Search results for: Three- Dimensional Finite Element Analysis.

Authors: N. Outili, A-H. Meniai

Abstract:

Modeling transfer phenomena in several chemical engineering operations leads to the resolution of partial differential equations systems. According to the complexity of the operations mechanisms, the equations present a nonlinear form and analytical solution became difficult, we have then to use numerical methods which are based on approximations in order to transform a differential system to an algebraic one.Finite element method is one of numerical methods which can be used to obtain an accurate solution in many complex cases of chemical engineering.The packed columns find a large application like contactor for liquid-liquid systems such solvent extraction. In the literature, the modeling of this type of equipment received less attention in comparison with the plate columns.A mathematical bidimensionnal model with radial and axial dispersion, simulating packed tower extraction behavior was developed and a partial differential equation was solved using the finite element method by adopting the Galerkine model. We developed a Mathcad program, which can be used for a similar equations and concentration profiles are obtained along the column. The influence of radial dispersion was prooved and it can-t be neglected, the results were compared with experimental concentration at the top of the column in the extraction system: acetone/toluene/water.

Keywords: finite element method, Galerkine method, liquidliquid extraction modelling, packed column simulation, two dimensional model

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Authors: Anas M. Fares

Abstract:

The using of finite element programs in analyzing and designing buildings are becoming very popular, but there are many engineers still using the tributary area method (TAM) in designing the structural members such as columns. This study is an attempt to investigate the accuracy of the TAM results with different load condition (gravity and lateral load), different floors numbers, and different columns stiffness's. To conduct this study, linear elastic analysis in ETABS program is used. The results from finite element method are compared to those obtained from TAM. According to the analysis of the data obtained, it can be seen that there is significance difference between the real load carried by columns and the load which is calculated by using the TAM. Thus, using 3-D models are the best choice to calculate the real load effected on columns and design these columns according to this load.

Keywords: Tributary area method, finite element method, ETABS, lateral load, axial loads, reinforced concrete, stiffness, multi-floor buildings.

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Authors: A. Vairis, M. Petousis, B. Kandyla, C. Chrisoulakis

Abstract:

The human knee joint has a three dimensional geometry with multiple body articulations that produce complex mechanical responses under loads that occur in everyday life and sports activities. To produce the necessary joint compliance and stability for optimal daily function various menisci and ligaments are present while muscle forces are used to this effect. Therefore, knowledge of the complex mechanical interactions of these load bearing structures is necessary when treatment of relevant diseases is evaluated and assisting devices are designed. Numerical tools such as finite element analysis are suitable for modeling such joints in order to understand their physics. They have been used in the current study to develop an accurate human knee joint and model its mechanical behavior. To evaluate the efficacy of this articulated model, static load cases were used for comparison purposes with previous experimentally verified modeling works drawn from literature.

Keywords: biomechanics, finite element modeling, knee joint

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Authors: M.Z. Islam, C.W. Lim

Abstract:

Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which governs the nonlocal material behavior. The new NL-FEM is adopted in such a way that the postulated nonlocal elastic behavior of material is captured by a finite element endowed with a set of (cross-stiffness) element itself by the other elements in mesh. An example with their analytical solutions and the relevant numerical findings for various load and boundary conditions are presented and discussed in details. It is observed from the numerical solutions that the torsional deformation angle decreases with increasing nonlocal nanoscale parameter. It is also noted that the analytical solution fails to capture the nonlocal effect in some cases where numerical solutions handle those situation effectively which prove the reliability and effectiveness of numerical techniques.

Keywords: NL-FEM, nonlocal elasticity, nanoscale, torsion.

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Authors: Y. Kurosawa, T. Yamaguchi

Abstract:

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: Rado Flajs, Miran Saje

Abstract:

In the present paper the displacement-based nonconforming quadrilateral affine thin plate bending finite element ARPQ4 is presented, derived directly from non-conforming quadrilateral thin plate bending finite element RPQ4 proposed by Wanji and Cheung [19]. It is found, however, that element RPQ4 is only conditionally unisolvent. The new element is shown to be inherently unisolvent. This convenient property results in the element ARPQ4 being more robust and thus better suited for computations than its predecessor. The convergence is proved and the rate of convergence estimated. The mathematically rigorous proof of convergence presented in the paper is based on Stummel-s generalized patch test and the consideration of the element approximability condition, which are both necessary and sufficient for convergence.

