Islamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Vibration Analysis of Magneto-Electro-Elastic Timoshenko Micro Beam Using Surface Stress Effect and Modified Strain Gradient Theory under Moving Nano-Particle122539690ENM MohammadimehrDepartment of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, IranH Mohammadi HooyehDepartment of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, IranJournal Article20170901In this article, the free vibration analysis of magneto-electro-elastic (MEE) Timoshenko micro beam model based on surface stress effect and modified strain gradient theory (MSGT) under moving nano-particle is presented. The governing equations of motion using Hamilton’s principle are derived and these equations are solved using differential quadrature method (DQM). The effects of dimensionless electric potential, dimensionless magnetic parameter, material length scale parameter, external electric voltage, external magnetic parameter, slenderness ratio, temperature change, surface stress effect, two parameters of elastic foundation on the dimensionless natural frequency are investigated. It is shown that the effect of electric potential and magnetic parameter simultaneously increases the dimensionless natural frequency. On the other hands, with considering two parameters, the stiffness of MEE Timoshenko micro beam model increases. It can be seen that the dimensionless natural frequency of micro structure increases by MSGT more than modified couple stress theory (MCST) and classical theory (CT). It is found that by increasing the mass of nano-particle, the dimensionless natural frequency of system decreases. The results of this study can be employed to design and manufacture micro-devices to prevent resonance phenomenon or as a sensor to control the dynamic stability of micro structures.http://jsm.iau-arak.ac.ir/article_539690_d2d55706e7c6eb2c9b05057419af21b5.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301A Nonlocal First Order Shear Deformation Theory for Vibration Analysis of Size Dependent Functionally Graded Nano beam with Attached Tip Mass: an Exact Solution2337539691ENM GhadiriFaculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, IranA JafariFaculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, IranJournal Article20170902In this article, transverse vibration of a cantilever nano- beam with functionally graded materials and carrying a concentrated mass at the free end is studied. Material properties of FG beam are supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM). The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory in order to consider the effect of shear deformation and rotary inertia. Hamilton’s principle is applied to obtain the governing differential equation of motion and boundary conditions and they are solved applying analytical solution. The purpose is to study the effects of parameters such as tip mass, small scale, beam thickness, power-law exponent and slenderness on the natural frequencies of FG cantilever nano beam with a point mass at the free end. It is explicitly shown that the vibration behavior of a FG Nano beam is significantly influenced by these effects. The response of Timoshenko Nano beams obtained using an exact solution in a special case is compared with those obtained in the literature and is found to be in good agreement. Numerical results are presented to serve as benchmarks for future analyses of FGM cantilever Nano beams with tip mass.http://jsm.iau-arak.ac.ir/article_539691_977b620996b5f81f455edb5c3f0c474b.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations3856539692ENR RanjanSchool of Aerospace and Mechanical Engineering, 865 Asp Avenue, Norman, OK, 73019, USAJ.N ReddyDepartment of Mechanical Engineering, 3123 TAMU, College Station, TX, USAJournal Article20170903Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation , and/or shear strain , as well as the variational method used (e.g., collocation, weak form Galerkin, or least-squares). When nonlinear shear deformation theories are used, the displacement finite element models experience membrane and shear locking. The present study is concerned with development of alternative beam finite elements using both uniform and non-uniform rational b-splines (NURBS) to eliminate shear and membrane locking in an hpk finite element setting for both the Euler-Bernoulli beam and Timoshenko beam theories. Both linear and non-linear analysis are performed using mixed finite element models of the beam theories studied. Results obtained are compared with analytical (series) solutions and non-linear finite element and spectral/hp solutions available in the literature, and excellent agreement is found for all cases.http://jsm.iau-arak.ac.ir/article_539692_7de7e45c949e258c87bffbd8a599183e.