Search results for: matrix inverse method

Authors: Xinjian Kou, Linlin Li, Yongju Zhou, Jimian Song

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We introduce the redundancy matrix that expresses clearly the geometrical/topological configuration of the structure. With the matrix, the redundancy of the structure is resolved into redundant components and assigned to each member or rigid joint. The values of the diagonal elements in the matrix indicates the importance of the corresponding members or rigid joints, and the geometrically correlations can be shown with the non-diagonal elements. If a member or rigid joint failures, reassignment of the redundant components can be calculated with the recursive method given in the paper. By combining the indexes of reliability and redundancy components, we define an index concerning the structural robustness. To further explain the properties of the redundancy matrix, we cited several examples of statically indeterminate structures, including two trusses and a rigid frame. With the examples, some simple results and the properties of the matrix are discussed. The examples also illustrate that the redundancy matrix and the relevant concepts are valuable in structural safety analysis.

Keywords: Structural Robustness, Structural Reliability, Redundancy Component, Redundancy Matrix

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: M. Hadji, N. Chiker, Y. Hadji, A. Haddad

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In this paper, we report for the first time on the synthesis and characterization of novel MAX phases (Ti3SiC2, Ti2AlC) reinforced Ni-matrix and Ti2AlC reinforced Al-matrix. The stability of MAX phases in Al-matrix and Ni-matrix at a temperature of 985°C has been investigated. All the composites were cold pressed and sintered at a temperature of 985°C for 20min in H2 environment, except (Ni/Ti3SiC2) who was sintered at 1100°C for 1h.Microstructure analysis by scanning electron microscopy and phase analysis by X-Ray diffraction confirmed that there was minimal interfacial reaction between MAX particles and Ni, thus Al/MAX samples shown that MAX phases was totally decomposed at 985°C.The Addition of MAX enhanced the Al-matrix and Ni-matrix.

Keywords: MAX phase, microstructures, composites, hardness, SEM

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Authors: Thomas Chinwe Urama, Patrick Oseloka Ezepue, Peters Chimezie Nnanwa

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This paper investigates the universal financial dynamics in two dominant stock markets in Sub-Saharan Africa, through an in-depth analysis of the cross-correlation matrix of price returns in Nigerian Stock Market (NSM) and Johannesburg Stock Exchange (JSE), for the period 2009 to 2013. The strength of correlations between stocks is known to be higher in JSE than that of the NSM. Particularly important for modelling Nigerian derivatives in the future, the interactions of other stocks with the oil sector are weak, whereas the banking sector has strong positive interactions with the other sectors in the stock exchange. For the JSE, it is the oil sector and beverages that have greater sectorial correlations, instead of the banks which have the weaker correlation with other sectors in the stock exchange.

Keywords: random matrix theory, cross-correlations, emerging markets, option pricing, eigenvalues eigenvectors, inverse participation ratios and implied volatility

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Authors: Dhruba Das

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In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: imprecise number, imprecise vector, membership surface, imprecise matrix

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: Chao Yu, Qing-Guo Wang, Dan Zhang

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The outlier detection problem for dynamic systems is formulated as a matrix decomposition problem with low-rank, sparse matrices and further recast as a semidefinite programming (SDP) problem. A fast algorithm is presented to solve the resulting problem while keeping the solution matrix structure and it can greatly reduce the computational cost over the standard interior-point method. The computational burden is further reduced by proper construction of subsets of the raw data without violating low rank property of the involved matrix. The proposed method can make exact detection of outliers in case of no or little noise in output observations. In case of significant noise, a novel approach based on under-sampling with averaging is developed to denoise while retaining the saliency of outliers and so-filtered data enables successful outlier detection with the proposed method while the existing filtering methods fail. Use of recovered “clean” data from the proposed method can give much better parameter estimation compared with that based on the raw data.