Keywords: Quadrilateral thin plate bending element, convergence, generalized patch test.

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Authors: Nopparat Pochai, Rujira Deepana

Abstract:

Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: Marco T. C. Faria

Abstract:

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: Jonathan H. Perez, Fumihiko Tanaka, Daisuke Hamanaka, Toshitaka Uchino

Abstract:

A finite element analysis was conducted to determine the effect of moisture diffusion and hygroscopic swelling in rice. A parallel simple stochastic modeling was performed to predict the number of grains cracked as a result of moisture absorption and hygroscopic swelling. Rice grains were soaked in thermally (25 oC) controlled water and then tested for compressive stress. The destructive compressive stress tests revealed through compressive stress calculation that the peak force required to cause cracking in grains soaked in water reduced with time as soaking duration was extended. Results of the experiment showed that several grains had their value of the predicted compressive stress below the von Mises stress and were interpreted as grains which become cracked and/or broke during soaking. The technique developed in this experiment will facilitate the approximation of the number of grains which will crack during soaking.

Keywords: Cracking, Finite element analysis, hygroscopic swelling, moisture diffusion, von Mises stress.

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Authors: Natural Frequency Analysis of a Porous Functionally Graded Shaft System

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The vibration characteristics of a functionally graded (FG) rotor model having porosities and micro-voids is investigated using three-dimensional finite element analysis. The FG shaft is mounted with a steel disc located at the midspan. The shaft ends are supported on isotropic bearings. The FG material is composed of a metallic (stainless-steel) and ceramic phase (zirconium oxide) as its constituent phases. The layer wise material property variation is governed by power law. Material property equations are developed for the porosity modelling. Python code is developed to assign the material properties to each layer including the effect of porosities. ANSYS commercial software is used to extract the natural frequencies and whirl frequencies for the FG shaft system. The obtained results show the influence of porosity volume fraction and power-law index, on the vibration characteristics of the ceramic-based FG shaft system.

Keywords: Finite element method, functionally graded material, porosity volume fraction, power law.

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Authors: Dong Wook Lee, Adrian Mistreanu

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The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: Computer Aided Engineering, CAE, containment analysis, Finite Element Analysis, FEA, impact analysis, penetration analysis.

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Authors: Dong Wook Lee

Abstract:

This paper presents a method to analyze the stiffness of the expansion joint with structural support using a hybrid method combining computational and analytical methods. Many expansion joints found in tubes and ducts of mechanical structures are designed to absorb thermal expansion mismatch between their structural members and deal with misalignments introduced from the assembly/manufacturing processes. One of the important design perspectives is the system’s vibrational characteristics. We calculate the stiffness as a characterization parameter for structural joint systems using a combined Finite Element Analysis (FEA) and an analytical method. We apply the methods to two sample applications: external configurations of aircraft engines and nuclear power plant structures.

Keywords: Expansion joint, expansion joint stiffness, Finite Element Analysis, FEA, nuclear power plants, aircraft engine external configurations.

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Authors: Nitish Kumar Vaja, Oumar Barry, Brian DeJong

Abstract:

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

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

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Authors: W. Lai, A. A. Khan

Abstract:

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing Runge- Kutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-dimensional shallow water equations. For each slope limiter, three different Riemann solvers based on HLL, LF, and Roe flux functions are used. The proposed water surface based slope limiter scheme is easy to implement and shows better conservation property compared to the slope limiter based on water depth. Of the three flux functions, the Roe approximation provides the best results while the LF function proves to be least suitable when used with either slope limiter scheme.

Keywords: Discontinuous finite element, TVD Runge-Kuttascheme, slope limiters, Riemann solvers, shallow water flow.

