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An Analytical Solution for Inverse Determination of Residual Stress Field
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2
An analytical solution is presented that reconstructs residual stress field from limited and incomplete data. The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function. This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon. The analytical solution is demonstrated by developing a reference solution from which selected “measurement” points are used. An artificial error is then randomly added to “measurement” points for studying the stability of the reconstruction method utilizing TikhonovMorozov regularization technique. It is found that there is an excellent agreement between the model prediction and limited set of residual stress data in the sense of leastsquare approximation.
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114
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S.A
Faghidian
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University
Department of Mechanical and Aerospace Engineering
Iran
faghidian@gmail.com


G.H
Farrahi
School of Mechanical Engineering, Sharif University of Technology
School of Mechanical Engineering, Sharif
Iran


D.J
Smith
Department of Mechanical Engineering, University of Bristol
Department of Mechanical Engineering, University
Iran
Residual Stress
Incomplete discrete data
Inverse problems
Approximation theory
Convex polygon domain
[[1] Smith D.J., Farrahi G.H., Zhu W X., McMahon C.A., 2001, Obtaining multiaxial residual stress distributions from limited measurements, Materials Science and Engineering A 303: 281–291. ##[2] Hill M.R., 1996, Determination of residual stress based on the estimation of eigenstrain, Ph.D. Thesis. Stanford University. ##[3] Cao Y.P., Hu N., Lu J., Yao Z.H., 2002, An inverse approach for constructing residual stress field induced by welding, Journal of Strain Analysis for Engineering Design 37: 345–359. ##[4] Qian X., Yao Z., Cao Y., Lu J., 2005, An inverse approach to construct residual stresses existing in axisymmetric structures using BEM, Journal of Engineering Analysis with Boundary Elements 29: 986–99. ##[5] Korsunsky A.M., Regino G.M., Nowell D., 2007, Variational eigenstrain analysis of residual stresses in a welded plate, International Journal of Solids and Structures 44(13): 4574–4591. ##[6] Jun T.S., Korsunsky A.M., 2010, Evaluation of residual stresses and strains using the eigenstrain reconstruction method, International Journal of Solids and Structures 47:1678–1686. ##[7] Ballard P., Constantinescu A., 1994, On the inversion of subsurface residual stresses from surface stress measurements, Journal of the Mechanics and Physics of Solids 42(11): 17671787. ##[8] Schajer G.S., Prime M.B., 2006, Use of inverse solutions for residual stress measurements, Journal of Engineering Materials and Technology 128: 375382. ##[9] Hoger A., 1986, On the determination of residual stress in an elastic body, Journal of Elasticity 16: 303324. ##[10] Mura T., Gao Z., 1991, Inverse method in micromechanics of defects in solids, Proceedings of the 3rd International Conference on Residual Stress 11571167. ##[11] Robertson R.L., 1998, Determining residual stress from boundary measurements: a linearized approach, Journal of Elasticity 52: 63–73. ##[12] Moore M.G., Evans W.P., 1958, Mathematical correction for stress in removed layers in Xray diffraction residual stress analysis, S A E Transactions 66: 340345. ##[13] Faghidian S.A., 2010, Estimation of Residual Stress Field Using Limited Measurements, Ph.D. Thesis. Sharif University of Technology, Tehran, Iran. ##[14] Farrahi G.H., Faghidian S.A., Smith D.J., 2009, An inverse approach to determination of residual stresses induced by shot peening, International Journal of Mechanical Science 51: 726–731. ##[15] Farrahi G.H., Faghidian S.A., Smith D.J., 2009, Reconstruction of residual stresses in autofrettaged thickwalled tubes from limited measurements, International Journal of Pressure Vessel and Piping 86: 777784. ##[16] Farrahi G.H., Faghidian S.A., Smith D.J., 2009, A new analytical approach to reconstruct residual atresses due to turning Process, Proceeding of World Academy of Science Engineering and Technology 55: 453457. ##[17] Farrahi G.H., Faghidian S.A., Smith D.J., 2010, An inverse method for reconstruction of the residual stress field in welded plates, Journal of Pressure Vessel Technology  Transactions of the ASME 132: 0612051:9. ##[18] Faghidian S.A., Goudar D., Farrahi G.H., Smith D.J., 2011, Measurement analysis and reconstruction of residual stresses, Journal of Strain Analysis for Engineering Design 47(4): 254264. ##[19] Gurtin M.E., 1972, The Linear Theory of Elasticity, Handbuch der Physik, Vol. VIa/2. SpringerVerlag, Berlin. ##[20] Cheney E.W., 1982, Introduction to Approximation Theory,American Mathematical Society, Chelsea Publishing, New York. ##[21] Groetsch C.W., 2007, Stable Approximate Evaluation of Unbounded Operators, Springer, Berlin. ##[22] Kandil F.A., Lord J.D., Fry A.T., Grant P.V., 2001, A Review of Residual Stress Measurement Methods a Guide to Technique Selection, MATC (A) 04, UK National Physical Laboratory (NPL) Materials Centre report . ##[23] King A.C., Billingham J., Otto S.R., 2003, Differential Equations: Linear, Nonlinear, Ordinary, Partial. Cambridge University Press, Cambridge. ##[24] Hirota R.Y., 2004,The Direct Method in Soliton Theory, Cambridge University Press, Cambridge. ##[25] Demmel J.W., 1997, Applied Numerical Linear Algebra, SIAM (Society for Industrial and Applied Mathematics), Philadelphia. ## ##]
Small Scale Effect on the Vibration of Orthotropic Plates Embedded in an Elastic Medium and Under Biaxial Inplane Preload Via Nonlocal Elasticity Theory
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2
In this study, the free vibration behavior of orthotropic rectangular graphene sheet embedded in an elastic medium under biaxial preload is studied. Using the nonlocal elasticity theory, the governing equation is derived for singlelayered graphene sheets (SLGS). Differential quadrature method (DQM) has been used to solve the governing equations for various boundary conditions. To verify the accuracy of the present results, a Navier’s approach is also developed. DQM results are successfully verified with those of the Navier’s approach. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, preload, Winkler and Pasternak foundations and material properties on natural frequencies are investigated. The results are shown that with the decrease of inplane preloads the curves isotropic and orthotropic nondimensional frequency in approaches close to each other.
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128
143


