Search results for: linear acceleration method

Authors: Mohammad Younus Bhat

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The quaternion offset linear canonical transform (QOLCT), which isa time-shifted and frequency-modulated version of the quaternion linear canonical transform (QLCT), provides a more general framework of most existing signal processing tools. For the generalized QOLCT, the classical Heisenberg’s and Lieb’s uncertainty principles have been studied recently. In this paper, we first define the short-time quaternion offset linear canonical transform (ST-QOLCT) and drive its relationship with the quaternion Fourier transform (QFT). The crux of the paper lies in the generalization of several well-known uncertainty principles for the ST-QOLCT, including Donoho-Stark’s uncertainty principle, Hardy’s uncertainty principle, Beurling’s uncertainty principle, and the logarithmic uncertainty principle.

Keywords: Quaternion Fourier transform, Quaternion offset linear canonical transform, short-time quaternion offset linear canonical transform, uncertainty principle

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Authors: Ayhan Ince

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In this paper, an analytical simplified method for calculating elasto-plastic stresses strains of notched bodies subject to non-proportional loading paths is discussed. The method was based on the Neuber notch correction, which relates the incremental elastic and elastic-plastic strain energy densities at the notch root and the material constitutive relationship. The validity of the method was presented by comparing computed results of the proposed model against finite element numerical data of notched shaft. The comparison showed that the model estimated notch-root elasto-plastic stresses strains with good accuracy using linear-elastic stresses. The prosed model provides more efficient and simple analysis method preferable to expensive experimental component tests and more complex and time consuming incremental non-linear FE analysis. The model is particularly suitable to perform fatigue life and fatigue damage estimates of notched components subjected to non-proportional loading paths.

Keywords: elasto-plastic, stress-strain, notch analysis, nonprortional loadings, cyclic plasticity, fatigue

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Authors: Martin Cermak, Stanislav Sysala

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In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MATLAB.

Keywords: isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution

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Authors: Nolvi Francisco Baggio Filho, Roniele Belusso

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Many industrial processes require a precise linear motion. Usually, this movement is achieved with the use of rotary motors combined with electrical control systems and mechanical systems such as gears, pulleys and bearings. Other types of devices are based on linear motors, where the linear motion is obtained directly. The Linear Stepper Motor (MLP) is an excellent solution for industrial applications that require precise positioning and high speed. This study presents an MLP formed by a linear structure and static ferromagnetic material, and a mover structure in which three coils are mounted. Mechanical suspension systems allow a linear movement between static and mover parts, maintaining a constant air gap. The operating principle is based on the tendency of alignment of magnetic flux through the path of least reluctance. The force proportional to the intensity of the electric current and the speed proportional to the frequency of the excitation coils. The study of this device is still based on the use of a numerical and experimental analysis to verify the relationship among electric current applied and planar force developed. In addition, the magnetic field in the air gap region is also monitored.

Keywords: linear stepper motor, planar traction force, reluctance magnetic, industry applications

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Authors: Sergey Kopysov, Nikita Nedozhogin, Leonid Tonkov

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The article presents a parallel iterative solver for large sparse linear systems which can be used on a heterogeneous platform. Traditionally, the problem of solving linear systems does not scale well on multi-CPU/multi-GPUs clusters. For example, most of the attempts to implement the classical conjugate gradient method were at best counted in the same amount of time as the problem was enlarged. The paper proposes the pipelined variant of the conjugate gradient method (PCG), a formulation that is potentially better suited for hybrid CPU/GPU computing since it requires only one synchronization point per one iteration instead of two for standard CG. The standard and pipelined CG methods need the vector entries generated by the current GPU and other GPUs for matrix-vector products. So the communication between GPUs becomes a major performance bottleneck on multi GPU cluster. The article presents an approach to minimize the communications between parallel parts of algorithms. Additionally, computation and communication can be overlapped to reduce the impact of data exchange. Using the pipelined version of the CG method with one synchronization point, the possibility of asynchronous calculations and communications, load balancing between the CPU and GPU for solving the large linear systems allows for scalability. The algorithm is implemented with the combined use of technologies: MPI, OpenMP, and CUDA. We show that almost optimum speed up on 8-CPU/2GPU may be reached (relatively to a one GPU execution). The parallelized solver achieves a speedup of up to 5.49 times on 16 NVIDIA Tesla GPUs, as compared to one GPU.

