Islamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930On Plane Waves for Mode-I Crack Problem in Generalized Thermoelasticity48649766668710.22034/jsm.2019.666687ENkhLotfyDepartment of Mathematics, Faculty of Science, Taibah University, Madina, Kingdom of Saudi Arabia---
Department of Mathematics, Faculty of Science, Zagazig University, EgyptJournal Article20190329<span>A general model of the equations of generalized thermoelasticity for an infinite space weakened by a finite linear opening Mode-I crack is solving. The material is homogeneous and has isotropic properties of elastic half space. The crack is subjected to prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, the Lord-Şhulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and micro-stress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the three theories. </span>http://jsm.iau-arak.ac.ir/article_666687_c1ac0b30b3d44c495f4252879930a16d.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930A Novel Method for Numerical Analysis of 3D Nonlinear Thermo-Mechanical Bending of Annular and Circular Plates with Asymmetric Boundary Conditions Using SAPM49851266676510.22034/jsm.2019.666765ENA. RGolkarianDepartment of Mechanical Engineering, Science & Research Branch, Islamic Azad University, Tehran, IranMJabbarzadehDepartment of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, IranShDastjerdiDepartment of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, IranJournal Article20190330This study is the first report of numerical solution of nonlinear bending analysis for annular and circular plates based on 3D elasticity theory with asymmetric boundary conditions using semi-analytical polynomial method (SAPM). Orthotropic annular and circular plates are subjected to transverse loading and 3D bending analysis in the presence of symmetric and asymmetric boundary conditions is studied. For asymmetry cases, the plate boundaries are divided to two or three parts and various boundary conditions such as clamped, simply-supported and free edges are defined for each part. The asymmetry in one and two directions is studied. The influence of elastic foundations, mechanical and thermo-mechanical loadings are examined. Regarding this fact that no study has been done in the case of asymmetric boundary conditions, the obtained results are compared with FEM results by ABAQUS. The results show good agreement with the literatures and FEM results, which it shows that the presented method can use to analyze the 3D bending of plates under asymmetric conditions. Also, it is observed that 3D elasticity estimates some higher deflections than other theories. But, the obtained results by 3D elasticity theory and those obtained by FEM analysis in the case of asymmetric conditions are so close.http://jsm.iau-arak.ac.ir/article_666765_23ea251bf2fe19f026f3a108db8062b2.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Generation of Love Wave in a Media with Temperature Dependent Properties Over a Heterogeneous Substratum51352266670010.22034/jsm.2019.666700ENSGuptaDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, IndiaPPatiDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India0000-0001-7098-295XBPrasadDepartment of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, IndiaJournal Article20190528The present paper deals with the generation of Love waves in a layer of finite thickness over an initially stressed heterogeneous semi-infinite media. The rigidity and density of the layer are functions of temperature, i.e. they are temperature dependent. The lower substratum is an initially stressed medium and its rigidity and density vary linearly with the depth. The frequency relation of Love waves has been acquired in compact form. Numerical calculations are accomplished and a number of graphs for non-dimensional phase velocity versus non-dimensional wave number are plotted to display the influence of intrinsic parameters like initial stress and inhomogeneity factors on the generation of Love waves. It is initiated that the non-dimensional phase velocity of Love wave decreases with increase in the non-dimensional wave number and is strongly influenced by the initial stress of the substratum and the inhomogeneity factors of the layer and the substratum. This study may provide effective information in the field of industrial engineering, civil engineering as well as geophysics and seismology.http://jsm.iau-arak.ac.ir/article_666700_53366e08d9d353702eb3e65999e46995.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Effect of the Multi Vibration Absorbers on the Nonlinear FG Beam Under Periodic Load with Various Boundary Conditions52353466668810.22034/jsm.2019.666688ENHAhmadiFaculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, IranKForoutanFaculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, IranJournal Article20190530A semi-analytical method is used to study the effects of the multi vibration absorbers on the nonlinear functionally graded (FG) Euler-Bernoulli beam subjected to periodic load. The material properties of the beam are assumed to be continuously graded in the thickness direction. The governing equations of functionally graded beam are obtained based on the Hamilton's principle and these equations are solved by using the Rayleigh-Ritz method. To validate the results, comparisons are made with the available solutions for the natural frequencies of isotropic beam. The effects of the multi vibration absorbers and material parameters on the vibration response of