Search results for: stiffness and damping coefficients

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

Abstract:

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: Nitish Kumar Vaja, Oumar Barry, Brian DeJong

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Aeolian vibrations are the major cause for the failure of conductor cables. Using a Stockbridge damper reduces these vibrations and increases the life span of the conductor cable. Designing an efficient Stockbridge damper that suits the conductor cable requires a robust mathematical model with minimum assumptions. However it is not easy to analytically model the complex geometry of the messenger. Therefore an equivalent stiffness must be determined so that it can be used in the analytical model. This paper examines the bending stiffness of the cable and discusses the effect of this stiffness on the natural frequencies. The obtained equivalent stiffness compensates for the assumption of modeling the messenger as a rod. The results from the free vibration analysis of the analytical model with the equivalent stiffness is validated using the full scale finite element model of the Stockbridge damper.

Keywords: equivalent stiffness, finite element model, free vibration response, Stockbridge damper

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Authors: H. K. Sachidananda, K. Raghunandana, B. Shivamurthy

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The estimation of gear tooth stiffness is important for finding the load distribution between the gear teeth when two consecutive sets of teeth are in contact. Based on dynamic model a C-program has been developed to compute mesh stiffness. By using this program position dependent mesh stiffness of spur gear tooth for various profile shifts have been computed for a fixed center distance and altering tooth-sum gearing (100 by ± 4%). It is found that the C-program using dynamic model is one of the rapid soft computing technique which helps in design of gears. The mesh tooth stiffness along the path of contact is studied for both 20° and 25° pressure angle gears at various profile shifts. Better tooth stiffness is noticed in case of negative alteration tooth-sum gears compared to standard and positive alteration tooth-sum gears. Also, in case of negative alteration tooth-sum gearing better mesh stiffness is noticed in 20° pressure angle when compared to 25°.

Keywords: altered tooth-sum gearing, bending fatigue, mesh stiffness, spur gear

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Authors: Nathi Ram, Saurabh K. Yadav

Abstract:

In turbomachinery, the turbulent flow occurs due to the use of high velocity of low kinematic viscosity lubricants and used in many industrial applications. In the present work, the performance of symmetric slot-entry hybrid worn journal bearing under laminar and turbulent lubrication has been investigated. For turbulent lubrication, the Reynolds equation has been modified using Constantinescu turbulent model. This modified equation has been solved using the finite element method. The effect of turbulent lubrication on bearing’s performance has been presented for symmetric hybrid journal bearing. The slot-entry hybrid worn journal bearing under turbulent/laminar regimes have been investigated. It has been observed that the stiffness and damping coefficients are more for the bearing having slot width ratio (SWR) of 0.25 than the bearing with SWR of 0.5 and 0.75 under the turbulent regime. Further, it is also observed that for constant wear depth parameter, stability threshold speed gets increased for bearing operates at slot width ratio 0.25 under turbulent lubrication.

Keywords: hydrostatic bearings, journal bearings, restrictors, turbulent flow models, finite element technique

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Authors: Ji Xi, Cheng Song Chin, Ehsan Mesbahi

Abstract:

Structure-borne noise is an important aspect of offshore platform sound field. It can be generated either directly by vibrating machineries induced mechanical force, indirectly by the excitation of structure or excitation by incident airborne noise. Therefore, limiting of the transmission of vibration energy throughout the offshore platform is the key to control the structure-borne noise. This is usually done by introducing damping treatment to the steel structures. Two types of damping treatment using on-board are presented. By conducting a statistical energy analysis (SEA) simulation on a jack-up rig, the noise level in the source room, the neighboring rooms, and remote living quarter cabins are compared before and after the damping treatments been applied. The results demonstrated that, in the source neighboring room and living quarter area, there is a significant noise reduction with the damping treatment applied, whereas in the source room where air-borne sound predominates that of structure-borne sound, the impact is not obvious. The subsequent optimization design of damping treatment in the offshore platform can be made which enable acoustic professionals to implement noise control during the design stage for offshore crews’ hearing protection and habitant comfortability.