Keywords: conjugate gradient, GPU, parallel programming, pipelined algorithm

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Authors: José E. Q. Souza, Marcio Fontana, Antonio C. C. Lima

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This paper presents analysis and characterization of a piezoelectric micro-generator for energy harvesting application. A low-cost experimental prototype was designed to operate as piezoelectric micro-generator in the laboratory. An input acceleration of 9.8m/s2 using a sine signal (peak-to-peak voltage: 1V, offset voltage: 0V) at frequencies ranging from 10Hz to 160Hz generated a maximum average power of 432.4μW (linear mass position = 25mm) and an average power of 543.3μW (angular mass position = 35°). These promising results show that the prototype can be considered for low consumption load application as an energy harvesting micro-generator.

Keywords: piezoelectric, micro-generator, energy harvesting, cantilever beam

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Authors: Xin-Yan Ji, Jing Wang, Chang Liu, Yan-Qiang Bi, Zhong-Xu Xu, Xi-Yuan Li

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Thermal tests of electronic units are critically important for the reliability validation and performance demonstration of the spacecraft hard-wares. The tailoring equation in MIL-STD-1540 is based on fatigue of solder date. In the present paper, a new test condition tailoring expression is proposed to fit different thermo-mechanical fatigue and different subsystems, by introducing an integrated evaluating method for the fatigue acceleration exponent. The validate test has been accomplished and the data has been analyzed and compared with that from the MIL-STD-1540 tailoring equations. The results are encouraging and reasonable.

Keywords: thermal cycling test, thermal fatigue, tailoring equation, test condition planning

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method of buckling analysis frame considering the effect of the axial load. The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. In this method, stiffness matrix of the structure is considered to be constant. The most important advantage of such a method is that it obtains both upper and lower critical loads. The advanced of the present method is fast convergence, ability to use computer simulations, and ability to model structures with semi-rigid support conditions using linear and rotational spring.

Keywords: buckling, stability, frame, modified newmark method

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

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Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model

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Authors: Guorong Sui, Xingwei Jia, Fei Tong, Xiumin Gao

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Camera calibration is a fundamental issue of high precision noncontact measurement. And it is necessary to analyze and study the reliability and application range of its linear model which is often used in the camera calibration. According to the imaging features of monocular cameras, a camera model which is based on the image pixel coordinates and three dimensional space coordinates is built. Using our own customized template, the image pixel coordinate is obtained by the subpixel corner detection method. Without considering the aberration of the optical system, the feature extraction and linearity analysis of the line segment in the template are performed. Moreover, the experiment is repeated 11 times by constantly varying the measuring distance. At last, the linearity of the camera is achieved by fitting 11 groups of data. The camera model measurement results show that the relative error does not exceed 1%, and the repeated measurement error is not more than 0.1 mm magnitude. Meanwhile, it is found that the model has some measurement differences in the different region and object distance. The experiment results show this linear model is simple and practical, and have good linearity within a certain object distance. These experiment results provide a powerful basis for establishment of the linear model of camera. These works will have potential value to the actual engineering measurement.

