad, Reza Kazemi, , Mohsen Bayani Khaknejad

Abstract:

Active Front Steering system (AFS) provides an electronically controlled superposition of an angle to the steering wheel angle. This additional degree of freedom enables a continuous and driving-situation dependent on adaptation of the steering characteristics. In an active steering system, there needs be no fixed relationship between the steering wheel and the angle of the road wheels. Not only can the effective steering ratio be varied with speed, for example, but also the road wheel angles can be controlled by a combination of driver and computer inputs. Features like steering comfort, effort and steering dynamics are optimized and stabilizing steering interventions can be performed. In contrast to the conventional stability control, the yaw rate was fed back to AFS controller and the stability performance was optimized with Sliding Mode control (SMC) method. In addition, tire uncertainties have been taken into account in SM controller to provide the control robustness. In this paper, 3-DOF nonlinear model is used to design the AFS controller and 8-DOF nonlinear model is used to model the controlled vehicle.

Keywords: Active Front Steering (AFS), Sliding Mode Control method (SMC), Yaw rate, Vehicle Stability, Robustness

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Authors: J. H. Kim, J. H. Kwon, J. S. Park, K. J. Lim

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This paper has been investigated a technique that predicts the performance of a bar-type unimorph piezoelectric vibration actuator depending on the frequency. This paper has been proposed an equivalent circuit that can be easily analyzed for the bar-type unimorph piezoelectric vibration actuator. In the dynamic analysis, rigidity and resonance frequency, which are important mechanical elements, were derived using the basic beam theory. In the equivalent circuit analysis, the displacement and bandwidth of the piezoelectric vibration actuator depending on the frequency were predicted. Also, for the reliability of the derived equations, the predicted performance depending on the shape change was compared with the result of a finite element analysis program.

Keywords: Actuator, performance, piezoelectric, unimorph.Actuator, performance, piezoelectric, unimorph.

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Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati

Abstract:

In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.

Keywords: Carbon nanotubes, vibration control, piezoelectric layers, elastic foundation.

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Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

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In the present study, the free vibration of magnetostrictive nano-plate (MsNP) resting on the Pasternak foundation is investigated. Firstly, the modified couple stress (MCS) and nonlocal elasticity theories are compared together and taken into account to consider the small scale effects; in this paper not only two theories are analyzed but also it improves the MCS theory is more accurate than nonlocal elasticity theory in such problems. A feedback control system is utilized to investigate the effects of a magnetic field. First-order shear deformation theory (FSDT), Hamilton’s principle and energy method are utilized in order to drive the equations of motion and these equations are solved by differential quadrature method (DQM) for simply supported boundary conditions. The MsNP undergoes in-plane forces in x and y directions. In this regard, the dimensionless frequency is plotted to study the effects of small scale parameter, magnetic field, aspect ratio, thickness ratio and compression and tension loads. Results indicate that these parameters play a key role on the natural frequency. According to the above results, MsNP can be used in the communications equipment, smart control vibration of nanostructure especially in sensor and actuators such as wireless linear micro motor and smart nano valves in injectors.

Keywords: Feedback control system, magnetostrictive nano-plate, modified couple stress theory, nonlocal elasticity theory, vibration analysis.

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Authors: James Kuria, John Kihiu

Abstract:

This work presents a numerical model developed to simulate the dynamics and vibrations of a multistage tractor gearbox. The effect of time varying mesh stiffness, time varying frictional torque on the gear teeth, lateral and torsional flexibility of the shafts and flexibility of the bearings were included in the model. The model was developed by using the Lagrangian method, and it was applied to study the effect of three design variables on the vibration and stress levels on the gears. The first design variable, module, had little effect on the vibration levels but a higher module resulted to higher bending stress levels. The second design variable, pressure angle, had little effect on the vibration levels, but had a strong effect on the stress levels on the pinion of a high reduction ratio gear pair. A pressure angle of 25o resulted to lower stress levels for a pinion with 14 teeth than a pressure angle of 20o. The third design variable, contact ratio, had a very strong effect on both the vibration levels and bending stress levels. Increasing the contact ratio to 2.0 reduced both the vibration levels and bending stress levels significantly. For the gear train design used in this study, a module of 2.5 and contact ratio of 2.0 for the various meshes was found to yield the best combination of low vibration levels and low bending stresses. The model can therefore be used as a tool for obtaining the optimum gear design parameters for a given multistage spur gear train.

Keywords: bending stress levels, frictional torque, gear designparameters, mesh stiffness, multistage gear train, vibration levels.

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