Keywords: statistical energy analysis, damping treatment, noise control, offshore platform

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Authors: Jose D. Herrera, Mario A. Rios

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This paper deals with the coordinated tuning of the Power System Stabilizer (PSS) controller and Power Oscillation Damping (POD) Controller of Flexible AC Transmission System (FACTS) in a multi-machine power systems. The coordinated tuning is based on the critical eigenvalues of the power system and a model reduction technique where the Hankel Singular Value method is applied. Through the linearized system model and the parameter-constrained nonlinear optimization algorithm, it can compute the parameters of both controllers. Moreover, the parameters are optimized simultaneously obtaining the gains of both controllers. Then, the nonlinear simulation to observe the time response of the controller is performed.

Keywords: electromechanical oscillations, power system stabilizers, power oscillation damping, hankel singular values

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Authors: Seyed Saeid Tabaee, Omid Bahar

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Nowadays, using energy dissipation devices has been commonly used in structures. A high rate of energy absorption during earthquakes is the benefit of using such devices, which results in damage reduction of structural elements specifically columns. The hysteretic damping capacity of energy dissipation devices is the key point that it may adversely complicate analysis and design of such structures. This effect may be generally represented by equivalent viscous damping. The equivalent viscous damping may be obtained from the expected hysteretic behavior under the design or maximum considered displacement of a structure. In this paper, the hysteretic damping coefficient of a steel moment resisting frame (MRF), which its performance is enhanced by a buckling restrained brace (BRB) system has been evaluated. Having the foresight of damping fraction between BRB and MRF is inevitable for seismic design procedures like Direct Displacement-Based Design (DDBD) method. This paper presents an approach to calculate the damping fraction for such systems by carrying out the dynamic nonlinear time history analysis (NTHA) under harmonic loading, which is tuned to the natural frequency of the system. Two steel moment frame structures, one equipped with BRB, and the other without BRB are simultaneously studied. The extensive analysis shows that proportion of each system damping fraction may be calculated by its shear story portion. In this way, the contribution of each BRB in the floors and their general contribution in the structural performance may be clearly recognized, in advance.

Keywords: buckling restrained brace, direct displacement based design, dual systems, hysteretic damping, moment resisting frames

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Authors: Yaping Zhao

Abstract:

In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: K. Doi, T. Nishimura, M. Umeda

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There are very few sound interfaces that both healthy people and hearing handicapped people can use to play together. In this study, we developed a sound tactile interface that makes use of the human sensation of stiffness. The interface comprises eight elastic objects having varying degrees of stiffness. Each elastic object is shaped like a column. When people with and without hearing disabilities press each elastic object, different sounds are produced depending on the stiffness of the elastic object. The types of sounds used were “Do Re Mi sounds.” The interface has a major advantage in that people with or without hearing disabilities can play with it. We found that users were able to recognize the hardness sensation and relate it to the corresponding Do Re Mi sounds.

Keywords: tactile sense, sound interface, stiffness perception, elastic object

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Authors: Shuenn-Yih Chang, Chiu-LI Huang, Ngoc-Cuong Tran

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A new family of structure-dependent integration methods, whose coefficients of the difference equation for displacement increment are functions of the initial structural properties and the step size for time integration, is proposed in this work. This family method can simultaneously integrate the controllable numerical dissipation, explicit formulation and unconditional stability together. In general, its numerical dissipation can be continuously controlled by a parameter and it is possible to achieve zero damping. In addition, it can have high-frequency damping to suppress or even remove the spurious oscillations high frequency modes. Whereas, the low frequency modes can be very accurately integrated due to the almost zero damping for these low frequency modes. It is shown herein that the proposed family method can have exactly the same numerical properties as those of HHT-α method for linear elastic systems. In addition, it still preserves the most important property of a structure-dependent integration method, which is an explicit formulation for each time step. Consequently, it can save a huge computational efforts in solving inertial problems when compared to the HHT-α method. In fact, it is revealed by numerical experiments that the CPU time consumed by the proposed family method is only about 1.6% of that consumed by the HHT-α method for the 125-DOF system while it reduces to be 0.16% for the 1000-DOF system. Apparently, the saving of computational efforts is very significant.