Keywords: outlier detection, system identification, matrix decomposition, low-rank matrix, sparsity, semidefinite programming, interior-point methods, denoising

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Authors: Takuro Kida, Yuichi Kida

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We show a base of the new trend of algorithm mathematically that treats a historical reason of continuous discrimination in the world as well as its solution by introducing new concepts of parallel world that includes an invisible set of errors as its companion. With respect to a matrix operator-filter bank that the matrix operator-analysis-filter bank H and the matrix operator-sampling-filter bank S are given, firstly, we introduce the detailed algorithm to derive the optimum matrix operator-synthesis-filter bank Z that minimizes all the worst-case measures of the matrix operator-error-signals E(ω) = F(ω) − Y(ω) between the matrix operator-input-signals F(ω) and the matrix operator-output signals Y(ω) of the matrix operator-filter bank at the same time. Further, feedback is introduced to the above approximation theory and it is indicated that introducing conversations with feedback does not superior automatically to the accumulation of existing knowledge of signal prediction. Secondly, the concept of category in the field of mathematics is applied to the above optimum signal approximation and is indicated that the category-based approximation theory is applied to the set-theoretic consideration of the recognition of humans. Based on this discussion, it is shown naturally why the narrow perception that tends to create isolation shows an apparent advantage in the short term and, often, why such narrow thinking becomes intimate with discriminatory action in a human group. Throughout these considerations, it is presented that, in order to abolish easy and intimate discriminatory behavior, it is important to create a parallel world of conception where we share the set of invisible error signals, including the words and the consciousness of both worlds.

Keywords: signal prediction, pseudo inverse matrix, artificial intelligence, conditional optimization

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Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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Authors: Ahmed Salam, Haithem Benkahla

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Recently, an efficient backward-stable algorithm for computing eigenvalues and vectors of a symmetric and Hamiltonian matrix has been proposed. The method preserves the symmetric and Hamiltonian structures of the original matrix, during the whole process. In this paper, we revisit the method. We derive a way for implementing the reduction of the matrix to the appropriate condensed form. Then, we construct a novel version of the implicit QR-algorithm for computing the eigenvalues and vectors.

Keywords: block implicit QR algorithm, preservation of a double structure, QR algorithm, symmetric and Hamiltonian structures

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Authors: Radha H. R., Krupakara P. V.

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Metal matrix composites are attracting today's manufacturers of many automobile parts so that they lost longer and their properties can be tailored according to the requirement. In this paper an attempt has been made to study the corrosion characteristics of Aluminium 6061 / quartz metal matrix composites in alkali medium like sodium hydroxide solutions. Metal matrix composites are heterogeneous mixtures of a matrix and reinforcement. In this work the matrix selected is Aluminium 6061 alloy which is commercially available and the reinforcement selected is quartz particulates of 50-80 micron size which is available in plenty in and around Bangalore district, India. Composites containing Aluminium 6061 with 2, 4 and 6 weight percent of quartz are manufactured by liquid melt metallurgy technique using vortex method. Corrosion tests like static weight loss and open circuit potential tests are conducted in different concentrated solutions of sodium hydroxide. To compare the results the matrix Aluminium 6061 is also casted in the same way. Specimens for the test are prepared according to ASTM standards. In all the tests the metal matrix composites showed better corrosion resistance than matrix alloy.

Keywords: aluminium 6061, corrosion, quartz, vortex

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Authors: Samai'la Abdullahi

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A graph is a pair of two set and so that a graph is a pictorial representation of a system using two basic element nodes and edges. A node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper, we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table.

Keywords: euler circuit and path, graph representation of circuit networks, representation of graph models, representation of circuit network using logical truth table

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Harendra Singh, Rajesh Pandey

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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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Authors: Slimane Souag, Amel Graa, Farid Benhamida

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In this paper we present a new method for solving the secured power flow problem by the economic dispatch using DC power flow method and Generation Shift Distribution Factor (GSDF), in this work we create a graphical interface in LabVIEW as a virtual instrument. Hence the dc power flow reduces the power flow problem to a set of linear equations, which make the iterative calculation very fast and the GSFD matrix present the effects of single and multiple generator MW change on the transmission line. The effectiveness of the method developed is identified through its application to an IEEE-14 bus test system. The calculation results show excellent performance of the proposed method, in regard to computation time and quality of results.