functionally graded beamare investigated. For case study the effect of two symmetrical vibration absorbers is considered, these absorbers are applicable in some of the mechanic systems. In those systems, two absorbers are used close to the beginning and end of the structures instead of using them in the middle of these structures. By considering the industrial applications, it is shown that using the two symmetrical vibration absorbers with lower mass is close to the end of functionally graded beam is better than the middle of one. Also, the effect of different numbers of the vibration absorbers on the nonlinear functionally graded beam with simply supported boundary condition is considered. The results shown that increasing the number of vibration absorbers leads to decreasing the maximum deflection.http://jsm.iau-arak.ac.ir/article_666688_ea3064577ba349d1fe627c7441aeb689.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Investigating Nonlinear Vibration Behavior of Rotors with Asymmetry Shaft Considering Misalignment53554966685110.22034/jsm.2019.666851ENA.AJafariDepartment of Mechanical Engineering, KNT University, Tehran, IranPJamshidiDepartment of Mechanical Engineering, KNT University, Tehran, IranJournal Article20190603In this paper, the nonlinear vibration behavior of a rotor with asymmetric shaft considering misalignment is studied. The system consists of a rectangular shaft and a disk which is connected to a motor through a flexible coupling. In order to consider higher order deformations, nonlinear Bernoulli beam is used for modeling the shaft. Gibbons’ equations are utilized to apply misaligned coupling forces. The equations of motion of the system are derived using the Lagrangian method and then discretized by the Rayleigh-Ritz method. In order to solve nonlinear equations and hence obtaining nonlinear responses, multiple scales method is used. The vibration behavior of the system near the resonance frequencies is studied by taking into account various parameters including unbalance forces and the effect of the asymmetry of cross section of the shaft. The analytical results are consistent with those of numerical method with a good accuracy. In addition, the effects of variations of the system parameters on the rotor vibration behavior have been shown graphically. In the end, the changes in the various parameters of the system and their effects on the rotor vibration response are discussed.http://jsm.iau-arak.ac.ir/article_666851_190ef0ff7ead7c05e32ca0a8e0bcc73e.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Higher-Order Stability Analysis of Imperfect Laminated Piezo-Composite Plates on Elastic Foundations Under Electro-Thermo-Mechanical Loads55056966668910.22034/jsm.2019.666689ENBMirzavandFaculty of New Sciences and Technologies, University of Tehran, Tehran, Iran0000-0002-5666-5445MBohloolyFaculty of New Sciences and Technologies, University of Tehran, Tehran, IranJournal Article20190605This article provides a fully analytical approach for nonlinear equilibrium path of rectangular sandwich plates. The core of structure is made of symmetric cross-ply laminated composite and the outer surfaces are piezoelectric actuators which perfectly bonded to inner core. The structure is subjected to electro-thermo-mechanical loads simultaneously. One side of plate is rested on Pasternak type elastic foundation. The equilibrium equations of plate are derived based on the higher-order shear deformation theory of Reddy taking into account initial geometrical imperfection, nonlinear strain-displacement relations of von-Karman, temperature dependent properties, and different types of boundary conditions. Some numerical examples are presented to verify the accuracy of the proposed formulation. The effects of various parameters such as voltage on actuators, elastic foundation, imperfection, and pre-load condition on the buckling and postbuckling behaviors are studied. As an important finding of current research, there may be exists bifurcation point for imperfect plates by applying voltage on actuators.http://jsm.iau-arak.ac.ir/article_666689_7fe5f1d8463c8108ebd8a936fe1755ff.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930An Analytic Study on the Dispersion of Love Wave Propagation in Double Layers Lying Over Inhomogeneous Half-Space57058066669010.22034/jsm.2019.666690ENAMandiIndian Institute of Technology (Indian School of Mines), Dhanbad-826004, IndiaSKunduIndian Institute of Technology (Indian School of Mines), Dhanbad-826004, IndiaPChandra PalIndian Institute of Technology (Indian School of Mines), Dhanbad-826004, IndiaPPatiIndian Institute of Technology (Indian School of Mines), Dhanbad-826004, IndiaJournal Article20190610In this work, attempts are made to study the dispersion of Love waves in dry sandy layer sandwiched between fiber reinforced layer and inhomogeneous half space.Inhomogeneity in half space associated with density and rigidity and considered in exponential form. Displacement components for fiber reinforced layer, dry sandy layer and inhomogeneous half-space have been obtained by using method of separable variables. Boundary conditions are defined at the free surface of the fiber reinforced layer and at the interfaces between layers and half space. The dispersion equation has derived in closed form. Numerical calculations for dispersion equation are performed. The study results show the effect of parameters on the velocity of Love waves and presented graphically. Graphs are plotted between wave number and phase velocity to show the effect of reinforced parameter, sandiness parameter and inhomogeneity on the phase velocity of Love waves. From the graphs it can be concluded that phase velocity decreases with respect to wave number.http://jsm.iau-arak.ac.ir/article_666690_3720bf366f14e12a6a22bdd92f5c3a58.