M
Mohammadi
Department of Engineering, Ahvaz branch, Islamic Azad university
Department of Engineering, Ahvaz branch,
Iran


M
Goodarzi
Department of Engineering, Ahvaz branch, Islamic Azad university
Department of Engineering, Ahvaz branch,
Iran


M
Ghayour
Department of Mechanical Engineering, Isfahan University of Technology
Department of Mechanical Engineering, Isfahan
Iran
m.ghayour.iut@gmail.com


S
Alivand
Department of Engineering, Ahvaz branch, Islamic Azad university
Department of Engineering, Ahvaz branch,
Iran
Nonlocal elasticity theory
Vibration
Biaxial inplane preload
Orthotropic Nanoplates
Pasternak foundation
[[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 56–58. ##[2] Wang J., 2005, CarbonNanotube based electrochemical biosensors: A Review, Electro Analysis 17: 7–14. ##[3] Kinaret J.M., Nord T., Viefers S., 2003, A carbonnanotubebased nanorelay, Physics Letters A 82: 1287–1289. ##[4] Reddy C.D., Rajendran S., Liew K.M., 2006, Equilibrium configuration and continuum elastic properties of finite sized grapheme, Nanotechnology 17: 864–870. ##[5] Sakhaeepour A., Ahmadian M., Vafai A., 2007, Applications of singlelayered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications 145: 168172. ##[6] Zhang Y.Q., Liu G.R., Han X., 2006, Effect of small length scale on elastic buckling of multiwalled carbon nanotubes under radial pressure, Physics Letters A 349: 370–376. ##[7] Aydogdu M., 2009, Axial vibration of the nanorods with the nonlocal continuum rod model, Physica E 41: 861–864. ##[8] Filiz S., Aydogdu M., 2010, Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity, Computational Materials Science 49: 619627. ##[9] Murmu T., Adhikari S., 2011, Nonlocal vibration of carbon nanotubes with attached buckyballs at tip, Mechanics Research Communications 38: 62–67. ##[10] Malekzadeh P., Setoodeh A.R, Alibeygibeni A., 2011,Small scale effect on the thermal buckling of orthotropic arbitrary straightsided quadrilateral nanoplates embedded in an elastic medium, Composite Structures 93: 20832089. ##[11] Khademolhosseini F., Rajapakse R.K.N.D., Nojeh A., 2010, Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models, Computational Materials Science 48: 736–742. ##[12] Eringen A.C., 1983, On differential of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal Applied Physic 54: 4703–4710. ##[13] Pradhan S.C., Murmu T., 2009, Small scale effect on the buckling of singlelayered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Materials Science 47: 268–274. ##[14] Pradhan S.C., 2009, Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory, Physics Letters A 373: 4182–4188. ##[15] Murmu, T. Pradhan, S.C., 2009, Vibration analysis of nanosinglelayered graphene sheets embedded in elastic medium based on nonlocal elasticity theory, Journal Applied Physic 105: 064319. ##[16] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multi layered graphene sheets based on nonlocal continuum models, Physics Letters A 373: 1062–1069. ##[17] Aghababaei R., Reddy J.N., 2009, Nonlocal thirdorder shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration 326: 277289. ##[18] Pradhan S.C., Murmu T., 2009, Small scale effect on the buckling of singlelayered graphene sheets under biaxial compression via nonlocal continuum mechanics, Computational Materials Science 47: 268–274. ##[19] Murmu T., Pradhan S.C., 2009, Buckling of biaxially compressed orthotropic plates at small scales, Mechanics Research Communications 36: 933–938. ##[20] Murmu T., Pradhan S.C., 2009, Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity, Journal Applied Physic 106: 104301. ##[21] Chen Y., Lee J.D., Eskandarian A., 2004, Atomistic viewpoint of the applicability of microcontinuum theories, International Journal Solids Structure 41: 20852097. ##[22] Bert CW., Malik M., 1996, Differential quadrature method in computational mechanics: a review, Applied Mechanic Review 49: 1–27. ##[23] Farajpour A., Shahidi A.R., Mohammadi M., Mahzoon M., 2012, Buckling of orthotropic micro/nanoscale plates under linearly varying inplane load via nonlocal continuum mechanics, Composite Structures 94: 1605–1615. ##[24] Danesh M., Farajpour A., Mohammadi M., 2012, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications 39: 23– 27. ##[25] Shu C, Richards Be.,1992, Application of generalized differential quadrature to solve twodimensional incompressible Navier Stokes equations, International Journal for Numerical Methods in Fluids 15: 791–798. ##[26] Shu C., 2000, Differential Quadrature and its Application in Engineering, Springer, Great Britain. ##[27] Wang Q., Wang C.M., 2007, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology 18: 075702. ##[28] Duan W.H., Wang C.M., 2007, Exact solutions for axisymmetric bending of micro/ nanoscale circular plates based on nonlocal plate theory, Nanotechnology 18: 385704. ##[29] Liew K., He M., X Q., Kitipornchai S., 2006, Predicting nanovibration of multilayered graphene sheets embedded in an elastic matrix, Acta Material 54: 42294236. ## ##]
ElectroThermoMechanical Vibration Analysis of a FoamCore Smart Composite Cylindrical Shell Containing Fluid
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2
In this study, free vibration of a foamcore orthotropic smart composite cylindrical shell (SCCS) filled with a nonviscous compressible fluid, subjected to combined electrothermomechanical loads is investigated. Piezoelectric polymeric cylindrical shell, is made from polyvinylidene fluoride (PVDF) and reinforced by armchair double walled boron nitride nanotubes (DWBNNTs). Characteristics of the equivalent composite are determined using microelectromechanical models. The poly ethylene (PE) foamcore is modeled based on Winkler and Pasternak foundations. Employing the charge equation for coupling electrical and mechanical fields, the problem is turned into an eigenvalue one, for which analytical frequency equations are derived considering free electrical and simply supported mechanical boundary conditions at circular surfaces at either ends of the cylindrical shell. The influence of electric potential generated, filledfluid, orientation angle of DWBNNTs, foamcore and a few other parameters on the resonance frequency of SCCS are investigated. Results show that SCCS and consequently the generated Φ improve sensor and actuator applications in several process industries, because it not only increases the vibration frequency, but also extends economic viability of the smart structure.
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144
158


A
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University
Iran
aghorban@kashanu.ac.ir