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Reflection From Free Surface of a Rotating Generalized Thermo-Piezoelectric Solid Half Space5766539693ENBaljeet SinghDepartment of Mathematics, Post Graduate Government College, Sector-11, Chandigarh, 160011,IndiaB SinghDepartment of Applied Sciences, Rayat Bahra Institute of Engineering and Nano Technology, Hoshiarpur, 146001, Punjab, IndiaJournal Article20170906The analysis of rotational effect on the characteristics of plane waves propagating in a half space of generalized thermo-piezoelectric medium is presented in context of linear theory of thermo-piezoelectricity including Coriolis and centrifugal forces. The governing equations for a rotating generalized thermo-piezoelectric medium are formulated and solved for plane wave solutions to show the propagation of three quasi plane waves in the medium. A problem on the reflection of these plane waves is considered from a thermally insulated/isothermal boundary of a rotating generalized thermo-piezoelectric solid half space. The expressions for reflection coefficients of three reflected waves are obtained in explicit from. For experimental data of LiNbO<sub>3 </sub>and BaTiO<sub>3</sub>, the speeds of various plane waves are computed. The reflection coefficients of various reflected waves are also obtained numerically by using the data of BaTiO<sub>3</sub>. The dependence of speeds of plane waves and reflection coefficients of various reflected waves is shown graphically on the rotation parameter at each angle of incidence. http://jsm.iau-arak.ac.ir/article_539693_1d90610775405560eac8b64d31e01f9d.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Two New Non-AFR Criteria for Depicting Strength Differential Effect (SDE) in Anisotropic Sheet Metals6785539694ENF MoayyedianDepartment of Mechanical Engineering, Eqbal Lahoori Institute of Higher Education, Mashhad, IranM KadkhodayanDepartment of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20170911The issue of pressure sensitivity of anisotropic sheet metals is investigated with introducing two new non-AFR criteria which are called here linear and non-Linear pressure sensitive criteria. The yield and plastic potential functions of these criteria are calibrated with directional tensile/compressive yield stresses and directional tensile Lankford coefficients, respectively. To determine unknown coefficients of yield and plastic potential functions of these criteria two error functions are presented which are minimized by Downhill Simplex Method. Three anisotropic materials are considered as case studies such as Al 2008-T4 (BCC), Al 2090-T3 (FCC) and AZ31 (HCP). It is shown that the non-Linear pressure sensitive criterion is more accurate than the linear one and other existed criteria compared to experimental results in calculating the directional mechanical properties of anisotropic sheet metals.http://jsm.iau-arak.ac.ir/article_539694_542f46d7fb2f38092ec7f84eb015acb6.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Influence of Notch Depth-to-Width Ratios on J-Integral and Critical Failure Load of Single-Edge Notched Tensile Aluminium 8011 Alloy Specimens8697539695ENC.S SumeshDepartment of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, India0000-0002-5270-0696P.J Arun NarayananDepartment of Mechanical Engineering, Amrita School of Engineering, Coimbatore Amrita Vishwa Vidyapeetham, IndiaJournal Article20170919In this paper, the influence of notch depth-to-width ratios on <em>J</em>-integral and critical load of Aluminium 8011 alloy specimens with <em>U</em>-notch under Mode I loading are studied. Using experiments, for a set of specimens having different notch depth–to–width ratios, <em>J</em>-integral was found and the same was verified using analytical methods. Further, using the results obtained from the experiments, failure assessment diagrams (FAD) were plotted for the same ratios, to determine the safe or critical load and the type of failure mechanism was also studied. The results show that, for both shallow and deep notch depths, the <em>J</em>-integral values obtained from the experimental method, are in very close agreement with the analytical values. <em>J</em>-integral values decrease with increase in notch depth and increase with increase in applied load. Furthermore, from FAD, the safe load decreases when the notch depth-to-width ratio increases and it was found that, all the tested specimens failed due to elastic plastic deformation mechanism.http://jsm.iau-arak.ac.ir/article_539695_2b358a90e04e0a68c39aca4cb501763f.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Improving Power Density of Piezoelectric Vibration-Based Energy Scavengers98109539696ENR HosseiniYoung Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, IranO ZargarSchool of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, IranM HamediDepartment of Mechanical Engineering, Faculty of Engineering, University of Tehran, IranJournal Article20170927Vibration energy harvesting with piezoelectric materials currently generate up to 300 microwatts per <em>cm<sup>2</sup></em>, using it to be mooted as an appropriate method of energy harvesting for powering low-power electronics. One of the important problems in bimorph piezoelectric energy harvesting is the generation of the highest power with the lowest weight. In this paper the effect of the shape and geometry of a bimorph piezoelectric cantilever beam harvester on the electromechanical efficiency of the system is studied. An analytic model has been presented using Rayleigh cantilever beam approximations for piezoelectric harvesters with tapered bimorph piezoelectric cantilever beam. In order to study the effect of a cantilever beam length and geometry on the generated voltage, finite element simulation has been performed using ABAQUS. Design optimization has been used to obtain the maximum output power and tapered beams are observed to lead to more uniform distribution of strain in the piezoelectric layer, thus increasing efficiency.http://jsm.iau-arak.ac.ir/article_539696_79670b78c8fb31c02ab4753916b77fc4.