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Authors: Dyi-Cheng Chen, Wen-Hsuan Ku, Ming-Ren Chen

Abstract:

The current of professional bicycle pedal-s manufacturing model mostly used casting, forging, die-casting processing methods, so the paper used 7075 aluminum alloy which is to produce the bicycle parts most commonly, and employs the rigid-plastic finite element (FE) DEFORMTM 3D software to simulate and to analyze the professional bicycle pedal design. First we use Solid works 2010 3D graphics software to design the professional bicycle pedal of the mold and appearance, then import finite element (FE) DEFORMTM 3D software for analysis. The paper used rigid-plastic model analytical methods, and assuming mode to be rigid body. A series of simulation analyses in which the variables depend on different temperature of forging billet, friction factors, forging speed, mold temperature are reveal to effective stress, effective strain, damage and die radial load distribution for forging bicycle pedal. The analysis results hope to provide professional bicycle pedal forming mold references to identified whether suit with the finite element results for high-strength design suitability of aluminum alloy.

Keywords: Bicycle pedal, finite element analysis, 7075 aluminum alloy, Taguchi method

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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: Saroj Kumar Sarangi, M. C. Ray

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This paper deals with the analysis of active constrained layer damping (ACLD) of doubly curved laminated composite shells using active fiber composite (AFC) materials. The constraining layer of the ACLD treatment has been considered to be made of the AFC materials. A three dimensional energy based finite element model of the smart doubly curved laminated composite shell integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of the doubly curved laminated composite shells. Particular emphasis has been placed on studying the effect of variation of piezoelectric fiber orientation angle in the constraining AFC layer on the control authority of the ACLD patch.

Keywords: Active constrained layer damping, Active fibercomposites, Finite element modeling, First order shear deformationtheory.

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Authors: Muhammad Waseem Ashraf, Shahzadi Tayyaba, Nitin Afzulpurkar, Asim Nisar, Adisorn Tuantranont, Erik L J Bohez

Abstract:

In this paper, design, fabrication and coupled multifield analysis of hollow out-of-plane silicon microneedle array with piezoelectrically actuated microfluidic device for transdermal drug delivery (TDD) applications is presented. The fabrication process of silicon microneedle array is first done by series of combined isotropic and anisotropic etching processes using inductively coupled plasma (ICP) etching technology. Then coupled multifield analysis of MEMS based piezoelectrically actuated device with integrated 2×2 silicon microneedle array is presented. To predict the stress distribution and model fluid flow in coupled field analysis, finite element (FE) and computational fluid dynamic (CFD) analysis using ANSYS rather than analytical systems has been performed. Static analysis and transient CFD analysis were performed to predict the fluid flow through the microneedle array. The inlet pressure from 10 kPa to 150 kPa was considered for static CFD analysis. In the lumen region fluid flow rate 3.2946 μL/min is obtained at 150 V for 2×2 microneedle array. In the present study the authors have performed simulation of structural, piezoelectric and CFD analysis on three dimensional model of the piezoelectrically actuated mcirofluidic device integrated with 2×2 microneedle array.

Keywords: Coupled multifield, finite element analysis, hollow silicon microneedle, transdermal drug delivery.

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Authors: M. E. Abou-Hashem El Dib, M. K. Swailem, M. M. Metwally, A. I. El Awady

Abstract:

This paper presents the effect of stiffeners on the behavior of slender steel I-beams. Nonlinear three dimensional finite element models are developed to represent the stiffened steel I-beams. The well established finite element (ANSYS 13.0) program is used to simulate the geometric and material nonlinear nature of the problem. Verification is achieved by comparing the obtained numerical results with the results of previous published experimental work. The parameters considered in the analysis are the horizontal stiffener's position and the horizontal stiffener's dimensions as well as the number of vertical stiffeners. The studied dimensions of the horizontal stiffeners include the stiffener width, the stiffener thickness and the stiffener length. The results of the achieved numerical parametric study for slender steel I-beams show the significant effect of stiffeners on the beam behavior and its failure load.

Keywords: Steel I-beams, local buckling, slender, stiffener, thin walled section.

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Authors: R. Hasanpour, N. Choupani

Abstract:

This paper studies mixed-mode fracture mechanics in rock based on experimental and numerical analyses. Experiments were performed on sharp-cracked specimens using the modified Arcan specimen test loading device. The modified Arcan specimen test was, in association with a special loading device, an appropriate apparatus for experimental mixed-mode fracture analysis. By varying the loading angle from 0° to 90°, pure mode-I, pure mode-II and a wide range of mixed-mode data were obtained experimentally. Using the finite element results, correction factors applied to the rectangular fracture specimen. By employing experimentally measured critical loads and the aid of the finite element method, mixed-mode fracture toughness for the limestone under consideration determined.