R
Kolahchi
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
DWBNNTs
Smart composite
Fluidfilled cylindrical shell
Foamcore
Free Vibration
[[1] Love A.E.H., 1888, On the small free vibrations and deformations of a thin elastic shell, Philosophical Transactions of the Royal Society A 179: 491–549. ##[2] Arnold R.N., Warburton G.B., 1948, Flexural vibrations of the walls of thin cylindrical shells, Philosophical Transactions of the Royal Society 197: 238256. ##[3] Bert C.W., Baker J.L., Egle B.M., 1969, Free vibration of multilayer anisotropic cylindrical shells, Journal of Composite Material 3: 480499. ##[4] Blevins R.D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold, New York. ##[5] Soedel W.A., 1980, New frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of Sound and Vibration 70: 309317. ##[6] Vanderpool M.E., Bert C.W., 1981, Vibration of materially monoclinic thickwall circular cylindrical shell, American Institute of Aeronautics and Astronautics 19: 634641 . ##[7] Ludwig A., Krieg R., 1981, An analysis quasiexact method for calculating eigen vibrations of thin circular shells, Journal of Sound and Vibration 74: 155174. ##[8] Chung H., Turul P., Mulcahy T.M., Jendrzejczyk J.A., 1981, Analysis of a cylindrical shell vibrating in a cylindrical fluid region, Nuclear Engineering Design 63: 109–120. ##[9] Markus S., 1988, The Mechanics of Vibrations of Cylindrical Shells, Elsevier, New York. ##[10] Xianga Y., Mab Y.F., Kitipornchaib S., Lim C.W., Lau C.W.H., 2002, Exact solutions for vibration of cylindrical shells with intermediate ring supports, International Journal of Mechanical Science 44: 1907–1924. ##[11] Ye L., Lun G., Ong L.S., 2011, Buckling of a thinwalled cylindrical shell with foam core under axial compression, ThinWalled Struct 49: 106–111. ##[12] Junger M.C., Mass C., 1952, Vibration of elastic shells in a fluid medium and the associated radiation of sound, Journal of Applied Mechanics 74: 439–445. ##[13] Jain R.K., 1974, Vibration of fluidfilled orthotropic cylindrical shells, Journal of Sound and Vibration 37: 379–388. ##[14] Goncalves P.B., Batista R.C., 1987, Frequency response of cylindrical shells partially submerged or filled with liquid, Journal of Sound and Vibration 113: 59–70. ##[15] Chen W.Q., Ding H.J., 1999, Natural frequencies of fluidfilled transversely isotropic cylindrical shells, International Journal of Mechanical Science 41: 677–684. ##[16] Chung H., 1981, Free vibration analysis of circular cylindrical shells, Journal of Sound and Vibration 74: 331359. ##[17] Amabili M. 1999, Vibrations of circular tubes and shells filled and partially immersed in dense fluids, Journal of Sound and Vibration 221: 567–585. ##[18] Amabili M., 1996, Free vibration of partially filled horizontal cylindrical shells, Journal of Sound and Vibration 191: 757–780. ##[19] Pellicano F., Amabili M., 2003, Stability and vibration of empty and fluidfilled circular cylindrical shells under static and periodic axial loads, International Journal of Solids and Structures 40: 3229–3251. ##[20] Chen W.Q., Bian Z.G., Ding H.J., 2004, Threedimensional vibration analysis of fluidfilled orthotropic FGM cylindrical shells, International Journal of Mechanical Science 46: 159–171. ##[21] Chen W.Q., Bian Z.G., Lv C.F., Ding H.J. 2004, 3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid International, International Journal of Solids and Structures 41: 947–964. ##[22] Tj H.G., Mikami T., Kanie S., Sato M., 2005, Free vibrations of fluidfilled cylindrical shells on elastic foundations, ThinWall Structures 43: 1746–1762. ##[23] Daneshmand F., Ghavanloo E., 2010, Coupled free vibration analysis of a fluidfilled rectangular container with a sagged bottom membrane, Journal of Fluids and Structures 26: 236–252. ##[24] Askari E., Daneshmand F., Amabili M., 