Search results for: finite difference Schemes

Authors: Chillali Abdelhakim

Abstract:

Groups where the discrete logarithm problem (DLP) is believed to be intractable have proved to be inestimable building blocks for cryptographic applications. They are at the heart of numerous protocols such as key agreements, public-key cryptosystems, digital signatures, identification schemes, publicly verifiable secret sharings, hash functions and bit commitments. The search for new groups with intractable DLP is therefore of great importance.The goal of this article is to study elliptic curves over the ring Fq[], with Fq a finite field of order q and with the relation n = 0, n ≥ 3. The motivation for this work came from the observation that several practical discrete logarithm-based cryptosystems, such as ElGamal, the Elliptic Curve Cryptosystems . In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In anther article we study their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.

Keywords: Elliptic Curve Over Ring, Discrete Logarithm Problem.

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Authors: Abdolamir Nekoubin

Abstract:

One of Effective parameters on the performance of linear induction motors is number of poles which must be selected and optimized to increase power efficiency and motor performance significantly. In this paper a double-sided linear induction motor with different poles number by using MAXWELL3D software is designed and with finite element method is analyzed electromagnetically. Then for dynamic simulation, linear motor by using MATLAB software is simulated. The results show that by adding poles number, system time response is increased and motor after more time reaches to steady state. Also propulsion force of motor is increased.

Keywords: Linear motor, poles number, finite element method.

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

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In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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Authors: M. Pala Prasad Reddy, Jeevamma Jacob

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Accurate dynamic modeling and analysis of flexible link manipulator (FLM) with non linear dynamics is very difficult due to distributed link flexibility and few studies have been conducted based on assumed modes method (AMM) and finite element models. In this paper a nonlinear dynamic model with first two elastic modes is derived using combined Euler/Lagrange and AMM approaches. Significant dynamics associated with the system such as hub inertia, payload, structural damping, friction at joints, combined link and joint flexibility are incorporated to obtain the complete and accurate dynamic model. The response of the FLM to the applied bang-bang torque input is compared against the models derived from LS-DYNA finite element discretization approach and linear finite element models. Dynamic analysis is conducted using LS-DYNA finite element model which uses the explicit time integration scheme to simulate the system. Parametric study is conducted to show the impact payload mass. A numerical result shows that the LS-DYNA model gives the smooth hub-angle profile.

 

Keywords: Flexible link manipulator, AMM, FEM, LS-DYNA, Bang-bang torque input.

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Authors: P. Meesuk, T. Kulworawanichpong, P. Pao-la-or

Abstract:

This paper proposes a set of quasi-static mathematical model of magnetic fields caused by high voltage conductors of distribution transformer by using a set of second-order partial differential equation. The modification for complex magnetic field analysis and time-harmonic simulation are also utilized. In this research, transformers were study in both balanced and unbalanced loading conditions. Computer-based simulation utilizing the threedimensional finite element method (3-D FEM) is exploited as a tool for visualizing magnetic fields distribution volume a distribution transformer. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. At present, the FEM has been widely applied in most engineering fields. Even for problems of magnetic field distribution, the FEM is able to estimate solutions of Maxwell-s equations governing the power transmission systems. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Distribution Transformer, Magnetic Field, Load Unbalance, 3-D Finite Element Method (3-D FEM)

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Authors: R. K. Apalowo, D. Chronopoulos, V. Thierry

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A wave finite element (WFE) and finite element (FE) based computational method is presented by which the dispersion properties as well as the wave interaction coefficients for one-dimensional structural system can be predicted. The structural system is discretized as a system comprising a number of waveguides connected by a coupling joint. Uniform nodes are ensured at the interfaces of the coupling element with each waveguide. Then, equilibrium and continuity conditions are enforced at the interfaces. Wave propagation properties of each waveguide are calculated using the WFE method and the coupling element is modelled using the FE method. The scattering of waves through the coupling element, on which damage is modelled, is determined by coupling the FE and WFE models. Furthermore, the central aim is to evaluate the effect of pressurization on the wave dispersion and scattering characteristics of the prestressed structural system compared to that which is not prestressed. Numerical case studies are exhibited for two waveguides coupled through a coupling joint.

Keywords: Finite element, prestressed structures, wave finite element, wave propagation properties, wave scattering coefficients.