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Effects of Viscosity on a Thick Circular Plate in Thermoelastic Diffusion Medium58159266724710.22034/jsm.2019.667247ENRKumarDepartment of Mathematics, Kurukshetra University, Kurukshetra, IndiaShDeviDepartment of Mathematics & Statistics, Himachal Pradesh University, Shimla, IndiaJournal Article20190615The problem treated here is to determinethe viscosity effect on stresses, temperature change and chemical potential in a circular plate. The mathematical formulation is applied to two theories of thermoelastic diffusion developed by Sherief et al. [27] with one relaxation time and Kumar and Kansal [9]with two relaxation times. Laplace and Hankel transform techniques are used to obtain the expression for the displacement components, stresses, temperature change and chemical potential. The resulting quantities are computed numerically and depicted graphically by using numerical inversion technique for a particular model. Effect of viscosity is shown in the normal stress, tangential stress, temperature change and chemical potential. Some particular cases of interest are also deduced. Viscoelastic materials play an important role in many branches of engineering, technology and, in recent years, biomechanics. Viscoelastic materials, such as amorphous polymers, semicrystalline polymers, and biopolymers, can be modelled in order to determine their stress or strain interactions as well as their temporal dependencies. http://jsm.iau-arak.ac.ir/article_667247_bb589a7afa134c523d34cea26cc43a9c.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Study of Love Waves in a Clamped Viscoelastic Medium with Irregular Boundaries59360566723410.22034/jsm.2019.667234ENPAlamDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore -632014, TN, IndiaM.KSinghDepartment of Mathematics, Madanapalle Institute of Technology & Science Madanapalle-517325, AP, IndiaJournal Article20190617A mathematical model is presented to investigate the effects of sandiness, irregular boundary interfaces, heterogeneity and viscoelasticity on the phase velocity of Love waves. Geometry of the problem is consisting of an initially stressed viscoelastic layer with corrugated irregular boundaries, which is sandwiched between heterogeneous orthotropic semi-infinite half-space with initial stress and pre-stressed dry sandy half-space. Heterogeneity arises in the upper half-space is due to trigonometric variation in elastic parameters of the orthotropic medium. Inclusion of the concept of corrugated irregular viscoelastic layer clamped between two dissimilar half-spaces under different physical circumstances such as initial stress and heterogeneity brings a novelty to the existing literature related to the study of Love wave. Dispersion equation for Love wave is obtained in closed form. The obtained dispersion relation is found to be in well agreement with classical Love wave equation. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, internal friction, wave number and amplitude of corrugations on the phase velocity of Love waves.http://jsm.iau-arak.ac.ir/article_667234_67e1782cd12c7818d7ba6c542721bc9c.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Displacement Fields Influence Analysis Caused by Dislocation Networks at a Three Layer System Interfaces on the Surface Topology60661466676610.22034/jsm.2019.666766ENABoussahaLaboratory LAMSM, Mechanical Engineering Department, Faculty of Technology, University of Batna 2 Mostafa Ben Boulaid, Batna, AlgeriaRMakhloufiLaboratory LAMSM, Mechanical Engineering Department, Faculty of Technology, University of Batna 2 Mostafa Ben Boulaid, Batna, AlgeriaSMadaniLaboratory LAMSM, Mechanical Engineering Department, Faculty of Technology, University of Batna 2 Mostafa Ben Boulaid, Batna, AlgeriaJournal Article20190620This work consists in a numerically evaluation of elastic fields distribution, caused by intrinsic dislocation networks placed at a nanometric trilayers interfaces, in order to estimate their influence on the surface topology during heterostructure operation. The organization of nanostructures is ensured by the knowledge of different elastic fields caused by buried dislocation networks and calculated in the case of anisotropic elasticity. The influence of elastic fields generated by induced square and parallel dislocation networks at <em>CdTe</em> / <em>GaAs</em> / (001) <em>GaAs</em> trilayer interfaces was investigated. By deposition, the nanostructures organization with respect to the topology was controled. http://jsm.iau-arak.ac.ir/article_666766_af2253ec589cf94faa00a00d5ca06a60.