2011, Coupled vibrations of a partially fluidfilled cylindrical container with an internal body including the effect of free surface waves, Journal of Fluids and Structures 27: 1049–1067. ##[25] Gibson K., Ronald F.,1994, Principles of Composite Material Mechanics, McGraw Hill, New York. ##[26] Bent A.A., Hagood N.W., Rodgers J.P., 1995, Anisotropic actuation with piezoelectric fiber composites, Journal of Material System Structures 6: 338–349. ##[27] Messina A., Soldatos K.P., 1999, Vibration of completely free composite plates and cylindrical shell panels by a higherorder theory, International Journal of Mechanical Science 41: 891918. ##[28] Tan P., Tong L., 2001, Microelectromechanics models for piezoelectricfiberreinforced composite materials, Composite Science Technology 61: 759–769. ##[29] Kadoli R., Ganesan N., 2003, Free vibration and buckling analysis of composite cylindrical shells conveying hot fluid, Composite Structures 60: 19–32. ##[30] Ray M.C., Reddy J.N., 2005, Active control of laminated cylindrical shells using piezoelectric fiber reinforced composites, Composite Science Technology 65: 1226–1236. ##[31] Matsuna H., 2007, Vibration and buckling of crossply laminated composite circular cylindrical shells according to a global higherorder theory, International Journal of Mechanical Science 49: 10601075. ##[32] Rahmani O., Khalili S.M.R., Malekzadeh K., 2010, Free vibration response of composite sandwich cylindrical shell with flexible core, Composite Structures 92: 1269–1281. ##[33] NguyenVan H., MaiDuy N., Karunasena W., TranCong T., 2011, Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with inplane rotations, Computers and Structures 89: 612–625. ##[34] Mosallaie Barzoki A.A., Ghorbanpour Arani A., Kolahchi R., Mozdianfard M.R., 2011, Electrothermomechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Applied Mathematical Modelling 27: 12781284. ##[35] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., 2011, Effect of material inhomogeneity on electrothermomechanical behaviors of functionally graded piezoelectric rotating cylinder, Applied Mathematical Modelling 35: 2771–2789. ##[36] Ghorbanpour Arani A., Kolahchi R., Mosalaei Barzoki A.A., Loghman A., 2012, Electrothermomechanical behaviors of FGPM Spheres Using Analytical Method and ANSYS Software, Applied Mathematical Modelling 36: 139–157. ##[37] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and ShellsTheory and Analysis, CRC Press, New York. ##[38] Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi R., Loghman A., 2011, Pasternak foundation effect on the axial and torsional waves propagation in embedded DWCNTs using nonlocal elasticity cylindrical shell theory, Journal of Mechanical Science and Technology 25: 18. ##[39] Timoshenko SP., 1951, Theory of Elasticity, McGrawHill, New York. ## ##]
Dynamic Analysis of a NanoPlate Carrying a Moving Nanoparticle Considering Eelectrostatic and Casimir Forces
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This paper reports an analytical method to show the effect of electrostatic and Casimir forces on the pullin instability and vibration of single nanoplate (SNP) carrying a moving nanoparticle. Governing equations for nonlocal forced vibration of the SNP under a moving nanoparticle considering electrostatic and Casimir forces are derived by using Hamilton’s principle for the case when two ends are simply supported. The problem is solved by using the analytically and the time integration methods. The detailed parametric study is considered, focusing on the remarkable effects of the nanoparticle position, nonlocal parameters, nanoplate length, mode number, electric voltage of the Casimir parameter, and dielectric spacer with an initial gap on vibration of SNP.
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159
169