Keywords: electrical power system security, economic dispatch, sensitivity matrix, labview

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Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

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This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: kinematics, degree of freedom, optimization, robot manipulator

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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: Vethathirri Ramanujam Srinivasan, S. M. Shiva Nagendra

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Air quality management in urban areas is a serious concern in both developed and developing countries. In this regard, more number of air quality monitoring stations are planned to mitigate air pollution in urban areas. In India, Central Pollution Control Board has set up 574 air quality monitoring stations across the country and proposed to set up another 500 stations in the next few years. The number of monitoring stations for each city has been decided based on population data. The setting up of ambient air quality monitoring stations and their operation and maintenance are highly expensive. Therefore, there is a need to optimize monitoring networks for air quality management. The present paper discusses the various methods such as Indian Standards (IS) method, US EPA method and European Union (EU) method to arrive at the minimum number of air quality monitoring stations. In addition, optimization of rain-gauge method and Inverse Distance Weighted (IDW) method using Geographical Information System (GIS) are also explored in the present work for the design of air quality network in Chennai city. In summary, additionally 18 stations are required for Chennai city, and the potential monitoring locations with their corresponding land use patterns are ranked and identified from the 1km x 1km sized grids.

Keywords: air quality monitoring network, inverse distance weighted method, population based method, spatial variation

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Authors: H. V. Jayaprakash, P. V. Krupakara

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This paper deals with the high corrosion resistance developed by the metal matrix composites when compared with that of matrix alloy by open circuit potential test. Matrix selected is ZA-27 and reinforcement selected is red mud particulates, which is a ceramic material. The composites are prepared using liquid melt metallurgy technique using vortex method. Preheated but uncoated red mud particulates are added to the melt. Metal matrix composites containing 2, 4 and 6 weight percentage of red mud are casted. Matrix was also casted in the same way for comparison. Specimen are fabricated according to ASTM standards. The corrodents used for the tests were 0.025, 0.05 and 0.1 molar sodium hydroxide solutions. They are subjected to Open Circuit Potential studies and weight loss corrosion tests. Corrosion rate was found to be decreased with increase in exposure time in both experiments. Effect of exposure time and presence of increased percentage of reinforcement red mud is discussed in detail.

Keywords: composites, vortex, particulates, red mud

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Authors: Nagaraju Jarugu, B. R. Narendra

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This paper focused on boost rectification by Single Phase Matrix Converter with fewer numbers of switches. The conventional matrix converter consists of 4 bidirectional switches, i.e. 8 set of IGBT/MOSFET with anti-parallel diodes. In this proposed matrix converter, only six switches are used. The switch commutation arrangements are also carried out in this work. The SPMC topology has many advantages as a minimal passive device use. It is very flexible and it can be used as a lot of converters. The gate pulses to the switches are provided by the PWM techniques. The duty ratio of the switches based on Pulse Width Modulation (PWM) technique was used to produce the output waveform of the circuit, simply by turning ON and OFF the switches. The simulation results using MATLAB/Simulink were provided to validate the feasibility of this proposed method.

Keywords: single phase matrix converter, reduced switches, AC voltage regulators, boost rectifier operation

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Authors: Noriyoshi Yamauchi, Etsuo Horikawa, Takunori Tsuji

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Training by exoskeleton robot is drawing attention as a rehabilitation method for body paralysis seen in many cases, and there are many forms that assist with the myoelectric signal generated by exercise commands from the brain. Rehabilitation requires more frequent training, but it is one of the reasons that the technology is required for the identification of the myoelectric potential derivation site and attachment of the device is preventing the spread of paralysis. In this research, we focus on improving the efficiency of gait training by exoskeleton type robots, improvement of myoelectric acquisition and analysis method using active matrix sensing method, and improvement of walking rehabilitation and walking by optimization of robot control.