Keywords: camera linear model, geometric imaging relationship, image pixel coordinates, three dimensional space coordinates, sub-pixel corner detection

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Authors: Alireza Vafaei Sadr, Vida Abedi, Jiang Li, Ramin Zand

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Missing data is a common challenge in medical research and can lead to biased or incomplete results. When the data bias leaks into models, it further exacerbates health disparities; biased algorithms can lead to misclassification and reduced resource allocation and monitoring as part of prevention strategies for certain minorities and vulnerable segments of patient populations, which in turn further reduce data footprint from the same population – thus, a vicious cycle. This study compares the performance of six imputation techniques grouped into Linear and Non-Linear models on two different realworld electronic health records (EHRs) datasets, representing 17864 patient records. The mean absolute percentage error (MAPE) and root mean squared error (RMSE) are used as performance metrics, and the results show that the Linear models outperformed the Non-Linear models in terms of both metrics. These results suggest that sometimes Linear models might be an optimal choice for imputation in laboratory variables in terms of imputation efficiency and uncertainty of predicted values.

Keywords: EHR, machine learning, imputation, laboratory variables, algorithmic bias

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

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Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: identification, Hammerstein-Wiener, optimization, quantization

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Authors: Haci Mehmet Guzey, Levent Acar

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In this paper, a novel decentralized controller is developed for linear systems with nonlinear unknown interconnections. A model linear decoupled system is assigned for each system. By using the difference actual and model state dynamics, the problem is formulated as inverse problem. Then, the interconnected dynamics are approximated by using Galerkin’s expansion method for inverse problems. Two different sets of orthogonal basis functions are utilized to approximate the interconnected dynamics. Approximated interconnections are utilized in the controller to cancel the interconnections and decouple the systems. Subsequently, the interconnected systems behave as a collection of decoupled systems.

Keywords: decentralized control, inverse problems, large scale systems, nonlinear interconnections, basis functions, system identification

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Nihat Dipova, Bulent Cangir

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This article presents the results of probabilistic seismic hazard analysis (PSHA) for Antalya (SW Turkey). South west of Turkey is characterized by large earthquakes resulting from the continental collision between the African, Arabian and Eurasian plates and crustal faults. Earthquakes around the study area are grouped into two; crustal earthquakes (D=0-50 km) and subduction zone earthquakes (50-140 km). Maximum observed magnitude of subduction earthquakes is Mw=6.0. Maximum magnitude of crustal earthquakes is Mw=6.6. Sources for crustal earthquakes are faults which are related with Isparta Angle and Cyprus Arc tectonic structures. A new earthquake catalogue for Antalya, with unified moment magnitude scale has been prepared and seismicity of the area around Antalya city has been evaluated by defining ‘a’ and ‘b’ parameters of the Gutenberg-Richter recurrence relationship. The Standard Cornell-McGuire method has been used for hazard computation utilizing CRISIS2007 software. Attenuation relationships proposed by Chiou and Youngs (2008) has been used for 0-50 km earthquakes and Youngs et. al (1997) for deep subduction earthquakes. Finally, Seismic hazard map for peak horizontal acceleration on a uniform site condition of firm rock (average shear wave velocity of about 1130 m/s) at a hazard level of 10% probability of exceedance in 50 years has been prepared.

Keywords: Antalya, peak ground acceleration, seismic hazard assessment, subduction

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Alok Madan, Ashok Gupta, Arshad K. Hashmi

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Non-linear dynamic time history analysis is considered as the most advanced and comprehensive analytical method for evaluating the seismic response and performance of multi-degree-of-freedom building structures under the influence of earthquake ground motions. However, effective and accurate application of the method requires the implementation of advanced hysteretic constitutive models of the various structural components including masonry infill panels. Sophisticated computational research tools that incorporate realistic hysteresis models for non-linear dynamic time-history analysis are not popular among the professional engineers as they are not only difficult to access but also complex and time-consuming to use. And, commercial computer programs for structural analysis and design that are acceptable to practicing engineers do not generally integrate advanced hysteretic models which can accurately simulate the hysteresis behavior of structural elements with a realistic representation of strength degradation, stiffness deterioration, energy dissipation and ‘pinching’ under cyclic load reversals in the inelastic range of behavior. In this scenario, push-over or non-linear static analysis methods have gained significant popularity, as they can be employed to assess the seismic performance of building structures while avoiding the complexities and difficulties associated with non-linear dynamic time-history analysis. “Push-over” or non-linear static analysis offers a practical and efficient alternative to non-linear dynamic time-history analysis for rationally evaluating the seismic demands. The present paper is based on the analytical investigation of the effect of distribution of masonry infill panels over the elevation of planar masonry infilled reinforced concrete (R/C) frames on the seismic demands using the capacity spectrum procedures implementing nonlinear static analysis (pushover analysis) in conjunction with the response spectrum concept. An important objective of the present study is to numerically evaluate the adequacy of the capacity spectrum method using pushover analysis for performance based design of masonry infilled R/C frames for near-field earthquake ground motions.