Keywords: structure-dependent integration method, nonlinear dynamic analysis, unconditional stability, numerical dissipation, accuracy

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Authors: Tohid Rahimi, Yahya Naderi, Babak Yousefi, Seyed Hossein Hoseini

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Today’s modern interconnected power system is highly complex in nature. In this, one of the most important requirements during the operation of the electric power system is the reliability and security. Power and frequency oscillation damping mechanism improve the reliability. Because of power system stabilizer (PSS) low speed response against of major fault such as three phase short circuit, FACTs devise that can control the network condition in very fast time, are becoming popular. However, FACTs capability can be seen in a major fault present when nonlinear models of FACTs devise and power system equipment are applied. To realize this aim, the model of multi-machine power system with FACTs controller is developed in MATLAB/SIMULINK using Sim Power System (SPS) blockiest. Among the FACTs device, Static synchronous series compensator (SSSC) due to high speed changes its reactance characteristic inductive to capacitive, is effective power flow controller. Tuning process of controller parameter can be performed using different method. However, Genetic Algorithm (GA) ability tends to use it in controller parameter tuning process. In this paper, firstly POD controller is used to power oscillation damping. But in this station, frequency oscillation dos not has proper damping situation. Therefore, FOD controller that is tuned using GA is using that cause to damp out frequency oscillation properly and power oscillation damping has suitable situation.

Keywords: power oscillation damping (POD), frequency oscillation damping (FOD), Static synchronous series compensator (SSSC), Genetic Algorithm (GA)

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Authors: Ajay Kumar Sinha, Sharad Singh, Anukriti Sinha

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Passive energy dissipation method for earthquake protection of structures is undergoing developments for improved performance. Combined use of different types of damping mechanisms has shown positive results in the near past. Different supplemental damping methods like viscous damping, frictional damping and metallic damping are being combined together for optimum performance. The conventional method of connecting passive dampers to structures is a parallel connection between the damper unit and structural member. Researchers are investigating coupling effect of different types of dampers. The most popular choice among the research community is coupling of viscous dampers and frictional dampers. The series and parallel coupling of these damping units are being studied for relative performance of the coupled system on response control of structures against earthquake. In this paper an attempt has been made to couple Fluid Viscous Dampers and Frictional Dampers in series and parallel to form a single unit of damping system. The relative performance of the coupled units has been studied on three dimensional reinforced concrete framed structure. The current theories of structural dynamics in practice for viscous damping and frictional damping have been incorporated in this study. The time history analysis of the structural system with coupled damper units, uncoupled damper units as well as of structural system without any supplemental damping has been performed in this study. The investigations reported in this study show significant improved performance of coupled system. A higher natural frequency of the system outside the forcing frequency has been obtained for structural systems with coupled damper units as against the other cases. The structural response of the structure in terms of storey displacement and storey drift show significant improvement for the case with coupled damper units as against the cases with uncoupled units or without any supplemental damping. The results are promising in terms of improved response of the structure with coupled damper units. Further investigations in this regard for a comparative performance of the series and parallel coupled systems will be carried out to study the optimum behavior of these coupled systems for enhanced response control of structural systems.

Keywords: frictional damping, parallel coupling, response control, series coupling, supplemental damping, viscous 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: Yashar Haghighatfar, Shahrzad Mirhosseini

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Pull-in instability is a nonlinear and crucial effect that is important for the design of microelectromechanical system devices. In this paper, the appropriate electrostatic voltage range is determined by measuring fluid flow pressure via micro pressure sensor based microbeam. The microbeam deflection contains two parts, the static and perturbation deflection of static. The second order equation regarding the equivalent stiffness, mass and damping matrices based on Galerkin method is introduced to predict pull-in instability due to the external voltage. Also the reduced order method is used for solving the second order nonlinear equation of motion. Furthermore, in the present study, the micro capacitive pressure sensor is designed for measuring special fluid flow pressure range. The results show that the measurable pressure range can be optimized, regarding damping field and external voltage.