Keywords: active matrix sensing, brain machine interface (BMI), the central pattern generator (CPG), myoelectric signal processing, robot rehabilitation

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Authors: Benny Alexander, Ikhlashia N. Fadhilah, Muhammad R. Pasha, Michelle Julia, Anne Z. Syahrial

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Brake shoe is a component that serves to reduce speed or stop the train's speed by utilizing the friction force. Generally, the material used as a brake shoe is cast iron, where cast iron itself is a heavy, expensive, and easily worn material. Aluminum matrix composites are one of candidates for the cast iron replacement material as the basic material for brake shoe. The matrix in the composite used is Aluminum AC4B. Reinforcement used in aluminum matrix composites is nano-alumina, where the use of nano-alumina of 0.25%, 0.3%, 0.35%, 0.4%, and 0.5% volume fraction will be tested. The sample is made using the stir casting method; then, it will be tested mechanically. The use of nano-alumina as a reinforcement will increase the strength of the matrix. SEM (scanning electron microscopy) testing is used to test the distribution of reinforcing particles due to stirring. Therefore, the addition of nano-alumina will improve AC4B aluminum matrix composites.

Keywords: aluminium matrix composites, brake shoe application, stir casting, nano-alumina

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Authors: Elham Allahmoradi, Bahman Allahmoradi, Ali Bonyadi Naeini

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Complex systems have many aspects. A variety of methods have been developed to analyze these systems. The most efficient of these methods should not only be simple, but also provide useful and comprehensive information about many aspects of the system. Matrix methods are considered the most commonly methods used to analyze and design systems. Each matrix method can examine a particular aspect of the system. If these methods are combined, managers can access to more comprehensive and broader information about the system. This study was conducted in four steps. In the first step, a process model of a real project has been extracted through IDEF3. In the second step, activity levels have been attained by writing a process model in the form of a design structure matrix (DSM) and sorting it through triangulation algorithm (TA). In the third step, sub-processes have been obtained by writing the process model in the form of an interface structure matrix (ISM) and clustering it through cluster identification algorithm (CIA). In the fourth step, a mixed model has been developed to provide a unified picture of the project structure through the simultaneous presentation of activities and sub-processes. Finally, the paper is completed with a conclusion.

Keywords: integrated definition for process description capture (IDEF3) method, design structure matrix (DSM), interface structure matrix (ism), mixed matrix model, activity level, sub-process

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Authors: Anand Ankush, Wani Mohammed Farooq

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A procedure based on digraph and matrix method is developed for modelling and evaluation of sustainability of Mechanical System in a concurrent engineering environment.The sustainability parameters of a Mechanical System are identified and are called sustainability attributes. Consideration of attributes and their interrelations is rudiment in modeling and evaluation of sustainability index. Sustainability attributes of a Mechanical System are modelled in termsof sustainability digraph. The graph is represented by a one-to-one matrix for sustainability expression which is based on sustainability attributes. A variable sustainability relationship permanent matrix is defined to develop sustainability expression(VPF-t) which is also useful in comparing two systems in a concurrent environment. The sustainability index of Mechanical System is obtained from permanent of matrix by substituting the numerical values of attributes and their interrelations. A higher value of index implies better sustainability of system.The ideal value of index is obtained from matrix expression which is useful in assessing relative sustainability of a Mechanical System in a concurrent engineering environment. The procedure is not only useful for evaluation of sustainability of a Mechanical System at conceptual design stage but can also be used for design and development of systems at system design stage. A step-by-step procedure for evaluation of sustainability index is also suggested and is illustrated by means of an example.

Keywords: digraph, matrix method, mechanical system, sustainability

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Authors: Atilla Bayram

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This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: computed force method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss

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Authors: M. S. Gadala, Khaled Ahmed, Elasadig Mahdi

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In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

Keywords: inverse analysis, function specification, neural net works, particle swarm, run-out table

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Authors: Xiaoqian Cheng, Jon Kleppe, Ole Torsæter