A
Ghgorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University
Iran
aghorban@kashanu.ac.ir


M
Shokravi
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
Casimir force
Vibration analysis
Moving nanoparticle
Mode number
[[1] Simsek M., 2010, Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science 48: 17211732. ##[2] Chaterjee S., Pohit G., 2009, A large deflection model for the pullin analysis of electro statically actuated micro cantilever beams, Journal of Sound and Vibration 322:969986. ##[3] Batra R.C., Porfiri M., Spinello D., 2008, Vibrations and pullin instabilities of microelectromechanical von Karman elliptic plates incorporating the Casimir force, Journal of Sound and Vibration 315: 939960. ##[4] Batra R.C., Porfiri M., Spinello D., 2006, Analysis of electrostatic MEMS using meshless local Petrov–Galerkin (MLPG) method, Engineering Analysis with Boundary Elements 30: 949962. ##[5] Casimir H.B.G., 1948, On the attraction between two perfectly conducting plates, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen 51: 793795. ##[6] Da Silva J.C., Matos Neto A., Placido H.Q., Revzen M., Santana A.E., 2001, Casimir effect for conducting and permeable plates at nite temperature, Physica A 292: 411421. ##[7] Wang Y.G., Lin W.H., Li X.M., Feng Z.J., 2011, Bending and vibration of an electrostatically actuated circular microplate in presence of Casimir force, Applied Mathematical Modelling 35: 23482357. ##[8] Zand M.M., Ahmadian M.T., 2009, Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects, Communications in Nonlinear Science and Numerical Simulation 14: 16641678. ##[9] Spinello D., 2008, Vibrations of parallel arrays of electrostatically actuated microplates, Journal of Sound and Vibration 315: 10711085. ##[10] Batra R.C., Porfiri M., Spinello D., 2008, Vibrations of narrow microbeams predeformed, Journal of Sound and Vibration 309: 600612. ##[11] Murmu T., Adhikari S., 2011, Nonlocal vibration of bonded doublenanoplatesystems, Composites: Part B 42: 19011911. ##[12] Murmu T., Adhikari S., 2011, Axial instability of doublenanobeamsystems, Physics Letters A 375: 601608. ##[13] Ghorbanpour Arani A., Shiravand A., Rahi M., Kolahchi R., 2012, Nonlocal vibration of coupled DLGS systems embedded on Visco Pasternak foundation, Physica B 407 (12): 41234131. ##[14] Batra R.C., Porfiri M., Spinello D., 2008, Reducedorder models for microelectromechanical rectangular and circular plates incorporating the Casimir force, International Journal of Solids and Structures 45: 3558–3583. ## ##]
Stress Relief and Material Properties Improvement Through Vibration VS. Common Thermal Method
2
2
The goal of this study is investigating reduction of residual stresses from welding carbon steel plates through vibrationstress reliefmethod vs. thermal method. In order to carry out the required experimental tests, carbon steel plates were welded together under specific conditions as samples. Some of the samples were vibration stress relieved, some were thermal stress relieved while the rest remained without any stress relief operation. Several destructive and nondestructive tests were performed on all the stress relieved and nonrelieved specimens and the data obtained from these tests were compared in order to reach the optimum vibration effect on stress relieved welded joints. The results attained for vibration method indicated an acceptable amount of reduction of residual stresses in the joints. In addition, some improvements in mechanical properties achieved vibration stress relief method were used.
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170
176


S
Jafari Mehrabadi
Department of Mechanical Engineering, Islamic Azad University, Arak Branch
Department of Mechanical Engineering, Islamic
Iran
sjafari@iauarak.ac.ir