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Authors: Kelemewerk Destalem, Jungjae Cho, Jaeseong Lee, Ju H. Park, Joonhyuk Yoo

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Background subtraction and temporal difference are often used for moving object detection in video. Both approaches are computationally simple and easy to be deployed in real-time image processing. However, while the background subtraction is highly sensitive to dynamic background and illumination changes, the temporal difference approach is poor at extracting relevant pixels of the moving object and at detecting the stopped or slowly moving objects in the scene. In this paper, we propose a simple moving object detection scheme based on adaptive background subtraction and temporal difference exploiting dynamic background updates. The proposed technique consists of histogram equalization, a linear combination of background and temporal difference, followed by the novel frame-based and pixel-based background updating techniques. Finally, morphological operations are applied to the output images. Experimental results show that the proposed algorithm can solve the drawbacks of both background subtraction and temporal difference methods and can provide better performance than that of each method.

Keywords: Background subtraction, background updating, real time and lightweight algorithm, temporal difference.

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Authors: Chun-Chuan Yang, Jeng-Yueng Chen, Yi-Ting Mai, Chen-Ming Yang

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In this paper, the design of integrated sleep scheduling for relay nodes and user equipments under a Donor eNB (DeNB) in the mode of Time Division Duplex (TDD) in LTE-A is presented. The idea of virtual time is proposed to deal with the discontinuous pattern of the available radio resource in TDD, and based on the estimation of the traffic load, three power saving schemes in the top-down strategy are presented. Associated mechanisms in each scheme including calculation of the virtual subframe capacity, the algorithm of integrated sleep scheduling, and the mapping mechanisms for the backhaul link and the access link are presented in the paper. Simulation study shows the advantage of the proposed schemes in energy saving over the standard DRX scheme.

Keywords: LTE-A, Relay, TDD, Power Saving.

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Authors: Youssou Faye, Ibrahima Niang, Thomas Noel

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Access control is a critical security service in Wire- less Sensor Networks (WSNs). To prevent malicious nodes from joining the sensor network, access control is required. On one hand, WSN must be able to authorize and grant users the right to access to the network. On the other hand, WSN must organize data collected by sensors in such a way that an unauthorized entity (the adversary) cannot make arbitrary queries. This restricts the network access only to eligible users and sensor nodes, while queries from outsiders will not be answered or forwarded by nodes. In this paper we presentee different access control schemes so as to ?nd out their objectives, provision, communication complexity, limits, etc. Using the node density parameter, we also provide a comparison of these proposed access control algorithms based on the network topology which can be flat or hierarchical.

Keywords: Access Control, Authentication, Key Management, Wireless Sensor Networks.

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Authors: Isaac Mugume, Charles Basalirwa, Daniel Waiswa, Triphonia Ngailo

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Rainfall is a major climatic parameter affecting many sectors such as health, agriculture and water resources. Its quantitative prediction remains a challenge to weather forecasters although numerical weather prediction models are increasingly being used for rainfall prediction. The performance of six convective parameterization schemes, namely the Kain-Fritsch scheme, the Betts-Miller-Janjic scheme, the Grell-Deveny scheme, the Grell-3D scheme, the Grell-Fretas scheme, the New Tiedke scheme of the weather research and forecast (WRF) model regarding quantitative rainfall prediction over Uganda is investigated using the root mean square error for the March-May (MAM) 2013 season. The MAM 2013 seasonal rainfall amount ranged from 200 mm to 900 mm over Uganda with northern region receiving comparatively lower rainfall amount (200–500 mm); western Uganda (270–550 mm); eastern Uganda (400–900 mm) and the lake Victoria basin (400–650 mm). A spatial variation in simulated rainfall amount by different convective parameterization schemes was noted with the Kain-Fritsch scheme over estimating the rainfall amount over northern Uganda (300–750 mm) but also presented comparable rainfall amounts over the eastern Uganda (400–900 mm). The Betts-Miller-Janjic, the Grell-Deveny, and the Grell-3D underestimated the rainfall amount over most parts of the country especially the eastern region (300–600 mm). The Grell-Fretas captured rainfall amount over the northern region (250–450 mm) but also underestimated rainfall over the lake Victoria Basin (150–300 mm) while the New Tiedke generally underestimated rainfall amount over many areas of Uganda. For deterministic rainfall prediction, the Grell-Fretas is recommended for rainfall prediction over northern Uganda while the Kain-Fritsch scheme is recommended over eastern region.

