Search results for: periodic boundary condition

Authors: Muhammad Naeem, Abdus Salam, Muhammad Asghar Bashir, Abir Ishtiaq, Qurat-ul-Ane Gillani and Asma Salam

Abstract:

In the present study, 49 Hybrid (Catla catla ♂ x Labeo rohita ♀) were sampled from Al-Raheem Fish Hatchery, Village Ali Pure Shamali, Jhang Road, 18 Km from Muzaffar Garh using a cast net and Live fishes were transported to research laboratory. Mean percentage for water found 79.13 %, ash 6.58 %, fat 2.22 % and protein content 12.06 % in whole wet body weight. It was observed that body constituents were found increasing in the same proportion with an increase in body weight while significant proportional increase was observed with total length. However, condition factor remained insignificant (P>0.05) with body constituents.

Keywords: Hybrid fish, Body composition, Condition factor, Predictive equations

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Authors: Sudhir Kumar Tiwari

Abstract:

The paper demonstrates a methodology that can be used at an early design stage of any conventional aircraft. This research activity assesses the feasibility derivation of methodology for aircraft loads estimation during the various phases of design for a transport category aircraft by utilizing potential of using commercial finite element analysis software, which may drive significant time saving. Early Design phase have limited data and quick changing configuration results in handling of large number of load cases. It is useful to idealize the aircraft as a connection of beams, which can be very accurately modelled using finite element analysis (beam elements). This research explores the correct approach towards idealizing an aircraft using beam elements. FEM Techniques like inertia relief were studied for implementation during course of work. The correct boundary condition technique envisaged for generation of shear force, bending moment and torque diagrams for the aircraft. The possible applications of this approach are the aircraft design process, which have been investigated.

Keywords: Multi-disciplinary optimization, aircraft load, finite element analysis, Stick Model.

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: Microstretch, deflection, exponential load, Laplace transforms, Residue theorem, simply supported.

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Authors: Xun Ge, Jingju Qian

Abstract:

To investigate some relations between higher mathe¬matics scores in Chinese graduate student entrance examination and calculus (resp. linear algebra, probability statistics) scores in subject's completion examination of Chinese university, we select 20 students as a sample, take higher mathematics score as a decision attribute and take calculus score, linear algebra score, probability statistics score as condition attributes. In this paper, we are based on rough-set theory (Rough-set theory is a logic-mathematical method proposed by Z. Pawlak. In recent years, this theory has been widely implemented in the many fields of natural science and societal science.) to investigate importance of condition attributes with respective to decision attribute and strength of condition attributes supporting decision attribute. Results of this investigation will be helpful for university students to raise higher mathematics scores in Chinese graduate student entrance examination.

Keywords: Rough set, higher mathematics scores, decision attribute, condition attribute.

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Authors: Fariba Jafari, Samaneh Heydarian

Abstract:

Al2(HPO4)3 was easily prepared and used as a solid acid in acetalization of carbonyl compounds at room temperature and under solvent-free conditions. The protection was done in short reaction times and in good to high isolated yields. The cheapness and availability of this reagent with easy procedure and work-up make this method attractive for the organic synthesis.

Keywords: Acetalization, acid catalysis, carbonylcompounds, green condition, protection.

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Authors: Aref Ghafouri, Mohammad Javad Mollakazemi, Farhad Asadi

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In this paper, model order reduction method is used for approximation in linear and nonlinearity aspects in some experimental data. This method can be used for obtaining offline reduced model for approximation of experimental data and can produce and follow the data and order of system and also it can match to experimental data in some frequency ratios. In this study, the method is compared in different experimental data and influence of choosing of order of the model reduction for obtaining the best and sufficient matching condition for following the data is investigated in format of imaginary and reality part of the frequency response curve and finally the effect and important parameter of number of order reduction in nonlinear experimental data is explained further.

Keywords: Frequency response, Order of model reduction, frequency matching condition.

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Authors: A. Pashayev, D. Askerov, R.Sadiqov, A. Samedov, C. Ardil

Abstract:

In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and cvazistationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine 1st stage nozzle blade

Keywords: multiconnected systems, method of the boundary integrated equations, splines, neural networks.