M
Azizmoradi
Department of Mechanical Engineering, Islamic Azad University, Arak Branch
Department of Mechanical Engineering, Islamic
Iran


M.M
Emami
Machin Sazi Arak Company
Machin Sazi Arak Company
Iran
Stress Releasing
Vibration
Thermal
Mechanical properties
[[1] McGoldrick R.T., Captain Harold E., 1943, Some experiments in stress relieving casting and welded structures by vibration, Journal of the American Society of Naval Engineers 55(4): 589609. ##[2] Dawnson R., Moffat D.G., 1980, Vibratory stress relief and fundamental study of its effectiveness, Journal of Engineering Materials and Technology 102(2):169176. ##[3] Shankar S., 1982, Vibratory stress relief in mild steel weldments, A Dissertation submitted to the faculty of Oregon Graduate center in partial fulfillment of the requirements for the degree of Doctor of Philosophy. ##[4] Luh G.C., Hwang R.M., 1998, Evaluating the effectiveness of vibratory stress relief by a modified hole – drilling method, The international Journal of Advanced Manufacturing Technology 14(11):815823. ##[5] Aoki Sh., Nishimura T., Hiroi T., 2005, Reduction method for residual stress of welded joint using random vibration, Journal of Nuclear engineering and design 235(14):14411445. ##[6] Robbins M.E., 2004, Topics in vibratory stress relief of weldments, A Seminar submitted to the faculty of Rensselaer at Hartford in partial fulfillment of the requirements for the degree of Master of Science, Applied Composite Material 16:321330. ##[7] Aoki Sh., Nishimura T., Hiroi T., Hirai S., 2006, Reduction method for residual stress of welded joint using harmonic vibrational load, Journal of Nuclear engineering and design 237(2):206212. ## ##]
Nonlinear Finite Element Eccentric LowVelocity Impact Analysis of Rectangular Laminated Composite Plates Subjected to Inphase/Antiphase Biaxial Preloads
2
2
All impact analyses performed so far for the composite plates, have treated central impacts. Furthermore, investigations on influences of the inplane biaxial compression, tension, or tensioncompression preloads on various responses of the lowvelocity impact, especially the indentation, have not been performed so far. In the present research, a finite element formulation is presented for response prediction of a lowvelocity eccentric impact between a rigid spherical indenter and a laminated composite rectangular plate with asymmetric lamination scheme. Different contact laws are considered for the loading and unloading phases. A parametric study is performed to investigate influence of the specifications of the plates and the indenter, the eccentric value, and the inplane preloads on the indentation and force time histories. Results show that the compressive and tensile inplane preloads reduce and increase the contact force (and consequently, the indentation values), respectively. Therefore, the extensive tensile preloads may lead to higher damages.
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177
194


M
Shariyat
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran
m_shariyat@yahoo.com