Keywords: MEMS, pull-in instability, electrostatically actuated microbeam, reduced order method

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Authors: Samir Hassan AL-Nesrawy, Mohammed Al-Maamori, A. S. Hassani

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Rebound resilience for various elastomeric composites has been measured by Tripsometer devise, in order to investigate the effect of mix of C.B & Reclaim loading on elastomeric materials to absorb or damping vibration or shocks by fenders uses in the Iraqi berths. After having been certain about attaining the physical and mechanical properties of the new samples which are similar to the levels of their standard ones, damping properties for the new samples have been measured and compared with those of the standard fenders. The new samples included four rubber blends from (SBR/NR/BR-cis) and four loading levels of mix carbon black (type N-375) and reclaim to become sixteen compound contain SBR(100,60,60,60), NR(0,10,20,30), BRcis(30,20,10,0) and loading level for C.B, Reclaim (10,20,30,40). Damping measurements have been carried out by the method Free Vibration Resilience Pendulum method (by using Wallace R2-Dunlop Tripsometer) and from this Resilience Pendulum method, both the resilience percentage value (R%) and time decay (t0) have been measured at 50oC. We found that the results of this method proved that the increment of C.B, Reclaim level in these robber composite lead to decreasing the resiliency (R%) and damping time.

Keywords: damping materials, carbon black mixture effect, mechanical properties, rubber blends SBR/NR/BRcis

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Authors: Fumiya Sugino, Naohiro Nakamura, Yuji Miyazu

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In earthquake resistant design of buildings, evaluation of vibration characteristics is important. In recent years, due to the increment of super high-rise buildings, the evaluation of response is important for not only the first mode but also higher modes. The knowledge of vibration characteristics in buildings is mostly limited to the first mode and the knowledge of higher modes is still insufficient. In this paper, using earthquake observation records of a SRC building by applying frequency filter to ARX model, characteristics of first and second modes were studied. First, we studied the change of the eigen frequency and the damping ratio during the 3.11 earthquake. The eigen frequency gradually decreases from the time of earthquake occurrence, and it is almost stable after about 150 seconds have passed. At this time, the decreasing rates of the 1st and 2nd eigen frequencies are both about 0.7. Although the damping ratio has more large error than the eigen frequency, both the 1st and 2nd damping ratio are 3 to 5%. Also, there is a strong correlation between the 1st and 2nd eigen frequency, and the regression line is y=3.17x. In the damping ratio, the regression line is y=0.90x. Therefore 1st and 2nd damping ratios are approximately the same degree. Next, we study the eigen frequency and damping ratio from 1998 after 3.11 earthquakes, the final year is 2014. In all the considered earthquakes, they are connected in order of occurrence respectively. The eigen frequency slowly declined from immediately after completion, and tend to stabilize after several years. Although it has declined greatly after the 3.11 earthquake. Both the decresing rate of the 1st and 2nd eigen frequencies until about 7 years later are about 0.8. For the damping ratio, both the 1st and 2nd are about 1 to 6%. After the 3.11 earthquake, the 1st increases by about 1% and the 2nd increases by less than 1%. For the eigen frequency, there is a strong correlation between the 1st and 2nd, and the regression line is y=3.17x. For the damping ratio, the regression line is y=1.01x. Therefore, it can be said that the 1st and 2nd damping ratio is approximately the same degree. Based on the above results, changes in eigen frequency and damping ratio are summarized as follows. In the long-term study of the eigen frequency, both the 1st and 2nd gradually declined from immediately after completion, and tended to stabilize after a few years. Further it declined after the 3.11 earthquake. In addition, there is a strong correlation between the 1st and 2nd, and the declining time and the decreasing rate are the same degree. In the long-term study of the damping ratio, both the 1st and 2nd are about 1 to 6%. After the 3.11 earthquake, the 1st increases by about 1%, the 2nd increases by less than 1%. Also, the 1st and 2nd are approximately the same degree.