Keywords: Rock Fracture Mechanics, Mixed-mode Loading, Finite Element Analysis, Arcan Test specimen.

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Authors: Hamid Mozafari, Andreas Öchsner, Amran Alias

Abstract:

Imperfect transmission conditions modeling a thin reactive 2D interphases layer between two dissimilar bonded strips have been extracted. In this paper, the soundness of these transmission conditions for heat conduction problems are examined by the finite element method for a strong temperature-dependent source or sink and non-monotonic temperature distributions around the faces..

Keywords: Imperfect interface, Transmission conditions, Finiteelement analysis, Interphase

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Authors: Adrian T. Plesca

Abstract:

This paper describes a three-dimensional thermal model of the current path included in the low voltage power circuit breakers. The model can be used to analyse the thermal behaviour of the current path during both steady-state and transient conditions. The current path lengthwise temperature distribution and timecurrent characteristic of the terminal connections of the power circuit breaker have been obtained. The influence of the electric current and voltage drop on main electric contact of the circuit breaker has been investigated. To validate the three-dimensional thermal model, some experimental tests have been done. There is a good correlation between experimental and simulation results.

Keywords: Current path, power circuit breakers, temperature distribution, thermal analysis.

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Authors: Xi Yang, Bulent Chavdar, Alan Vonseggern, Taylan Altan

Abstract:

Fracture in hot precision forging of engine valves was investigated in this paper. The entire valve forging procedure was described and the possible cause of the fracture was proposed. Finite Element simulation was conducted for the forging process, with commercial Finite Element code DEFORMTM. The effects of material properties, the effect of strain rate and temperature were considered in the FE simulation. Two fracture criteria were discussed and compared, based on the accuracy and reliability of the FE simulation results. The selected criterion predicted the fracture location and shows the trend of damage increasing with good accuracy, which matches the experimental observation. Additional modification of the punch shapes was proposed to further reduce the tendency of fracture in forging. Finite Element comparison shows a great potential of such application in the mass production.

Keywords: Hot forging, engine valve, fracture, tooling.

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Authors: S. Parida, S. C. Mohanty

Abstract:

The free vibration behavior of thick pretwisted cantilevered functionally graded material (FGM) plate subjected to the thermal environment is investigated numerically in the present paper. A mathematical model is developed in the framework of higher order shear deformation theory (HOST) with C⁰ finite element formulation i.e. independent displacement and rotations. The material properties are assumed to be temperature dependent and vary continuously through the thickness based on the volume fraction exponent in simple power rule. The finite element model has been discretized into eight node quadratic serendipity elements with node wise seven degrees of freedom. The effect of plate geometry, temperature field, material composition, and the modal analysis on the vibrational characteristics is examined. Finally, the results are verified by comparing with those available in literature.

Keywords: FGM, pretwisted plate, thermal environment, HOST, simple power law.

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

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There exist a wide range of failure modes in composite structures due to the increased usage of the structures especially in aerospace industry. Moreover, temperature dependent wave response of composite and layered structures have been continuously studied, though still limited, in the last decade mainly due to the broad operating temperature range of aerospace structures. A wave finite element (WFE) and finite element (FE) based computational method is presented by which the temperature dependent wave dispersion characteristics and interaction phenomenon in composite structures can be predicted. Initially, the temperature dependent mechanical properties of the panel in the range of -100 ◦C to 150 ◦C are measured experimentally using the Thermal Mechanical Analysis (TMA). Temperature dependent wave dispersion characteristics of each waveguide of the structural system, which is discretized as a system of a number of waveguides coupled by a coupling element, is calculated using the WFE approach. The wave scattering properties, as a function of temperature, is determined by coupling the WFE wave characteristics models of the waveguides with the full FE modelling of the coupling element on which defect is included. Numerical case studies are exhibited for two waveguides coupled through a coupling element.

Keywords: Temperature dependent mechanical characteristics, wave propagation properties, damage detection, wave finite element, composite structure.