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Natural Frequency and Dynamic Analyses of Functionally Graded Saturated Porous Beam Resting on Viscoelastic Foundation Based on Higher Order Beam Theory61563466669110.22034/jsm.2019.666691ENMBabaeiDepartment of Mechanical Engineering, Shahid Beheshti University, Tehran, IranKAsemiDepartment of Mechanical Engineering, Islamic Azad University, Tehran North Branch, Tehran, IranPSafarpourDepartment of Mechanical Engineering, Shahid Beheshti University, Tehran, IranJournal Article20190621In this paper, natural frequencies and dynamic response of thick beams made of saturated porous materials resting on viscoelastic foundation are investigated for the first time. The beam is modeled using higher-order beam theory. Kelvin-voight model is used to model the viscoelastic foundation. Distribution of porosity along the thickness is considered in two different patterns, which are symmetric nonlinear and nonlinear asymmetric distributions. The relationship between stress and strain is based on the Biot constitutive law. Lagrange equations are used to express the motion equations. Finite element and Newark methods are used to solve the governing equations. The effect of different boundary conditions and various parameters such as porosity and Skempton coefficients, slenderness ratio as well as stiffness and damping coefficients of viscoelastic foundation on natural frequency and transient response of beam have been studied. Results show that in a drained condition, beam has smallest fundamental frequency and by increasing the Skempton coefficient, the fundamental frequency of the beam increases.http://jsm.iau-arak.ac.ir/article_666691_b4da0ed645a37898ac1dde568ae46c68.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Effect of Thickness on Fracture Toughness of Al6061-Graphite63564366669510.22034/jsm.2019.666695ENSDoddamaniDepartment of Mechanical Engineering, Jain Institute of Technology, Davangere, Karnataka, India0000-0002-8498-1488MKaleemullaDepartment of Studies in Mechanical Engineering, U B.D.T. College of Engineering, Karnataka, IndiaJournal Article20190623This research work presents the study on fracture behavior of Al6061 with graphite particulate composite produced by the stir casting technique. The materials selected for the proposed work is Al6061 and graphite particles. Compact tension (CT) specimens were utilized to determine fracture toughness for different thickness of composite. In the present work, optimizing the parameters of the compact tension specimens is carried out using Taguchi method. Four parameters and two factors are considered to optimize the parameters. Factors considered are material composition and <em>a/W</em> ratio. From the Taguchi analysis, on compact tension specimens, Al6061-9%graphite is the optimized composition and fracture toughness is maximum for <em>a/W</em> ratio = 0.45. All the compact tension specimens of different thickness (<em>B</em> = 4, 5, 7, 10, 12, 15, 18 and 20<em>mm</em>) of <em>a/W</em>=0.45 were tested to find the fracture toughness. From the results, it was observed that the <em>K<sub>q</sub></em> reduces with increment in thickness to width (<em>B/W</em>) proportions and found to stay consistent for <em>B/W</em>≥0.3. This consistent estimation of <em>K<sub>q</sub> </em>for <em>B/W</em>≥0.3 prevail the plane strain fracture toughness (<em>K<sub>Ic</sub></em>) of the composite.http://jsm.iau-arak.ac.ir/article_666695_15d0dcfd256aa761cfd1c82625f76ef5.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Buckling Analysis of Functionally Graded Shallow Spherical Shells Under External Hydrostatic Pressure64465666669210.22034/jsm.2019.666692ENMHosseiniMechanical Engineering Department, Faculty of Engineering, Malayer University, Malayer, IranFKaramiMechanical Engineering Department, Faculty of Engineering, Malayer University, Malayer, IranJournal Article20190623The aim of this paper is to determine the critical buckling load for simply supported thin shallow spherical shells made of functionally graded material (FGM) subjected to uniform external pressure. A metal-ceramic functionally graded (FG) shell with a power law distribution for volume fraction is considered, where its properties vary gradually through the shell thickness direction from pure metal on the inner surface to pure ceramic on the outer surface. First, the total potential energy functional is obtained using the first-order shell theory of Love and Kirchhoff, Donnell-Mushtari-Vlasov kinematic equations and Hooke''''''''''''''''s Law. Then, equilibrium equations are derived through the minimization of the total potential energy functional by employing the Euler equations. The stability equations are derived by application of the adjacent - equilibrium criterion. As the nonlinear strain-displacement relations are employed, so the presented analysis is nonlinear with high accuracy. The Galerkin method is used to determine the critical buckling load. The present problem is also analyzed numerically by simulating it in Abaqus software. For validation, the present analytical results are compared with the present numerical results and with the known data in the literature. Also, the effects of some important geometrical and mechanical parameters on the hydrostatic buckling pressure are investigated. http://jsm.iau-arak.ac.ir/article_666692_b4486c4885b42ae6c436343379bd8d65.