Keywords: Convective parameterization schemes, March-May 2013 rainfall season, spatial variation of parameterization schemes over Uganda, WRF model.

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Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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Authors: Hassen M. Ouakad

Abstract:

In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin method.

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Authors: N. Thongjub, B. Puangkird, V. Ngamaramvaranggul

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The numerical simulation of the slip effect via vicoelastic fluid for 4:1 contraction problem is investigated with regard to kinematic behaviors of streamlines and stress tensor by models of the Navier-Stokes and Oldroyd-B equations. Twodimensional spatial reference system of incompressible creeping flow with and without slip velocity is determined and the finite element method of a semi-implicit Taylor-Galerkin pressure-correction is applied to compute the problem of this Cartesian coordinate system including the schemes of velocity gradient recovery method and the streamline-Upwind / Petrov-Galerkin procedure. The slip effect at channel wall is added to calculate after each time step in order to intend the alteration of flow path. The result of stress values and the vortices are reduced by the optimum slip coefficient of 0.1 with near the outcome of analytical solution.

Keywords: Slip effect, Oldroyd-B fluid, slip coefficient, time stepping method.

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Authors: A.Roshandel, N.Hedayat, H.kiamanesh

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Today, numerical simulation is a powerful tool to solve various hydraulic engineering problems. The aim of this research is numerical solutions of shallow water equations using finite volume method for Simulations of dam break over wet and dry bed. In order to solve Riemann problem, Roe-s approximate solver is used. To evaluate numerical model, simulation was done in 1D and 2D states. In 1D state, two dam break test over dry bed (with and without friction) were studied. The results showed that Structural failure around the dam and damage to the downstream constructions in bed without friction is more than friction bed. In 2D state, two tests for wet and dry beds were done. Generally in wet bed case, waves are propagated to canal sides but in dry bed it is not significant. Therefore, damage to the storage facilities and agricultural lands in wet bed case is more than in dry bed.

Keywords: dam break, dry bed, finite volume method, shallow water equations.

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Authors: Hyung-Jin Jang, Kwang-Bok Shin, Sung-Ho Han

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This paper describes the crashworthiness assessment and improvement of tlting train made of sandwich composites. The crashworhiness assessment of tilting train was conducted according to four collision scenarios of the Korean railway safety law. Collision analysis was carried out using explicit finite element analysis code LS-DYNA 3D. The finite element model consists of 3-D finite element model and 1-D equivalent model to save the finite element modeling and calculation time. It found that the crashworthiness analysis results were satisfied with the performance requirements except the crash scenario-2. In order to meet the crashworthiness requirements for crash scenario-2, the stiffness reinforcement for the laminate composite cover and metal frames of cabmask structure were proposed. Consequentially, it has satisfied the requirement for crash scenario-2.

Keywords: Crashworthiness, collision scenario, Korean railway safety law, sandwich composite, tilting train.

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Authors: B. S. Jayashankarbabu, Karisiddappa

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The finite element method is used to obtain the elastic buckling load factor for square isotropic plate containing circular, square and rectangular cutouts. ANSYS commercial finite element software had been used in the study. The applied inplane loads considered are uniaxial and biaxial compressions. In all the cases the load is distributed uniformly along the plate outer edges. The effects of the size and shape of concentric cutouts with different plate thickness ratios and the influence of plate edge conditions, such as SSSS, CCCC and mixed boundary condition SCSC on the plate buckling strength have been considered in the analysis.

Keywords: Concentric cutout, Elastic buckling, Finite element method, Inplane loads, Thickness ratio.