Keywords: nonlinear analysis, capacity spectrum method, response spectrum, seismic demand, near-field earthquakes

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Authors: K. Khlifi, A. Haddouk, M. Hlaili, H. Mechergui

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The present paper provides a detailed analysis of prior methods and approaches for non-linear load identification in residential buildings. The main goal of this analysis is to decipher the distorted signals and to estimate the harmonics influence on power systems. We have performed an analytical study of non-linear loads behavior in the residential environment. Simulations have been performed in order to evaluate the distorted rate of the current and follow his behavior. To complete this work, an instrumental platform has been realized to carry out practical tests on single-phase non-linear loads which illustrate the current consumption of some domestic appliances supplied with single-phase sinusoidal voltage. These non-linear loads have been processed and tracked in order to limit their influence on the power grid and to reduce the Joule effect losses. As a result, the study has allowed to identify responsible circuits of harmonic pollution.

Keywords: distortion rate, harmonic analysis, harmonic pollution, non-linear load, power factor

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Authors: Jiya Mohammed, Tsadu Shuaib, Yusuf Abdulhakeem

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The research work focuses on the cases of MHD boundary layer flow past a stretching plate with heat transfer and viscous dissipation. The non-linear of momentum and energy equation are transform into ordinary differential equation by using similarity transformation, the resulting equation are solved using Adomian Decomposition Method (ADM). An attempt has been made to show the potentials and wide range application of the Adomian decomposition method in the comparison with the previous one in solving heat transfer problems. The Pade approximates value (η= 11[11, 11]) is use on the difficulty at infinity. The results are compared by numerical technique method. A vivid conclusion can be drawn from the results that ADM provides highly precise numerical solution for non-linear differential equations. The result where accurate especially for η ≤ 4, a general equating terms of Eckert number (Ec), Prandtl number (Pr) and magnetic parameter ( ) is derived which was used to investigate velocity and temperature profiles in boundary layer.

Keywords: MHD, Adomian decomposition, boundary layer, viscous dissipation

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Authors: Musaab Mohammed Ahmed Ali, Vladimir Vodichev

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work deals with an universal control technique or single controller for linear and nonlinear stabilization and tracing control systems. These systems may be structured as SISO and MIMO. Parameters of controlled plants can vary over a wide range. Introduced a novel control systems design method, construction of stable platform orbits using derivative balance, solved transfer function stability preservation problem of linear system under partial substitution of a rational function. Universal controller is proposed as a polar system with the multiple orbits to simplify design procedure, where each orbit represent single order of controller transfer function. Designed controller consist of proportional, integral, derivative terms and multiple feedback and feedforward loops. The controller parameters synthesis method is presented. In generally, controller parameters depend on new polynomial equation where all parameters have a relationship with each other and have fixed values without requirements of retuning. The simulation results show that the proposed universal controller can stabilize infinity number of linear and nonlinear plants and shaping desired previously ordered performance. It has been proven that sensor errors and poor performance will be completely compensated and cannot affect system performance. Disturbances and noises effect on the controller loop will be fully rejected. Technical and economic effect of using proposed controller has been investigated and compared to adaptive, predictive, and robust controllers. The economic analysis shows the advantage of single controller with fixed parameters to drive infinity numbers of plants compared to above mentioned control techniques.