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Authors: A. Pashayev, D. Askerov, C. Ardil, R. Sadiqov

Abstract:

In contrast to existing methods which do not take into account multiconnectivity in a broad sense of this term, we develop mathematical models and highly effective combination (BIEM and FDM) numerical methods of calculation of stationary and quasi-stationary temperature field of a profile part of a blade with convective cooling (from the point of view of realization on PC). The theoretical substantiation of these methods is proved by appropriate theorems. For it, converging quadrature processes have been developed and the estimations of errors in the terms of A.Ziqmound continuity modules have been received. For visualization of profiles are used: the method of the least squares with automatic conjecture, device spline, smooth replenishment and neural nets. Boundary conditions of heat exchange are determined from the solution of the corresponding integral equations and empirical relationships. The reliability of designed methods is proved by calculation and experimental investigations heat and hydraulic characteristics of the gas turbine first stage nozzle blade.

Keywords: Multiconnected systems, method of the boundary integrated equations, splines, neural networks.

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Authors: Ranajay Bhowmick

Abstract:

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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Authors: Ippei Kamihira, Takashi Nakajima, Taiyo Matsumura, Hikaru Miura, Takashi Ono

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In this research, the goal was construction of a system by which multiple sensors were used to observe the daily life behavior of persons living alone (while respecting their privacy), using this information to judge such conditions as bad physical condition or falling in the home, etc., so that these abnormal conditions can be made known to relatives and third parties. The daily life patterns of persons living alone are expressed by the number of responses of sensors each time that a set time period has elapsed. By comparing data for the prior two weeks, it was possible to judge a situation as “normal” when the person was in good physical condition or as “abnormal” when the person was in bad physical condition.

Keywords: Sensors, Elderly living alone, Abnormality detection, Lifestyle habit.

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Authors: Soon-ok Myong, B.G. Nurzhanov

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This paper applies an anthropological approach to illuminate the dynamic cultural geography of Kazakhstani Korean ethnicity focusing on its turning point, the historic “Seoul Olympic Games in 1988." The Korean ethnic group was easily considered as a harmonious and homogeneous community by outsiders, but there existed deep-seated conflicts and hostilities within the ethnic group. The majority-s oppositional dichotomy of superiority and inferiority toward the minority was continuously reorganized and reinforced by difference in experience, memory and sentiment. However, such a chronic exclusive boundary was collapsed following the patriotism ignited by the Olympics held in their mother country. This paper explores the fluidity of subject by formation of the boundary in which constructed cultural differences are continuously essentialized and reproduced, and by dissolution of cultural barrier in certain contexts.

Keywords: Former Soviet Korean's Russianization, inferior/superior dichotomy, Seoul Olympic Games, subject's fluidity.

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Authors: Seyed Abolhasan Naeini, Mohammad Hossein Zade

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This article is an attempt to present a numerically study of the behaviour of an eccentrically loaded circular footing resting on sand to determine ‎its ultimate bearing capacity. A surface circular footing of diameter 12 cm (D) was used as ‎shallow foundation. For this purpose, three dimensional models consist of foundation, and medium sandy soil was modelled by ABAQUS software. Bearing capacity of footing was evaluated and the ‎effects of the load eccentricity on bearing capacity, its settlement, and modulus of subgrade reaction were studied. Three different values of load eccentricity with equal space from inside the core on the core boundary and outside the core boundary, which were respectively e=0.75, 1.5, and 2.25 cm, were considered. The results show that by increasing the load eccentricity, the ultimate load and the ‎modulus of subgrade reaction decreased.

Keywords: Circular foundation, eccentric loading, sand, modulus of subgrade reaction.

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Authors: Hyun-Jee Yang, Bit-Na Kwon, Yong-Jun Kim, Hyoung-Kyu Song

Abstract:

In the cooperative transmission scheme, both the cellular system and broadcasting system are composed. Two cellular base stations (CBSs) communicating with a user in the cell edge use cooperative transmission scheme in the conventional scheme. In the case that the distance between two CBSs and the user is distant, the conventional scheme does not guarantee the quality of the communication because the channel condition is bad. Therefore, if the distance between CBSs and a user is distant, the performance of the conventional scheme is decreased. Also, the bad channel condition has bad effects on the performance. The proposed scheme uses two relays to communicate well with CBSs when the channel condition between CBSs and the user is poor. Using the relay in the high attenuation environment can obtain both advantages of the high bit error rate (BER) and throughput performance.