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Authors: Adrián D. García-Soto, Alejandro Hernández-Martínez, Jesús G. Valdés-Vázquez, Reyna A. Vizguerra-Alvarez

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Reinforced concrete bridges designed by code are intended to achieve target reliability levels adequate for the geographical environment where the code is applicable. Several methods can be used to estimate such reliability levels. Many of them require the establishment of an explicit limit state function (LSF). When such LSF is not available as a close-form expression, the simulation techniques are often employed. The simulation methods are computing intensive and time consuming. Note that if the reliability of real bridges designed by code is of interest, numerical schemes, the finite element method (FEM) or computational mechanics could be required. In these cases, it can be quite difficult (or impossible) to establish a close-form of the LSF, and the simulation techniques may be necessary to compute reliability levels. To overcome the need for a large number of simulations when no explicit LSF is available, the point estimate method (PEM) could be considered as an alternative. It has the advantage that only the probabilistic moments of the random variables are required. However, in the PEM, fitting of the resulting moments of the LSF to a probability density function (PDF) is needed. In the present study, a very simple alternative which allows the assessment of the reliability levels when no explicit LSF is available and without the need of extensive simulations is employed. The alternative includes the use of the PEM, and its applicability is shown by assessing reliability levels of reinforced concrete bridges in Mexico when a numerical scheme is required. Comparisons with results by using the Monte Carlo simulation (MCS) technique are included. To overcome the problem of approximating the probabilistic moments from the PEM to a PDF, a well-known distribution is employed. The approach mixes the PEM and other classic reliability method (first order reliability method, FORM). The results in the present study are in good agreement whit those computed with the MCS. Therefore, the alternative of mixing the reliability methods is a very valuable option to determine reliability levels when no close form of the LSF is available, or if numerical schemes, the FEM or computational mechanics are employed.

Keywords: Structural reliability, reinforced concrete bridges, mixing approaches, point estimate method, Monte Carlo simulation.

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Authors: Amin Esmaeilzadeh, Mohammad Sadeghi, Farhad Kolahan

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Arc welding is an important joining process widely used in many industrial applications including production of automobile, ships structures and metal tanks. In welding process, the moving electrode causes highly non-uniform temperature distribution that leads to residual stresses and different deviations, especially buckling distortions in thin plates. In order to control the deviations and increase the quality of welded plates, a fixture can be used as a practical and low cost method with high efficiency. In this study, a coupled thermo-mechanical finite element model is coded in the software ANSYS to simulate the behavior of thin plates located by a 3-2-1 positioning system during the welding process. Computational results are compared with recent similar works to validate the finite element models. The agreement between the result of proposed model and other reported data proves that finite element modeling can accurately predict the behavior of welded thin plates.

Keywords: Welding, thin plate, buckling distortion, fixture locators, finite element modelling.

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Authors: R. I. Liban, N. Tayşi

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

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

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

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A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: Annular fin, Dehumidification, Fin efficiency, Heat and mass transfer, Wet fin.

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Authors: Hassan Saberi-Nik, Mahin Golchaman

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This paper applies the homotopy analysis method method to a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. Comparison of the approximate solution with the exact one reveals that the method is very effective.

Keywords: Homotopy analysis method, differential-difference, nanotechnology.

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Authors: Tamara Nestorović, Jean Lefèvre, Stefan Ringwelski, Ulrich Gabbert

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Two approaches for model development of a smart acoustic box are suggested in this paper: the finite element (FE) approach and the subspace identification. Both approaches result in a state-space model, which can be used for obtaining the frequency responses and for the controller design. In order to validate the developed FE model and to perform the subspace identification, an experimental set-up with the acoustic box and dSPACE system was used. Experimentally obtained frequency responses show good agreement with the frequency responses obtained from the FE model and from the identified model.

Keywords: Acoustic box, experimental verification, finite element model, subspace identification.

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Authors: Magdy B. Eteiba, Essam A. Alzahab, Yomna O. Shaker

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In this paper, a thermal model of cast- resin dry type transformer is proposed. The proposed thermal model is solved by finite element technique to get the temperature at any location of the transformer. The basic modes of heat transfer such as conduction; convection and radiation are used to get the steady state temperature distribution of the transformer. The predicted temperatures are compared with experimental results reported in this paper and it is found a good agreement between them. The effects of various parameters such as width of air duct, ambient temperature and emissivity of the outer surface were also studied.

Keywords: Convection, dry type transformer, finite-elementtechnique, thermal model.