Keywords: derivative balance, fixed parameters, stable platform, universal control

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Authors: Yousef I. Salamin

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Theoretical investigations, analytical as well as numerical, have shown that electrons can be accelerated to GeV energies by the process of cyclotron auto-resonance acceleration (CARA). In CARA, the particle would be injected along the lines of a uniform magnetic field aligned parallel to the direction of propagation of a plane-wave radiation field. Unfortunately, an accelerator based on CARA would be prohibitively too long and too expensive to build and maintain. However, the process stands a better chance of success near the polar cap of a compact object (such as a neutron star, a black hole or a magnetar) or in an environment created in the wake of a binary neutron-star or blackhole merger. Dynamics of the nuclides ₁H¹, ₂He⁴, ₂₆Fe⁵⁶, and ₂₈Ni⁶², in such astrophysical conditions, have been investigated by single-particle calculations and many-particle simulations. The investigations show that these nuclides can reach ZeV energies (1 ZeV = 10²¹ eV) due to interaction with super-intense radiation of wavelengths = 1 and 10 m and = 50 pm and magnetic fields of strengths at the mega- and giga-tesla levels. Examples employing radiation intensities in the range 10³²-10⁴² W/m² have been used. Employing a two-parameter model for representing the radiation field, CARA is analytically generalized to include any state of polarization, and the basic working equations are derived rigorously and in closed analytic form.

Keywords: compact objects, cosmic-ray acceleration, cyclotron auto-resonance, polarization effects, zevatron

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Authors: Asim Qureshi, R. S. Jangid

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Seismic response control of structures is generally achieved by using control devices which either dissipate the input energy or modify the dynamic properties of structure.In this paper, the response of a 20-storey benchmark building supplemented by viscous dampers and Negative Stiffness Device (NSD) is assessed by numerical simulations using the Newmark-beta method. True negative stiffness is an adaptive passive device which assists the motion unlike positive stiffness. The structure used in this study is subjected to four standard ground motions varying from moderate to severe, near fault to far-field earthquakes. The objective of the present study is to show the effectiveness of the adaptive negative stiffness device (NSD and passive dampers together) relative to passive dampers alone. This is done by comparing the responses of the above uncontrolled structure (i.e., without any device) with the structure having passive dampers only and also with the structure supplemented with adaptive negative stiffness device. Various performance indices, top floor displacement, top floor acceleration and inter-storey drifts are used as comparison parameters. It is found that NSD together with passive dampers is quite effective in reducing the response of aforementioned structure relative to structure without any device or passive dampers only. Base shear and acceleration is reduced significantly by incorporating NSD at the cost of increased inter-storey drifts which can be compensated using the passive dampers.

Keywords: adaptive negative stiffness device, apparent yielding, NSD, passive dampers

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Authors: Tarek Sayed Taha Ali

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The dependence of the axial-vector coupling constant gA on the quark masses has been investigated in the frame work of the extended linear sigma model. The field equations have been solved in the mean-field approximation. Our study shows a better fitting to the experimental data compared with the existing models.

Keywords: extended linear sigma model, nucleon properties, axial coupling constant, physic

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Authors: John Mark Payawal, Francis Aldrine Uy, John Paul Carreon