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Authors: F. Al-Mufadi, F. Djavanroodi

Abstract:

During the last decade ultrafine grained (UFG) and nano-structured (NS) materials have experienced a rapid development. In this research work finite element analysis has been carried out to investigate the plastic strain distribution in equal channel angular process (ECAP). The magnitudes of Standard deviation (S. D.) and inhomogeneity index (C_i) were compared for different ECAP passes. Verification of a three-dimensional finite element model was performed with experimental tests. Finally the mechanical property including impact energy of ultrafine grained pure commercially pure Aluminum produced by severe plastic deformation method has been examined. For this aim, equal channel angular pressing die with the channel angle, outer corner angle and channel diameter of 90^°, 20^° and 20mm had been designed and manufactured. Commercial pure Aluminum billets were ECAPed up to four passes by route B_C at the ambient temperature. The results indicated that there is a great improvement at the hardness measurement, yield strength and ultimate tensile strength after ECAP process. It is found that the magnitudes of HV reach 67HV from 21HV after the final stage of process. Also, about 330% and 285% enhancement at the YS and UTS values have been obtained after the fourth pass as compared to the as-received conditions, respectively. On the other hand, the elongation to failure and impact energy have been reduced by 23% and 50% after imposing four passes of ECAP process, respectively.

Keywords: SPD, ECAP, FEM, Pure Al, Mechanical properties.

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Authors: A. Armin, R. Fotouhi, W. Szyszkowski

Abstract:

In this paper a 3-D finite element (FE) investigation of soil-blade interaction is described. The effects of blade’s shape and rake angle are examined both numerically and experimentally. The soil is considered as an elastic-plastic granular material with non-associated Drucker-Prager material model. Contact elements with different properties are used to mimic soil-blade sliding and soil-soil cutting phenomena. A separation criterion is presented and a procedure to evaluate the forces acting on the blade is given and discussed in detail. Experimental results were derived from tests using soil bin facility and instruments at the University of Saskatchewan. During motion of the blade, load cells collect data and send them to a computer. The measured forces using load cells had noisy signals which are needed to be filtered. The FE results are compared with experimental results for verification. This technique can be used in blade shape optimization and design of more complicated blade’s shape.

Keywords: Finite element analysis, soil-blade contact modeling, blade force, experimental results.

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Authors: Tariq T. Darabseh

Abstract:

The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.

Keywords: Finite element method, thermal stresses, Green-Lindsay theory, functionally graded material.

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Authors: Porojan S., Sandu L., Topală F.

Abstract:

Simulation of occlusal function during laboratory material-s testing becomes essential in predicting long-term performance before clinical usage. The aim of the study was to assess the influence of chamfer preparation depth on failure risk of heat pressed ceramic crowns with and without zirconia framework by means of finite element analysis. 3D models of maxillary central incisor, prepared for full ceramic crowns with different depths of the chamfer margin (between 0.8 and 1.2 mm) and 6-degree tapered walls together with the overlying crowns were generated using literature data (Fig. 1, 2). The crowns were designed with and without a zirconia framework with a thickness of 0.4 mm. For all preparations and crowns, stresses in the pressed ceramic crown, zirconia framework, pressed ceramic veneer, and dentin were evaluated separately. The highest stresses were registered in the dentin. The depth of the preparations had no significant influence on the stress values of the teeth and pressed ceramics for the studied cases, only for the zirconia framework. The zirconia framework decreases the stress values in the veneer.

Keywords: Finite element analysis, full ceramic crown, zirconia framework, stresses.

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Authors: M. Najafi

Abstract:

In the present paper, a large turbo-generator shaft train including a heavy-duty gas turbine engine, a coupling, and a generator is established. The method of analysis is based on finite element simplified model for lateral and torsional vibration calculation. The basic elements of rotor are the shafts and the disks which are represented as circular cross section flexible beams and rigid body elements, respectively. For more accurate results, the gyroscopic effect and bearing dynamics coefficients and function of rotation are taken into account, and for the influence of shear effect, rotor has been modeled in the form of Timoshenko beam. Lateral critical speeds, critical speed map, damped mode shapes, Campbell diagram, zones of instability, amplitudes, phase angles response due to synchronous forces of excitation and amplification factor are calculated. Also, in the present paper, the effect of imbalanced rotor and effects of changing in internal force and temperature are studied.

Keywords: Rotor dynamic analysis, Finite element method, shaft train, Campbell diagram.

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