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The properties of rocks have effects on efficiency of surfactant. One objective of this study is to analyze the effects of rock properties (permeability, porosity, initial water saturation) on surfactant spontaneous imbibition at laboratory scale. The other objective is to evaluate existing upscaling methods and establish a modified upscaling method. A core is put in a container that is full of surfactant solution. Assume there is no space between the bottom of the core and the container. The core is modelled as a cuboid matrix with a length of 3.5 cm, a width of 3.5 cm, and a height of 5 cm. The initial matrix, brine and oil properties are set as the properties of Ekofisk Field. The simulation results of matrix permeability show that the oil recovery rate has a strong positive linear relationship with matrix permeability. Higher oil recovery is obtained from the matrix with higher permeability. One existing upscaling method is verified by this model. The study on matrix porosity shows that the relationship between oil recovery rate and matrix porosity is a negative power function. However, the relationship between ultimate oil recovery and matrix porosity is a positive power function. The initial water saturation of matrix has negative linear relationships with ultimate oil recovery and enhanced oil recovery. However, the relationship between oil recovery and initial water saturation is more complicated with the imbibition time because of the transition of dominating force from capillary force to gravity force. Modified upscaling methods are established. The work here could be used as a reference for the surfactant application in fractured reservoirs. And the description of the relationships between properties of matrix and the oil recovery rate and ultimate oil recovery helps to improve upscaling methods.

Keywords: initial water saturation, permeability, porosity, surfactant EOR

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Authors: Yeongyu Choi, Ju H. Park, Ho-Youl Jung

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In this paper, we propose labeling based RANSAC algorithm for lane detection. Advanced driver assistance systems (ADAS) have been widely researched to avoid unexpected accidents. Lane detection is a necessary system to assist keeping lane and lane departure prevention. The proposed vision based lane detection method applies Canny edge detection, inverse perspective mapping (IPM), K-means algorithm, mathematical morphology operations and 8 connected-component labeling. Next, random samples are selected from each labeling region for RANSAC. The sampling method selects the points of lane with a high probability. Finally, lane parameters of straight line or curve equations are estimated. Through the simulations tested on video recorded at daytime and nighttime, we show that the proposed method has better performance than the existing RANSAC algorithm in various environments.

Keywords: Canny edge detection, k-means algorithm, RANSAC, inverse perspective mapping

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Authors: Ashis Mallick, Rajeev Ranjan

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The closed form solution for thermal stresses in an annular fin with hyperbolic profile is derived using Adomian decomposition method (ADM). The conductive-convective fin with variable thermal conductivity is considered in the analysis. The nonlinear heat transfer equation is efficiently solved by ADM considering insulated convective boundary conditions at the tip of fin. The constant of integration in the solution is to be estimated using minimum decomposition error method. The solution of temperature field is represented in a polynomial form for convenience to use in thermo-elasticity equation. The non-dimensional thermal stress fields are obtained using the ADM solution of temperature field coupled with the thermo-elasticity solution. The influence of the various thermal parameters in temperature field and stress fields are presented. In order to show the accuracy of the ADM solution, the present results are compared with the results available in literature. The stress fields in fin with hyperbolic profile are compared with those of uniform thickness profile. Result shows that hyperbolic fin profile is better choice for enhancing heat transfer. Moreover, less thermal stresses are developed in hyperbolic profile as compared to rectangular profile. Next, Nelder-Mead based simplex search method is employed for the inverse estimation of unknown non-dimensional thermal parameters in a given stress fields. Owing to the correlated nature of the unknowns, the best combinations of the model parameters which are satisfying the predefined stress field are to be estimated. The stress fields calculated using the inverse parameters give a very good agreement with the stress fields obtained from the forward solution. The estimated parameters are suitable to use for efficient and cost effective fin designing.

Keywords: Adomian decomposition, inverse analysis, hyperbolic fin, variable thermal conductivity

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Authors: Mohammad Hadi Jalali, Mostafa Ghayour, Saeed Ziaei-Rad, Behrooz Shahriari

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The vibration problems that can be occurred in the operational conditions of rotating machines may cause damage to the machine or even failure of the machine completely. Therefore, dynamic analysis of rotors is vital in the design and development stages of the rotating machines. In this study, the uncoupled torsional and lateral vibration analysis of a rotor-bearing system is carried out using transfer matrix method. The Campbell diagram, critical speed and the mode shape corresponding to the critical speed are obtained in order to evaluate the dynamic behavior of the rotor.

Keywords: transfer matrix method, rotor-bearing system, campbell diagram, critical speed

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