Keywords: eigenfrequency, damping ratio, ARX model, earthquake observation records

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Authors: R. Resmi, M. R. Baiju

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The thermal damping of a dynamic vibrating micromirror is an important factor affecting the design of MEMS based actuator systems. In the development process of new micromirror systems, assessing the extent of energy loss due to thermal damping accurately and predicting the performance of the system is very essential. In this paper, the depth of the thermal penetration layer at different eigenfrequencies and the temperature variation distributions surrounding a vibrating micromirror is analyzed. The thermal penetration depth corresponds to the thermal boundary layer in which energy is lost which is a measure of the thermal damping is found out. The energy is mainly dissipated in the thermal boundary layer and thickness of the layer is an important parameter. The detailed thermoacoustics is used to model the air domain surrounding the micromirror. The thickness of the boundary layer, temperature variations and thermal power dissipation are analyzed for a Si based torsional mode micromirror. It is found that thermal penetration depth decreases with eigenfrequency and hence operating the micromirror at higher frequencies is essential for reducing thermal damping. The temperature variations and thermal power dissipations at different eigenfrequencies are also analyzed. Both frequency-response and eigenfrequency analyses are done using COMSOL Multiphysics software.

Keywords: Eigen frequency analysis, micromirrors, thermal damping, thermoacoustic interactions

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Authors: S. A. Alotaibi, M. A. Al-Ajmi

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This work introduces a new concept for controlling the mechanical vibrations via variable stiffness coil spring. The concept relies on fitting a screw though the spring to change the number of active spring coils. A prototype has been built and tested with promising results toward an innovation in the field of vibration control.

Keywords: variable stiffness, coil spring, vibration control, computer science

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Authors: Shahzad Yousaf, Imran Shafi

Abstract:

This paper presents a new method for calculation of pressure loss coefficients by use of the artificial neural network (ANN) in tee junctions. Geometry and flow parameters are feed into ANN as the inputs for purpose of training the network. Efficacy of the network is demonstrated by comparison of the experimental and ANN based calculated data of pressure loss coefficients for combining flows in a tee junction. Reynolds numbers ranging from 200 to 14000 and discharge ratios varying from minimum to maximum flow for calculation of pressure loss coefficients have been used. Pressure loss coefficients calculated using ANN are compared to the models from literature used in junction flows. The results achieved after the application of ANN agrees reasonably to the experimental values.

Keywords: artificial neural networks, combining flow, pressure loss coefficients, solar collector tee junctions

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Authors: Gurubasavaraju T. M.

Abstract:

The magnetorheological (MR) damper could provide variable damping force with respect to the different input magnetic field. The damping force could be estimated through computational analysis using finite element and computational fluid dynamics analysis. The double-ended damper operates without changing the total volume of fluid. In this paper, damping force of double ended damper under different magnetic field is computed. Initially, the magneto-statics analysis carried out to evaluate the magnetic flux density across the fluid flow gap. The respective change in the rheology of the MR fluid is computed by using the experimentally fitted polynomial equation of shear stress versus magnetic field plot of MR fluid. The obtained values are substituted in the Herschel Buckley model to express the non-Newtonian behavior of MR fluid. Later, using computational fluid dynamic (CFD) analysis damping characteristics in terms of force versus velocity and force versus displacement for the respective magnetic field is estimated. The purpose of the present approach is to characterize the preliminary designed MR damper before fabricating.

Keywords: MR fluid, double ended MR damper, CFD, FEA

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Authors: Kourosh Fatehi, Niloofar Hanafi

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One of the challenges in providing optimal prosthetic legs for lower limb amputees is to select the appropriate foot stiffness that suits their individual needs and preferences. Foot stiffness affects various aspects of walking, such as stability, comfort, and energy expenditure. However, the current prescription process is largely based on trial-and-error, manufacturer recommendations, or clinician judgment, which may not reflect the prosthesis user’s subjective experience or psychophysical sensitivity. Therefore, there is a need for more scientific and technological tools to measure and understand how prosthesis users perceive and prefer different foot stiffness levels, and how this preference relates to clinical outcomes. This review covers how to measure and design lower leg prostheses based on user preference and foot stiffness. It also explores how these factors affect walking outcomes and quality of life, and identifies the current challenges and gaps in this field from a mechanical engineering standpoint.