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Effect of Temperature Dependency on Thermoelastic Behavior of Rotating Variable Thickness FGM Cantilever Beam65766966676810.22034/jsm.2019.666768ENM.M.HMirzaeiDepartment of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, IranALoghmanDepartment of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran0000-0002-8292-8958MArefiDepartment of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, IranJournal Article20190625Thermoelastic behavior of temperature-dependent (TD) and independent (TID) functionally graded variable thickness cantilever beam subjected to mechanical and thermal loadings is studied based on shear deformation theory using a semi-analytical method. Loading is composed of a transverse distributed force, a longitudinal distributed temperature field due to steady-state heat conduction from root to the tip surface of the beam and an inertia body force due to rotation. A successive relaxation (SR) method for solving temperature-dependent steady-state heat conduction equation is employed to obtain the accurate temperature field. The beam is made of functionally graded material (FGM) in which the mechanical and thermal properties are variable in longitudinal direction based on the volume fraction of constituent. Using first-order shear deformation theory, linear strain–displacement relations and Generalized Hooke’s law, a system of second order differential equation is obtained. Using division method, differential equations are solved for every division. As a result, longitudinal displacement, transverse displacement, and consequently longitudinal stress, shear stress and effective stress are investigated. The results are presented for temperature dependent and independent properties. It has been found that the temperature dependency of the material has a significant effect on temperature distribution, displacements and stresses. This model can be used for thermoelastic analysis of simple turbine blades. http://jsm.iau-arak.ac.ir/article_666768_5e5e14b79d5847b05eafbd2443c1b864.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Stress Concentration Factor of Single-Layered Graphene Sheets Containing Elliptical Vacancies67067766725010.22034/jsm.2019.667250ENS.KJalaliDepartment of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, IranM.JBeigrezaeeDepartment of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, IranJournal Article20190626In the present study, potential of finite element based molecular structural mechanics (MSM) for evaluating stress concentration factor of single-layered graphene sheets (SLGSs) with elliptical vacancies is successfully addressed. The MSM approach mimics the interatomic forces of the nanostructure by defining an equivalent frame structure containing beam elements. To obtain the mechanical and cross sectional properties of the equivalent beam, the potential energies of chemical bonds between carbon atoms in the hexagonal lattice of SLGSs are equaled to the strain energies of the beams. This novel proposed approach accurately predicts the stress concentration in graphene sheets with significantly less computational effort in comparison to computational physics methods. Both armchair and zigzag configurations are considered. Furthermore, a comparison between the results obtained by presented MSM approach and theory of elasticity for thin infinite panels having elliptical holes is presented. Influence of chirality, and geometry of elliptical vacancies are investigated in details. Results reveal that MSM approach can successfully predicts stress concentration factor phenomena in nano structures, especially SLGSs. It is seen that chirality has a significant effect on the stress concentration factor so that armchair SLGSs show a larger value of stress concentration.http://jsm.iau-arak.ac.ir/article_667250_14c275d79d1ca8d89766c093f02f4d12.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350511320190930Noise Effects on Modal Parameters Extraction of Horizontal Tailplane by Singular Value Decomposition Method Based on Output Only Modal Analysis67868966680910.22034/jsm.2019.666809ENPJalaliVibration and Modal Analysis Research Lab, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, IranSVarahramVibration and Modal Analysis Research Lab, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, IranRHassannejadVibration and Modal Analysis Research Lab, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, IranM.HSadeghiVibration and Modal Analysis Research Lab, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, IranJournal Article20190629According to the great importance of safety in aerospace industries, identification of dynamic parameters of related equipment by experimental tests in operating conditions has been in focus. Due to the existence of noise sources in these conditions the probability of fault occurrence may increases. This study investigates the effects of noise in the process of modal parameters identification by Output only Modal Analysis (OMA) method using Singular Value Decomposition (SVD) algorithm. The study case is the horizontal tailplane of the aircraft; therefore, at first, the modal parameters of the tailplane are obtained numerically. Then a cantilever beam is used to perform experimental tests with regard to the high aspect ratio of the modeled tailplane. The modal parameters of the beam are obtained nonparametrically by Experimental Modal Analysis (EMA) and OMA. In order to investigate the effects of noise in a controlled manner, the artificial excitation namely the shaker with the random force is used. Then, the effects of noisy measurements on the specifications of the system in EMA and OMA methods are investigated. The results indicate that: 1. The OMA method has more resistance against the noise for extracting natural frequencies. 2. The results of the Modal Assurance Criterion (MAC) values by EMA method, in the condition of noise existence in output data, are worse than the noise existence in input data. 3. The average of MAC values in general condition of EMA method by noisy input & output data is worse than the OMA method.http://jsm.iau-arak.ac.ir/article_666809_4adcc86f3e3af5b1628d1e5d87a815c8.pdf