M
Moradi
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran


S
Samaee
Faculty of Mechanical Engineering, K.N. Toosi University of Technology
Faculty of Mechanical Engineering, K.N. Toosi
Iran
Finite Element
Eccentric lowvelocity impact
Composite plate
Contact law
Preload
[[1] Gong S.W., Lam K.Y., 2000, Effects of structural damping and stiffness on impact response of layered structures, Amerian Institute of Aeronautics and Astronautics 38(9): 1730–1735. ##[2] Jacquelin E., Laine´ J.P., Bennani A., Massenzio M., 2007, A modelling of an impacted structure based on constraint modes, Journal of Sound and Vibration 301(35), 789–802 . ##[3] Pashah S., Massenzio M., Jacquelin E., 2008, Prediction of structural response for low velocity impact, International Journal of Impact Engineering 35(2): 119–132 . ##[4] Anderson T.A., 2005, An investigation of SDOF models for large mass impact on sandwich composites. Journal Composites: Part B 36(2): 135–142. ##[5] Abrate S., 1997, Localized impact on sandwich structures with laminated facing, Applied Mechanics Reviews 50(2): 69–82. ##[6] Abrate S., 2011, Impact Engineering of Composite Structures, CISM, Udine, Springer. ##[7] Chai G.B., Zhu S., 2011, A review of lowvelocity impact on sandwich structures, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of MaterialsDesign and Applications 225(4): 207230 . ##[8] Qiu X.M., Yu T.X., 2011, Some topics in recent advances and applications of structural impact dynamics, Applied Mechanics Reviews 64(3). ##[9] Nosier A., Kapania R.K., Reddy J.N., 1994, Lowvelocity impact of laminated composites using a layerwise theory, Computational Mechanics 13: 360 379. ##[10] Sun D., Luo S.N., 2011, Wave propagation and transient response of a FGM plate under a point impact load based on higherorder shear deformation theory, Composite Structures 93: 1474–1484. ##[11] Yigit A.S., Christoforou A.P., 1995, On the impact between a rigid sphere and a thin composite laminate supported by a rigid substrate, Composite Structures 30(2):169–177. ##[12] Christoforou A.P., Yigit A.S., 1998, Effect of flexibility on low velocity impact response, Journal of Sound and Vibration 217: 563–578 . ##[13] Yigit A.S., Christoforou A.P., 2007, Limits of asymptotic solutions in lowvelocity impact of composite plates, Composite Structures 81: 568–574. ##[14] Christoforou A.P., Yigit A.S., 2009, Scaling of lowvelocity impact response in composite structures, Composite Structures 91: 358–365. ##[15] Shariyat M., Ghajar R., Alipour M.M., 2012, An analytical solution for a low velocity impact between a rigid sphere and a transversely isotropic strainhardening plate supported by a rigid substrate, Journal of Engineering Mathematics 75: 107125. ##[16] Guan Z., Yang C., 2002, Lowvelocity impact and damage process of composite laminates, Journal Composites Material 36, 851871. ##[17] Zheng D., Binienda W.K., 2009, Semianalytical solution of wavecontrolled impact on composite laminates, ASCE Journal of Aerospace Engineering 22: 318323. ##[18] Olsson R., 2010, Analytical model for delamination growth during small mass impact on plates, International Journal of Solids and Structures 47: 2884–2892. ##[19] Yang J., Shen H.S., 2001, Dynamic response of initially stressed functionally graded thin plates, Composite Structures 21: 497508. ##[20] Choi I.H., 2008, Lowvelocity impact analysis of composite laminates under initial inplane load, Composite Structures 86, 251–257. ##[21] Shariyat M., Farzan F., 2012, Nonlinear eccentric lowvelocity impact analysis of a highly prestressed FGM rectangular plate, using a refined contact law, Archive of Applied Mechanics, DOI: 10.1007/s0041901207083. ##[22] Shariyat M., Jafari R., 2013, Nonlinear lowvelocity impact response analysis of a radially preloaded twodirectionalfunctionally graded circular plate: A refined contact stiffness approach, Composites Part B 45: 981994. ##[23] Khalili S.M.R., Mittal R.K., Mohammad Panah N., 2007, Analysis of fiber reinforced composite plates subjected to transverse impact in the presence of initial stresses, Composite Structures 77: 263–268. ##[24] Heimbs S., Heller S., Middendorf P., Ha¨hnel F., Weiße J., 2009, Low velocity impact on CFRP plates with compressive preload: Test and modeling, International Journal of Impact Engineering 36: 1182–1193. ##[25] Choi I.H., 2008, Lowvelocity impact analysis of composite laminates under initial inplane load, Composite Structures 86: 251–257. ##[26] Reddy J.N., 2006, Theory and Analysis of Elastic Plates and Shells, 2nd edition, CRC Press. ##[27] Turner J.R., 1980, Contact on a transversely isotropic halfspace, or between two transversely isotropic bodies, International Journal of Solids and Structures 16: 409–19 . ##[28] Yang S.H., Sun C.T., 1982, Indentation law for composite laminates, in: Composite Materials , Testing and Design (6th conference), ASTM STP787, 425–449. ##[29] Huebner K.H., Dewhirst D.L., Smith D.E., Byrom T.G., 2001, The Finite Element Method for Engineers, 4th Edition, John Wiley & Sons. ##[30] Bathe K.J., 2007, Finite Element Procedures, Cambridge. ##[31] Tiberkak R., 2008, Damage prediction in composite plates subjected to low velocity impact, Composite Structures 83: 73–82. ##[32] Pierson M.O., Vaziri R., 1996, Analytical solution for lowvelocity impact response of composite plates, Amerian Institute of Aeronautics and Astronautics 34: 16331640. ## ##]
Wave Propagation in Micropolar Thermoelastic Diffusion Medium
2
2
The present investigation is concerned with the reflection of plane waves from a free surface of a micropolar thermoelastic diffusion half space in the context of coupled theory of thermoelastic diffusion. The amplitude ratios of various reflected waves are obtained in a closed form. The dependence of these amplitude ratios with an angle of propagation as well as other material parameter are shown graphically. Effects of micropolarity and diffusion are observed on these amplitude ratios. Some special cases of interest are also deduced from the present investigation.
1

195
208


A
Miglani
Department of Mathematics, C.D.L.University, SirsaHaryana ,India
Department of Mathematics, C.D.L.University,
Iran