Keywords: Cooperative communications, diversity gain, OFDM, interworking system.

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Authors: Omid A. Zargar

Abstract:

One of the most challenging times in operation of big industrial plant or utilities is the time that alert lamp of Bently Nevada connection in main board substation turn on and show the alert condition of machine. All of the maintenance groups usually make a lot of discussion with operation and together rather this alert signal is real or fake. This will be more challenging when condition monitoring vibrationdata shows 1X(X=current rotor frequency) in fast Fourier transform(FFT) and vibration phase trends show 90 degree shift between two non-contact probedirections with overall high radial amplitude amounts. In such situations, CM (condition monitoring) groups usually suspicious about unbalance in rotor. In this paper, four critical case histories related to SIEMENS V94.2 Gas Turbines in Iran power industry discussed in details. Furthermore, probe looseness and fake (unreal) trip in gas turbine power plants discussed. In addition, critical operation decision in alert condition in power plants discussed in details.

Keywords: Gas turbine, field balance, turbine compressors, balancing tools, balancing data collectors.

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Authors: R. Pilafkan, M. Kaffash Irzarahimi, S. F. Asbaghian Namin

Abstract:

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.

Keywords: Biaxial buckling, single-layered graphene sheets, nonlocal elasticity, molecular dynamics simulation, classical plate theory.

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Authors: Nitin Kumar Jain

Abstract:

The distributions of stresses and deflection in rectangular isotropic and orthotropic plates with central circular hole under transverse static loading have been studied using finite element method. The aim of author is to analyze the effect of D/A ratio (where D is hole diameter and A is plate width) upon stress concentration factor (SCF) and deflection in isotropic and orthotropic plates under transverse static loading. The D/A ratio is varied from 0.01 to 0.9. The analysis is done for plates of isotropic and two different orthotropic materials. The results are obtained for three different boundary conditions. The variations of SCF and deflection with respect to D/A ratio are presented in graphical form and discussed. The finite element formulation is carried out in the analysis section of the ANSYS package.

Keywords: Finite Element Method, SCF, Deflection, Plate, Boundary conditions

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Authors: Punya Chupanit, Chayatan Phromsorn

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In the past, there were many bridge-s collapses due to lack of bridge structural capacity information. Most of concrete bridge health was relied on information from visual inspection, which sometime was inadequate. This study was conducted in order to investigate relationship between bridge structural condition and bridge visual condition. This study was a part of a big project conducted at Department of Highways of Thailand. In this study, 31 bridges including slab-type bridges, plank-girder bridges, prestressed box-beam bridges, prestressed I-girder bridges and prestressed multibeam bridges were selected for visual inspection and load test. It was found a positive correlation between bridge appearance and bridge-s load carrying capacity. However, statistical characteristic revealed low correlation between them.

Keywords: Bridge, Visual Inspection, Load Test, Condition Rating, Rating Factor

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

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In this study, a validated 3D finite volume model of human eye is developed to study the fluid flow and heat transfer in the human eye at steady state conditions. For this purpose, discretized bio-heat transfer equation coupled with Boussinesq equation is analyzed with different anatomical, environmental, and physiological conditions. It is demonstrated that the fluid circulation is formed as a result of thermal gradients in various regions of eye. It is also shown that posterior region of the human eye is less affected by the ambient conditions compared to the anterior segment which is sensitive to the ambient conditions and also to the way the gravitational field is defined compared to the geometry of the eye making the circulations and the thermal field complicated in transient states. The effect of variation in material and boundary conditions guides us to the conclusion that thermal field of a healthy and non-healthy eye can be distinguished via computer simulations.

Keywords: Bio-heat, Boussinesq, conduction, convection, eye.