Keywords: perception, preference, prosthetics, stiffness

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Authors: Yaping Zhao, Yimin Zhang

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In the present paper, the stationary random vibration of a uniform cantilever beam is investigated. Two types of damping mechanism, i.e. the external and internal viscous dampings, are taken into account simultaneously. The excitation form is the support motion, and it is ideal white. Because two type of damping mechanism are considered concurrently, the product of the modal damping ratio and the natural frequency is not a constant anymore. As a result, the infinite definite integral encountered in the process of computing the mean square response is more complex than that in the existing literature. One signal progress of this work is to have calculated these definite integrals accurately. The precise solution of the mean square response is thus obtained in the infinite series form finally. Numerical examples are supplied and the numerical outcomes acquired confirm the validity of the theoretical analyses.

Keywords: random vibration, cantilever beam, mean square response, white noise

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Authors: Chih-Jer Lin, Chun-Ying Lee, Ying Liu, Chiang-Ho Cheng

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The main objective of this article is to present the semi-active vibration control using an electro-rheological fluid embedded sandwich structure for a cantilever beam. ER fluid is a smart material, which cause the suspended particles polarize and connect each other to form chain. The stiffness and damping coefficients of the ER fluid can be changed in 10 micro seconds; therefore, ERF is suitable to become the material embedded in the tunable vibration absorber to become a smart absorber. For the ERF smart material embedded structure, the fuzzy control law depends on the experimental expert database and the proposed self-tuning strategy. The electric field is controlled by a CRIO embedded system to implement the real application. This study investigates the different performances using the Type-1 fuzzy and interval Type-2 fuzzy controllers. The Interval type-2 fuzzy control is used to improve the modeling uncertainties for this ERF embedded shock absorber. The self-tuning vibration controllers using Type-1 and Interval Type-2 fuzzy law are implemented to the shock absorber system. Based on the resulting performance, Internal Type-2 fuzzy is better than the traditional Type-1 fuzzy control for this vibration control system.

Keywords: electro-rheological fluid, semi-active vibration control, shock absorber, type 2 fuzzy control

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Authors: Ahmed Noor Al-qayyim, Barlas Özden Çağlayan

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Structural failure is caused mainly by damage that often occurs on structures. Many researchers focus on obtaining very efficient tools to detect the damage in structures in the early state. In the past decades, a subject that has received considerable attention in literature is the damage detection as determined by variations in the dynamic characteristics or response of structures. This study presents a new damage identification technique. The technique detects the damage location for the incomplete structure system using output data only. The method indicates the damage based on the free vibration test data by using “Two Points - Condensation (TPC) technique”. This method creates a set of matrices by reducing the structural system to two degrees of freedom systems. The current stiffness matrices are obtained from optimization of the equation of motion using the measured test data. The current stiffness matrices are compared with original (undamaged) stiffness matrices. High percentage changes in matrices’ coefficients lead to the location of the damage. TPC technique is applied to the experimental data of a simply supported steel beam model structure after inducing thickness change in one element. Where two cases are considered, the method detects the damage and determines its location accurately in both cases. In addition, the results illustrate that these changes in stiffness matrix can be a useful tool for continuous monitoring of structural safety using ambient vibration data. Furthermore, its efficiency proves that this technique can also be used for big structures.