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Nonlinear Dynamic Analysis of Cracked Micro-Beams Below and at the Onset of Dynamic Pull-In Instability110123539697ENR HassannejadDepartment of Mechanical Engineering, University of Tabriz, Tabriz, IranSh Amiri JahedDepartment of Mechanical Engineering, University of Tabriz, Tabriz, IranJournal Article20171102In this paper, the effect of the crack on dynamic behavior of cracked micro-beam in the presence of DC and AC loads are investigated. By applying the residual axial stress and fringing field stress, a nonlinear analytical model of cracked micro-beam is presented and crack is modeled by a massless rotational spring. The governing equation of the system is solved using Galerkin procedure and shooting method. The equilibria curve and dynamic response of cracked cantilever and clamped-clamped micro-beam are extracted below and at the onset of the dynamic pull-in instability. The results show that the behavior of cracked micro-beam is different from ordinary cracked beam due to nonlinear effects. For a fixed relative crack location, increasing the crack depth causes increasing in the resonance amplitude and reduction in the resonance frequency below dynamic pull-in instability. Also, in cracked cantilever micro-beams, by approaching the crack to fixed end, the resonance frequency reduces and the resonance amplitude increases. In cracked clamped-clamped micro-beam, trend of variations of resonance frequency and resonance amplitude against the crack location is not regular. At the onset pull-in instability, the presence of the crack causes cyclic-fold bifurcation points to appear at the lower frequency. Therefore, it causes early pull-in phenomenon or unwanted abrupt change at the micro-beam behavior. The achievement of this study is simulation of the response of the faulty low-voltage switch and MEMS resonators for different severity of crack at the onset of dynamic pull-in phenomenon. http://jsm.iau-arak.ac.ir/article_539697_20af6913b602e12a32ca272bc4531793.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Preparation and Mechanical Properties of Compositionally Graded Polyethylene/Clay Nanocomposites124129539699ENM.H YasDepartment of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, IranM Karami KhorramabadiDepartment of Mechanical Engineering, Engineering Faculty, Razi University, Kermanshah, IranJournal Article20171104This paper presents the preparation and mechanical properties of compatibilized compositionally graded Polyethylene/ low density polyethylene (LDPE)/ modified montmorillonite (MMT) nanocomposites prepared by solution and melt mixing techniques. Use of polyethylene glycol as compatibilizer improves compatibility of modified montmorillonite and low density polyethylene. Comparisons between two techniques show that the melt mixing technique is the preferred method for preparation the Polyethylene/Clay nanocomposites for uniform and compositionally graded distributions. It is observed, the addition of Nano clay improves the mechanical properties like tensile strength. Also, it is noticed the mechanical properties of compositionally graded Polyethylene/Clay nanocomposites are improved rather than the uniform distribution of Polyethylene/Clay nanocomposites. The morphology of nanocomposites cross section samples is studied by Scanning Electron Microscopy (SEM) and finally the comparison are made between two techniques and then between compositionally graded polyethylene/clay nanocomposites with uniform ones. Its show that when the compatibilizer was added for melt mixing technique, the density and the size of the aggregates decreased, which indicates that the dispersion of nano clays within the polymer matrix is much better. http://jsm.iau-arak.ac.ir/article_539699_013e2a350ca5083367892447f830bbc0.