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Authors: Mohammad Talha, B. N. Singh

Abstract:

This paper deals with the thermo-mechanical deformation behavior of shear deformable functionally graded ceramicmetal (FGM) plates. Theoretical formulations are based on higher order shear deformation theory with a considerable amendment in the transverse displacement using finite element method (FEM). The mechanical properties of the plate are assumed to be temperaturedependent and graded in the thickness direction according to a powerlaw distribution in terms of the volume fractions of the constituents. The temperature field is supposed to be a uniform distribution over the plate surface (XY plane) and varied in the thickness direction only. The fundamental equations for the FGM plates are obtained using variational approach by considering traction free boundary conditions on the top and bottom faces of the plate. A C0 continuous isoparametric Lagrangian finite element with thirteen degrees of freedom per node have been employed to accomplish the results. Convergence and comparison studies have been performed to demonstrate the efficiency of the present model. The numerical results are obtained for different thickness ratios, aspect ratios, volume fraction index and temperature rise with different loading and boundary conditions. Numerical results for the FGM plates are provided in dimensionless tabular and graphical forms. The results proclaim that the temperature field and the gradient in the material properties have significant role on the thermo-mechanical deformation behavior of the FGM plates.

Keywords: Functionally graded material, higher order shear deformation theory, finite element method, independent field variables.

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: Yuzana, Khin Marlar Tun

Abstract:

Personal name matching system is the core of essential task in national citizen database, text and web mining, information retrieval, online library system, e-commerce and record linkage system. It has necessitated to the all embracing research in the vicinity of name matching. Traditional name matching methods are suitable for English and other Latin based language. Asian languages which have no word boundary such as Myanmar language still requires sounds alike matching system in Unicode based application. Hence we proposed matching algorithm to get analogous sounds alike (phonetic) pattern that is convenient for Myanmar character spelling. According to the nature of Myanmar character, we consider for word boundary fragmentation, collation of character. Thus we use pattern conversion algorithm which fabricates words in pattern with fragmented and collated. We create the Myanmar sounds alike phonetic group to help in the phonetic matching. The experimental results show that fragmentation accuracy in 99.32% and processing time in 1.72 ms.

Keywords: natural language processing, name matching, phonetic matching

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Authors: A. P. Anvar, T. Dowling, T. Putland, A. M. Anvar, S.Grainger

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This paper presents the application of Intelligent Techniques to the various duties of Intelligent Condition Monitoring Systems (ICMS) for Unmanned Aerial Vehicle (UAV) Robots. These Systems are intended to support these Intelligent Robots in the event of a Fault occurrence. Neural Networks are used for Diagnosis, whilst Fuzzy Logic is intended for Prognosis and Remedy. The ultimate goals of ICMS are to save large losses in financial cost, time and data.

Keywords: Intelligent Techniques, Condition Monitoring Systems, ICMS, Robots, Fault, Unmanned Aerial Vehicle, UAV, Neural Networks, Diagnosis, Fuzzy Logic, Prognosis, Remedy.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.

Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.

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Authors: A. K. Prajapati

Abstract:

In this paper, the periodic surveillance scheme has been proposed for any convex region using mobile wireless sensor nodes. A sensor network typically consists of fixed number of sensor nodes which report the measurements of sensed data such as temperature, pressure, humidity, etc., of its immediate proximity (the area within its sensing range). For the purpose of sensing an area of interest, there are adequate number of fixed sensor nodes required to cover the entire region of interest. It implies that the number of fixed sensor nodes required to cover a given area will depend on the sensing range of the sensor as well as deployment strategies employed. It is assumed that the sensors to be mobile within the region of surveillance, can be mounted on moving bodies like robots or vehicle. Therefore, in our scheme, the surveillance time period determines the number of sensor nodes required to be deployed in the region of interest. The proposed scheme comprises of three algorithms namely: Hexagonalization, Clustering, and Scheduling, The first algorithm partitions the coverage area into fixed sized hexagons that approximate the sensing range (cell) of individual sensor node. The clustering algorithm groups the cells into clusters, each of which will be covered by a single sensor node. The later determines a schedule for each sensor to serve its respective cluster. Each sensor node traverses all the cells belonging to the cluster assigned to it by oscillating between the first and the last cell for the duration of its life time. Simulation results show that our scheme provides full coverage within a given period of time using few sensors with minimum movement, less power consumption, and relatively less infrastructure cost.

Keywords: Sensor Network, Graph Theory, MSN, Communication.