Keywords: damage detection, optimization, signals processing, structural health monitoring, two points–condensation

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Authors: Fabrizio Iezzi, Claudio Valente

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The viscous damping in dynamic systems can be proportional or non-proportional. In the first case, the mode shapes are real whereas in the second case they are complex. From an engineering point of view, the complexity of the mode shapes is important in order to quantify the non-proportional damping. Different indices exist to provide estimates of the modal complexity. These indices are or not zero, depending whether the mode shapes are not or are complex. The modal density problem arises in the experimental identification when the dynamic systems have close modal frequencies. Depending on the entity of this closeness, the mode shapes can hold fictitious imaginary quantities that affect the values of the modal complexity indices. The results are the failing in the identification of the real or complex mode shapes and then of the proportional or non-proportional damping. The paper aims to show the influence of the modal density on the values of these indices in case of both proportional and non-proportional damping. Theoretical and pseudo-experimental solutions are compared to analyze the problem according to an appropriate mechanical system.

Keywords: complex mode shapes, dynamic systems identification, modal density, non-proportional damping

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Authors: Edina Koch, Péter Hudacsek

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In railways transition zone is present at the boundaries of zones with different stiffness. When a train rides from an embankment onto a stiff structure, such as a bridge, tunnel or culvert, an abrupt change in the support stiffness occurs possibly inducing differential settlements. This in long term can yield to the degradation of the tracks and foundations in the transition zones. A number of techniques have been proposed or implemented to provide gradual stiffness transition at the problem zones, such as methods to ensure gradually changing pad stiffness, application of long sleepers or installation of auxiliary rails in the transition zone. Aim of the research presented in this paper is to analyze the 3D and the dynamic effects induced by the passing train over an area where significant difference in the support stiffness exists. The effects were analyzed for different arrangements associated with certain differential settlement mitigation strategies of the transition zones.

Keywords: culvert, dynamic load, HS small model, railway transition zone

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

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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: Donatello Cardone

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Bilinear hysteresis models are usually used to describe the cyclic behavior of high damping rubber bearings. However, they neglect a number of phenomena (such as the interaction between axial load and shear force, buckling and post-buckling behavior, cavitation, scragging effects, etc.) that can significantly influence the dynamic behavior of such isolation devices. In this work, an advanced hysteresis model is examined and properly calibrated using consolidated procedures. Results of preliminary numerical analyses, performed in OpenSees, are shown and compared with the results of experimental tests on high damping rubber bearings and simulation analyses using alternative nonlinear models. The findings of this study can provide an useful tool for the accurate evaluation of the seismic response of structures with rubber-based isolation systems.

Keywords: seismic isolation, high damping rubber bearings, numerical modeling, axial-shear force interaction

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Authors: H. M. Mobarak, Helen Wu, Chunhui Yang

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In this study, an analytical model is developed to study crack breathing behavior under the effect of crack location and unbalance force. Crack breathing behavior is determined using effectual bending angle by studying the transient change in closed area of the crack. The status of the crack of a balanced shaft is symmetrical about shaft rotational angle and the duration of each crack status remains unchanged. The global stiffness of the balanced shaft is independent of crack location. Different crack breathing behavior for the unbalanced shaft has been observed. The influence of crack location on the unbalanced shaft stiffness can be divided into three regions. When the crack is located between 0.3L and 0.8335L, where L is the total length of the shaft, the unbalanced shaft is less stiff and when located outside this region it is stiffer than the balanced shaft. It was also found that unbalanced shaft stiffness has a maximum value with a crack at 0.1946L, a minimum value at 0.8053L and same value as balanced shaft at 0.3L and 0.8335L.

Keywords: cracked shaft, crack location, shaft stiffness, unbalanced force

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Authors: Aleš Kratochvíl, Svatomír Slavík

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The paper presents an aircraft flutter suppression by active damping of supplementary control surface at trailing edge. The mathematical model of thin oscillation airfoil with control surface driven by pilot is developed. The supplementary control surface driven by control law is added. Active damping of flutter by several control law is present. The structural model of tailplane with an aerodynamic strip theory based on the airfoil model is developed by a finite element method. The optimization process of stiffens parameters is carried out to match the structural model with results from a ground vibration test of a small sport airplane. The implementation of supplementary control surface driven by control law is present. The active damping of tailplane model is shown.

Keywords: active damping, finite element method, flutter, tailplane model

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