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Magneto-Electro-Thermo-Mechanical Response of a Multiferroic Doubly-Curved Nano-Shell130141539700ENS RazaviYoung Researchers and Elite Club, Tabriz Branch, Islamic Azad University, Tabriz, Iran0000-0002-0281-9373Journal Article20171109Free vibration of a simply-supported magneto-electro-elastic doubly-curved nano-shell is studied based on the first-order shear deformation theory in the presence of the rotary inertia effect. To model the electric and magnetic behaviors of the nano-shell, Gauss’s laws for electrostatics and magneto statics are used. By using Navier’s method, the partial differential equations of motion are reduced to a single ordinary differential equation. Then, an analytical relation is obtained for the natural frequency of magneto-electro-elastic doubly-curved nano-shell. Some examples are presented to validate the proposed model. Moreover, the effects of the electric and magnetic potentials, temperature rise, nonlocal parameter, parameters of Pasternak foundation, and the geometry of the nano-shell on the natural frequencies of magneto-electro-elastic doubly-curved nano-shells are investigated. It is found that natural frequency of magneto-electro-elastic doubly-curved nano-shell decreases with increasing the temperature, increasing the electric potential, or decreasing the magnetic potential. http://jsm.iau-arak.ac.ir/article_539700_0d46779d43e8a55531d9f90425aaf696.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Mathematical Modeling of Thermoelastic State of a Thick Hollow Cylinder with Nonhomogeneous Material Properties142156539715ENV. R ManthenaDepartment of Mathematics, RTM Nagpur University, Nagpur, IndiaN.K LambaDepartment of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, IndiaG.D KedarDepartment of Mathematics, RTM Nagpur University, Nagpur, IndiaJournal Article20171112The object of the present paper is to study heat conduction and thermal stresses in a hollow cylinder with nonhomogeneous material properties. The cylinder is subjected to sectional heating at the curved surface. All the material properties except for Poisson’s ratio and density are assumed to be given by a simple power law in the axial direction. A solution of the two-dimensional heat conduction equation is obtained in the transient state. The solutions are obtained in the form of Bessel’s and trigonometric functions. For theoretical treatment, all the physical and mechanical quantities are taken as dimensional, whereas we have considered non-dimensional parameters, for numerical analysis. The influence of inhomogeneity on the thermal and mechanical behaviour is examined. The transient state temperature field and its associated thermal stresses are discussed for a mixture of copper and tin metals in the ratio 70:30 respectively. Numerical calculations are carried out for both homogeneous and nonhomogeneous cylinders and are represented graphically.http://jsm.iau-arak.ac.ir/article_539715_76a9f43b0cd1d8e44502c55f211a3057.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Global Optimization of Stacking Sequence in a Laminated Cylindrical Shell Using Differential Quadrature Method157174539716ENM.R SavizMechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, IranA Ziaei AslMechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, IranJournal Article20171203Based on 3-D elasticity approach, differential quadrature method (DQM) in axial direction is adopted along with Globalized Nelder–Mead (GNM) algorithm to optimize the stacking sequence of a laminated cylindrical shell. The anisotropic cylindrical shell has finite length with simply supported boundary conditions. The elasticity approach, combining the state space method and DQM is used to obtain a relatively accurate objective function. Shell thickness is fixed and orientations of layers change in a set of angles. The partial differential equations are reduced to ordinary differential equations with variable coefficients by applying DQM to the equations, then, the equations with variables at discrete points are obtained. Natural frequencies are attained by solving the Eigen-frequency equation, which appears by incorporating boundary conditions into the state equation. A GNM algorithm is devised for optimizing composite lamination. This algorithm is implemented for maximizing the lowest natural frequency of cylindrical shell. The results are presented for stacking sequence optimization of two to five-layered cylindrical shells. Accuracy and convergence of developed formulation is verified by comparing the natural frequencies with the results obtained in the literature. Finally, the effects of mid-radius to thickness ratio, length to mid-radius ratio and number of layers on vibration behavior of optimized shell are investigated. Results are compared with those of Genetic Algorithm (GA) method, showing faster and more accurate convergence.http://jsm.iau-arak.ac.ir/article_539716_2f43cf8cbcc601fb10152cb6c9498487.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Rayleigh Surface Wave Propagation in Transversely Isotropic Medium with Three-Phase-Lag Model175185539717ENS BiswasDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, IndiaB MukhopadhyayDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, IndiaJournal Article20171208The present paper is dealing with the propagation of Rayleigh surface waves in a homogeneous transversely isotropic medium .This thermo-dynamical analysis is carried out in the context of three-phase-lags thermoelasticity model. Three phase lag model is very much useful in the problems of nuclear boiling, exothermic catalytic reactions, phonon-electron interactions, phonon scattering etc. The normal mode analysis is employed to obtain the exact expressions of the considered variables. The frequency equations for thermally insulated and isothermal surface in the closed form are derived. Some special cases of frequency equation are also discussed. In order to illustrate the analytical developments, the numerical solution is carried out and the computer simulated results in respect of phase velocity and attenuation coefficient are presented graphically. It is found that the results obtained in the present problem agree with that of the existing results obtained by various researchers. This study may find its applications in the design of surface acoustic waves (SAW) devices, structural health monitoring and damage characterization of materials.http://jsm.iau-arak.ac.ir/article_539717_522d0bce3f86e1528332d3ec9fe9f092.