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Authors: Erna Astuti, Supranto, Rochmadi, Agus Prasetya

Abstract:

Biodiesel production from vegetable oil will produce glycerol as by-product about 10% of the biodiesel production. The amount of glycerol that was produced needed alternative way to handling immediately so as to not become the waste that polluted environment. One of the solutions was to process glycerol to polyglycidyl nitrate (PGN). PGN is synthesized from glycerol by three-step reactions i.e. nitration of glycerol, cyclization of 13- dinitroglycerine and polymerization of glycosyl nitrate. Optimum condition of nitration of glycerol with nitric acid has not been known. Thermodynamic feasibility should be done before run experiments in the laboratory. The aim of this study was to determine the parameters those affect nitration of glycerol and nitric acid and chose the operation condition. Many parameters were simulated to verify its possibility to experiment under conditions which would get the highest conversion of 1, 3-dinitroglycerine and which was the ideal condition to get it. The parameters that need to be studied to obtain the highest conversion of 1, 3-dinitroglycerine were mol ratio of nitric acid/glycerol, reaction temperature, mol ratio of glycerol/dichloromethane and pressure. The highest conversion was obtained in the range of mol ratio of nitric acid /glycerol between 2/1 – 5/1, reaction temperature of 5-25oC and pressure of 1 atm. The parameters that need to be studied further to obtain the highest conversion of 1.3 DNG are mol ratio of nitric acid/glycerol and reaction temperature.

Keywords: Nitration, glycerol, thermodynamic, optimum condition.

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Authors: Ioannis N. Koukoulis, Clio G. Vossou, Christopher G. Provatidis

Abstract:

The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

Keywords: Elastostatic, inverse problem, optimization.

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Authors: Jahedul Islam Chowdhury, Bao Kha Nguyen, David Thornhill, Roy Douglas, Stephen Glover

Abstract:

Organic Rankine Cycle (ORC) is the most commonly used method for recovering energy from small sources of heat. The investigation of the ORC in supercritical condition is a new research area as it has a potential to generate high power and thermal efficiency in a waste heat recovery system. This paper presents a steady state ORC model in supercritical condition and its simulations with a real engine’s exhaust data. The key component of ORC, evaporator, is modelled using finite volume method, modelling of all other components of the waste heat recovery system such as pump, expander and condenser are also presented. The aim of this paper is to investigate the effects of mass flow rate and evaporator outlet temperature on the efficiency of the waste heat recovery process. Additionally, the necessity of maintaining an optimum evaporator outlet temperature is also investigated. Simulation results show that modification of mass flow rate is the key to changing the operating temperature at the evaporator outlet.

Keywords: Organic Rankine cycle, supercritical condition, steady state model, waste heat recovery.

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Authors: Mahdi Hamzeh, Sied Mehdi Fakhraie, Caro Lucas

Abstract:

All practical real-time scheduling algorithms in multiprocessor systems present a trade-off between their computational complexity and performance. In real-time systems, tasks have to be performed correctly and timely. Finding minimal schedule in multiprocessor systems with real-time constraints is shown to be NP-hard. Although some optimal algorithms have been employed in uni-processor systems, they fail when they are applied in multiprocessor systems. The practical scheduling algorithms in real-time systems have not deterministic response time. Deterministic timing behavior is an important parameter for system robustness analysis. The intrinsic uncertainty in dynamic real-time systems increases the difficulties of scheduling problem. To alleviate these difficulties, we have proposed a fuzzy scheduling approach to arrange real-time periodic and non-periodic tasks in multiprocessor systems. Static and dynamic optimal scheduling algorithms fail with non-critical overload. In contrast, our approach balances task loads of the processors successfully while consider starvation prevention and fairness which cause higher priority tasks have higher running probability. A simulation is conducted to evaluate the performance of the proposed approach. Experimental results have shown that the proposed fuzzy scheduler creates feasible schedules for homogeneous and heterogeneous tasks. It also and considers tasks priorities which cause higher system utilization and lowers deadline miss time. According to the results, it performs very close to optimal schedule of uni-processor systems.

Keywords: Computational complexity, Deadline, Feasible scheduling, Fuzzy scheduling, Priority, Real-time multiprocessor systems, Robustness, System utilization.

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Authors: Kejun Zhuang

Abstract:

In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.

Keywords: Chaotic system, Hopf bifurcation, normal form theory.

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Authors: M.Eskandari-Ghadi, M.Mahmoodian

Abstract:

In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform, the displacement is obtained in the real domain. With the aid of boundary conditions, the involved boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. Integral representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem coincides with existing solutions in the literature.

Keywords: Cosine transform, Half space, Isotropic, Singular integral equation, Torsion

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