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This paper shows the application of Structural Health Monitoring, SHM into bridges. Bridges are structures built to provide passage over a physical obstruction such as rivers, chasms or roads. The Philippines has a total of 8,166 national bridges as published on the 2015 atlas of the Department of Public Works and Highways (DPWH) and only 2,924 or 35.81% of these bridges are in good condition. As a result, PHP 30.464 billion of the 2016 budget of DPWH is allocated on roads and/or bridges maintenance alone. Intensive spending is owed to the present practice of outdated manual inspection and assessment, and poor structural health monitoring of Philippine infrastructures. As the School of Civil, Environmental, & Geological Engineering of Mapua Institute of Technology (MIT) continuous its well driven passion in research based projects, a partnership with the Department of Science and Technology (DOST) and the DPWH launched the application of Structural Health Monitoring, (SHM) in Padre Jacinto Zamora Flyover. The flyover is located along Nagtahan Boulevard in Sta. Mesa, Manila that connects Brgy. 411 and Brgy. 635. It gives service to vehicles going from Lacson Avenue to Mabini Bridge passing over Legarda Flyover. The flyover is chosen among the many located bridges in Metro Manila as the focus of the pilot testing due to its site accessibility, and complete structural built plans and specifications necessary for SHM as provided by the Bureau of Design, BOD department of DPWH. This paper focuses on providing a method to calibrate theoretical readings from STAAD Vi8 Pro and sync the data to actual MEMS accelerometer readings. It is observed that while the design standards used in constructing the flyover was reflected on the model, actual readings of MEMS accelerometer display a large difference compared to the theoretical data ran and taken from STAAD Vi8 Pro. In achieving a true seismic response of the modeled bridge or hence syncing the theoretical data to the actual sensor reading also called as the independent variable of this paper, analysis using single degree of freedom (SDOF) of the flyover under free vibration without damping using STAAD Vi8 Pro is done. The earthquake excitation and bridge responses are subjected to earthquake ground motion in the form of ground acceleration or Peak Ground Acceleration, PGA. Translational acceleration load is used to simulate the ground motion of the time history analysis acceleration record in STAAD Vi8 Pro.

Keywords: accelerometer, analysis using single degree of freedom, micro electro mechanical system, peak ground acceleration, structural health monitoring

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Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: dynamic response, nonlinear impact response, finite element analysis, numerical analysis

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Authors: Wei Liu, Shuquan Wang, Yang Gao

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Microgravity Science Experiment Rack (MSER) will be onboard TianHe (TH) spacecraft planned to be launched in 2018. TH is one module of Chinese Space Station. Microgravity Vibration Isolation System (MVIS), which is MSER’s core part, is used to isolate disturbance from TH and provide high-level microgravity for science experiment payload. MVIS is two stage vibration isolation system, consisting of Follow Unit (FU) and Experiment Support Unit (ESU). FU is linked to MSER by umbilical cables, and ESU suspends within FU and without physical connection. The FU’s position and attitude relative to TH is measured by binocular vision measuring system, and the acceleration and angular velocity is measured by accelerometers and gyroscopes. Air-jet thrusters are used to generate force and moment to control FU’s motion. Measurement module on ESU contains a set of Position-Sense-Detectors (PSD) sensing the ESU’s position and attitude relative to FU, accelerometers and gyroscopes sensing ESU’s acceleration and angular velocity. Electro-magnetic actuators are used to control ESU’s motion. Firstly, the linearized equations of FU’s motion relative to TH and ESU’s motion relative to FU are derived, laying the foundation for control system design and simulation analysis. Subsequently, two control schemes are proposed. One control scheme is that ESU tracks FU and FU tracks TH, shorten as E-F-T. The other one is that FU tracks ESU and ESU tracks TH, shorten as F-E-T. In addition, motion spaces are constrained within ±15 mm、±2° between FU and ESU, and within ±300 mm between FU and TH or between ESU and TH. A Proportional-Integrate-Differentiate (PID) controller is designed to control FU’s position and attitude. ESU’s controller includes an acceleration feedback loop and a relative position feedback loop. A Proportional-Integrate (PI) controller is designed in the acceleration feedback loop to reduce the ESU’s acceleration level, and a PID controller in the relative position feedback loop is used to avoid collision. Finally, simulations of E-F-T and F-E-T are performed considering variety uncertainties, disturbances and motion space constrains. The simulation results of E-T-H showed that control performance was from 0 to -20 dB for vibration frequency from 0.01 to 0.1 Hz, and vibration was attenuated 40 dB per ten octave above 0.1Hz. The simulation results of T-E-H showed that vibration was attenuated 20 dB per ten octave at the beginning of 0.01Hz.