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301A New Eight Nodes Brick Finite Element Based on the Strain Approach186199539718ENKh GuerraicheDepartment of Mechanical Engineering, Djelfa University, Batna, AlgeriaL BelounarNMISSI Laboratory, Biskra University, Biskra, AlgeriaL BouzidiNMISSI Laboratory, Biskra University, Biskra, AlgeriaJournal Article20171209In this paper, a new three dimensional brick finite element based on the strain approach is presented with the purpose of identifying the most effective to analyze linear thick and thin plate bending problems. The developed element which has the three essential external degrees of freedom (<em>U, V</em> and <em>W</em>) at each of the eight corner nodes, is used with a modified elasticity matrix in order to satisfy the basic hypotheses of the theory of plates. The displacements field of the developed element is based on assumed functions for the various strains satisfying the compatibility and the equilibrium equations. New and efficient formulations of this element is discussed in detail, and the results of several examples related to thick and thin plate bending in linear analysis are used to demonstrate the effectiveness of the proposed element. The linear analyses using this developed element exhibit an excellent performance over a set of problems.http://jsm.iau-arak.ac.ir/article_539718_981b69b160e797c70051b2a471b55881.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Thermoelastic Analysis of a Rectangular Plate with Nonhomogeneous Material Properties and Internal Heat Source200215539719ENV. R ManthenaDepartment of Mathematics, RTM Nagpur University, Nagpur, IndiaN.K LambaDepartment of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, IndiaG.D KedarDepartment of Mathematics, RTM Nagpur University, Nagpur, IndiaJournal Article20180109This article deals with the determination of temperature distribution, displacement and thermal stresses of a rectangular plate having nonhomogeneous material properties with internal heat generation. The plate is subjected to sectional heating. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law along <em>x</em> direction. Solution of the two-dimensional heat conduction equation is obtained in the transient state. Integral transform method is used to solve the system of fundamental equation of heat conduction. The effects of inhomogeneity on temperature and thermal stress distributions are examined. For theoretical treatment, all the physical and mechanical quantities are taken as dimensional, whereas for numerical computations we have considered non-dimensional parameters. The transient state temperature field and its associated thermal stresses are discussed for a mixture of copper and zinc metals in the ratio 70:30 respectively. Numerical calculations are carried out for both homogeneous and nonhomogeneous cases and are represented graphically.http://jsm.iau-arak.ac.ir/article_539719_89990b6ee5e44f20691aec7be32a4c22.pdfIslamic Azad University Arak BranchJournal of Solid Mechanics2008-350510120180301Calculation of Natural Frequencies of Bi-Layered Rotating Functionally Graded Cylindrical Shells216231539720ENI Fakhari GolpayeganiDepartment of Mechanical Engineering, Golpayegan University of Technology, Golpayegan, IranJournal Article20180114In this paper, an exact analytical solution for free vibration of rotating bi-layered cylindrical shell composed of two independent functionally graded layers was presented. The thicknesses of the shell layers were assumed to be equal and constant. The material properties of the constituents of bi-layered FGM cylindrical shell were graded in the thickness direction of the layers of the shell according to a volume fraction power-law distribution. In order to derive the equations of motion, the Sanders’ thin shell theory and Rayleigh-Ritz method were used. Also the results were extracted by considering Coriolis, centrifugal and initial hoop tension effects. Effects of rotating speed, geometrical parameters, and material distribution in the two functionally graded layers of the shell, circumferential and longitudinal wave number on the forward and backward natural frequencies were investigated. A comparison of the results was made with those available in the literature for the validity and accuracy of the present methodology.http://jsm.iau-arak.ac.ir/article_539720_1840b8742de2a284ee65d63068456218.pdf