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Authors: Alena Zemanová, Jan Zeman, Michal Šejnoha

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The polymer foil used for manufacturing of laminated glass members behaves in a viscoelastic manner with temperature dependance. This contribution aims at incorporating the time/temperature-dependent behavior of interlayer to our earlier elastic finite element model for laminated glass beams. The model is based on a refined beam theory: each layer behaves according to the finite-strain shear deformable formulation by Reissner and the adjacent layers are connected via the Lagrange multipliers ensuring the inter-layer compatibility of a laminated unit. The time/temperature-dependent behavior of the interlayer is accounted for by the generalized Maxwell model and by the time-temperature superposition principle due to the Williams, Landel, and Ferry. The resulting system is solved by the Newton method with consistent linearization and the viscoelastic response is determined incrementally by the exponential algorithm. By comparing the model predictions against available experimental data, we demonstrate that the proposed formulation is reliable and accurately reproduces the behavior of the laminated glass units.

Keywords: Laminated glass, finite element method, finite-strain Reissner model, Lagrange multipliers, generalized Maxwell model, Williams-Landel-Ferry equation, Newton method.

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Authors: Guixia Lv, Longjun Shen

Abstract:

This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.

Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.

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Authors: Wang Chengcheng, Li Chuanri, Xu Fei, Guo Ying

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Aiming at most of the aviation products are facing the problem of fatigue fracture in vibration environment, we makes use of the testing result of a bracket, analysis for the structure with ANSYS-Workbench, predict the life of the bracket by different ways, and compared with the testing result. With the research on analysis methods, make an organic combination of simulation analysis and testing, Not only ensure the accuracy of simulation analysis and life predict, but also make a dynamic supervision of product life process, promote the application of finite element simulation analysis in engineering practice.

Keywords: Random vibration, finite element simulation, fatigue, frequency domain.

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Authors: Nawel Mezigheche, Abdelhacine Gouasmia, Allaeddine Athmani, Mouloud Merzoud

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Masonry infill walls are inevitable in the selfsupporting structures, but their contribution in the resistance to earthquake loads is generally neglected in the structural analyses. The principal aim of this work through a numerical study of masonry infill walls behavior in structures subjected to horizontal load is to propose by finite elements numerical modeling, a more reliable approach, faster and close to reality. In this study, 3D Finite Element Analysis was developed to study the behavior of masonry infill walls in structures subjected to horizontal load; the finite element software being used was ABAQUS, it is observed that more rigidity of the masonry filling is significant, more the structure is rigid, we can so conclude that the filling brings an additional rigidity to the structure not to be neglected; it is also observed that when the framework is subjected to horizontal loads, the framework separates from the filling on the level of the tended diagonal.

Keywords: Finite element, Masonry infill walls, Rigidity of the masonry, Tended diagonal.

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Authors: Y. Kurosawa, T. Yamaguchi

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A numerical method is proposed to calculate damping properties for sound-proof structures involving elastic body, viscoelastic body, and porous media. For elastic and viscoelastic body displacement is modeled using conventional finite elements including complex modulus of elasticity. Both effective density and bulk modulus have complex quantities to represent damped sound fields in the porous media. Particle displacement in the porous media is discretised using finite element method. Displacement vectors as common unknown variables are solved under coupled condition between elastic body, viscoelastic body and porous media. Further, explicit expressions of modal loss factor for the mixed structures are derived using asymptotic method. Eigenvalue analysis and frequency responded were calculated for automotive test panel laminated viscoelastic and porous structures using this technique, the results almost agreed with the experimental results.

Keywords: Damping, Porous Media, Finite Element Method, Computer Aided Engineering.

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Authors: Marco T. C. Faria

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Fixed-geometry hydrodynamic journal bearings are one of the best supporting systems for several applications of rotating machinery. Cylindrical journal bearings present excellent loadcarrying capacity and low manufacturing costs, but they are subjected to the oil-film instability at high speeds. An attempt of overcoming this instability problem has been the development of non-circular journal bearings. This work deals with an analysis of oil-lubricated elliptical journal bearings using the finite element method. Steadystate and dynamic performance characteristics of elliptical bearings are rendered by zeroth- and first-order lubrication equations obtained through a linearized perturbation method applied on the classical Reynolds equation. Four-node isoparametric rectangular finite elements are employed to model the bearing thin film flow. Curves of elliptical bearing load capacity and dynamic force coefficients are rendered at several operating conditions. The results presented in this work demonstrate the influence of the bearing ellipticity on its performance at different loading conditions.

Keywords: Elliptical journal bearings, non-circular journal bearings, hydrodynamic bearings, finite element method.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

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This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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