Keywords: microgravity science experiment rack, microgravity vibration isolation system, PID control, vibration isolation performance

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Authors: G. Alston Rush, Gus A. Rush III, M. F. Horstemeyer

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This study compares the shell-facemask responses of four commonly used American football helmets, under the National Operating Committee on Standards for Athletic Equipment (NOCSAE) drop impact test method, to show that the test standard would more accurately simulate in-use conditions by modification to include the facemask. In our study, the need for a more vigorous systematic approach to football helmet testing procedures is emphasized by comparing the Head Injury Criterion (HIC), the Gadd Severity Index (SI), and peak acceleration values for different helmets at different locations on the helmet under modified NOCSAE standard drop tower tests. Drop tests were performed on the Rawlings Quantum Plus, Riddell 360, Schutt Ion 4D, and Xenith X2 helmets at eight impact locations, impact velocities of 5.46 and 4.88 meters per second, and helmet configurations with and without facemasks. Analysis of NOCSAE drop test results reveal significant differences (p < 0.05) for when the facemasks were attached to helmets, as compared to the NOCSAE Standard, without facemask configuration. The boundary conditions of the facemask attachment can have up to a 50% decrease (p < 0.001) in helmet performance with respect to peak acceleration. While generally, all helmets with the facemasks gave greater HIC, SI, and acceleration values than helmets without the facemasks, significant helmet dependent variations were observed across impact locations and impact velocities. The variations between helmet responses could be attributed to the unique design features of each helmet tested, which include different liners, chin strap attachments, and faceguard attachment systems. In summary, these comparative drop test results revealed that the current NOCSAE standard test methods need improvement by attaching the facemasks to helmets during testing. The modified NOCSAE football helmet standard test gives a more accurate representation of a helmet’s performance and its ability to mitigate the on-field impact.

Keywords: football helmet testing, gadd severity index, head injury criterion, mild traumatic brain injury

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Authors: Yanisa Chaiya, Jintana Sanwong

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Let V be a vector space over a field and W a subspace of V. Let Fix(V,W) denote the set of all linear transformations on V with fix all elements in W. In this paper, we show that Fix(V,W) is a semigroup under the composition of maps and describe Green’s relations on this semigroup in terms of images, kernels and the dimensions of subspaces of the quotient space V/W where V/W = {v+W : v is an element in V} with v+W = {v+w : w is an element in W}. Let dim(U) denote the dimension of a vector space U and Vα = {vα : v is an element in V} where vα is an image of v under a linear transformation α. For any cardinal number a let a'= min{b : b > a}. We also show that the ideals of Fix(V,W) are precisely the sets. Fix(r) ={α ∊ Fix(V,W) : dim(Vα/W) < r} where 1 ≤ r ≤ a' and a = dim(V/W). Moreover, we prove that if V is a finite-dimensional vector space, then every ideal of Fix(V,W) is principle.

Keywords: Green’s relations, ideals, linear transformation semi-groups, principle ideals

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Authors: Mehdi Ghatei, Masoomeh Lorestani

Abstract:

Upstream Tailings Storage Facilities (TSFs) may experience slope instabilities due to soil liquefaction, especially in regions known to be seismically active. In this study, liquefaction susceptibility of an upstream-raised TSF in Western Australia was assessed using two different approaches. The first approach assessed liquefaction susceptibility using Cone Penetration Tests with pore pressure measurement (CPTu) as described by the National Centre for Earthquake Engineering Research (NCEER). This assessment was based on the four CPTu tests that were conducted on the perimeter embankment of the TSF. The second approach used the Finite Element (FE) method with application of an equivalent linear model to predict the undrained cyclic behavior, the pore water pressure and the liquefaction of the materials. The tailings parameters were estimated from the CPTu profiles and from the laboratory tests. The cyclic parameters were estimated from the literature where test results of similar material were available. The results showed that there was a good agreement, in the liquefaction susceptibility of the tailings material, between the NCEER and FE methods with equivalent linear model.

Keywords: liquefaction , CPTU, NCEER, finite element method, equivalent linear model

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

Abstract:

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, functionally graded material

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