S
Kaushal
Department of Mathematics, Maharishi Markandeshwar University, MullanaAmbala (Haryana),
Department of Mathematics, Maharishi Markandeshwar
Iran
sachin_kuk@yahoo.co.in
Micropolar
Diffusion
Amplitude ratios
Reflection
Free plane
[[1] Eringen A.C., 1968, Theory of Micropolar Elasticity, In Fractuce,ed H.Lieboneitz Vol5. Acamdemic press, Newyork. ##[2] Eringen A.C., 1999, Micro Continum Field TheoriesI, Foundation and Solids, Springer Verlag, Berlin. ##[3] Nowacki W., 1986, Theory of Asymmetric Elasticity, Pergamon, Oxford. ##[4] Touchert T. R., Claus W.D., Jr and Ariman T., 1968, The linear theory of micropolar thermoelasticity, International Journal of Engineering Science 6:3747. ##[5] Nowacki W., 1974, Dynamical problems of thermo diffusion in solidsI, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Techniques 22: 5564. ##[6] Nowacki W., 1974, Dynamical problems of thermo diffusion in solids II, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Techniques 22:129135. ##[7] Nowacki W., 1974, Dynamical problems of thermo diffusion in solids III, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Techniques 22: 257266. ##[8] Nowacki W., 1976, Dynamical problems of thermo diffusion in solids, Engineering Fracture Mechanics8: 261266. ##[9] Sherief H.H., Saleh H., Hamza F., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42:591608. ##[10] Singh B., 2005, Reflection of P and SV waves from free surface of an elastic soild with generalized thermodiffusion, Journal of Earth Sciences 114 (2): 159168. ##[11] Singh B., 2006, Reflection of SV waves from free surface of an elastic soild with generalized thermoelastic diffusion, Journal of Sound and Vibration 291(35):764778. ##[12] Aouadi M., 2007, Uniqueness and recipocity theorem in the theory of generalized thermoelasic diffusion, Journal of Thermal streses 30:665678. ##[13] Aouadi M., 2008, Generalized theory of thermoelasic diffusion for an anisotropic media, Journal of Thermal streses 31:270285. ##[14] Sharma N., Kumar R., Ram P., 2008, Plane strain deformation in generalized thermoelastic diffusion, International Journal of Thermophysics 29: 15031522. ##[15] Sherief H.H., ElMaghraby N.M., 2009, A thick plate problem in the theory of generalized thermoelastic diffusion, International Journal of Thermophysics 30:20442057. ##[16] Othman M.I.A., Farouk R. M., Hamied H., A. El., 2009, The dependence of the modulus of elasticity on reference temperature in the theory of generalized thermoelastic diffusion with one relaxation time, International Journal Industrial Mathematics 1(4): 277289. ##[17] Othman M.I.A., Atwa S. Y., Farouk R.M., 2009, The effect of diffusion on twodimensional problem of generalized thermoelasticity with Green–Naghdi theory 36(8): 857864. ##[18] Kumar R., Kaushal S., Milani A., 2010, Analysis of deformation due to various sources in micropolar thermodiffusive elastic medium, International Journal for Computational Methods in Engineering Science and Mechanics 11: 196–210. ##[19] Kumar R., Singh B., 1998, Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic halfspace with stretch, Indian journal of Pure and applied math 29(6): 657669. ##[20] Eringen A.C., 1984, Plane waves in nonlocal micropolar elasticity, International Journal of Engineering Science 22:11131121. ##[21] Thomas L., 1980,Fundamental of Heat Transfer, Prentice hall IncEnglewmd Diffs, Newjersey. ##]
Propagation of Waves at an Interface of Heat Conducting Elastic Solid and Micropolar Fluid Media
2
2
The present investigation is concerned with the reflection and transmission coefficients of plane waves at the interface of generalized thermoelastic solid half space and heat conducting micropolar fluid half space. The amplitude ratios of various reflected and transmitted waves with various angle of incidence have been computed numerically and depicted graphically. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for specific model. Some special and particular cases are also deduced from the present investigation.
1

209
225


R
Kumar
Department of Mathematics, Kurukshetra University
Department of Mathematics, Kurukshetra University
Iran
rajneesh_kuk@rediffmail.com


M
Kaur
Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana
Department of Applied Sciences, Guru Nanak
Iran
mandeep1125@yahoo.com


S.C
Rajvanshi
Department of Applied Sciences, Gurukul Vidyapeeth, Institute of Engineering and Technology
Department of Applied Sciences, Gurukul Vidyapeeth
Iran
Elastic solid
Micropolar fluid
Thermoelastic
Reflection coefficient
Transmission coefficient
Angle of incidence
[[1] Eringen A.C., 1964, Simple microfluids, International Journal of Engineering Science 2: 205217. ##[2] Eringen A.C., 1966 a, Theory of microfluids, Journal of Applied Mathematics and Mechanics 16: 118. ##[3] Ariman T., Sylvester N.D., Turk M.A., 1973, Microcontinuum fluid mechanicsa review, International Journal of Engineering Science 11: 905930. ##[4] Ariman T., Sylvester N.D., Turk M.A., 1974, Review article applications of microcontinuum fluid mechanics, International Journal of Engineering Science 12: 273293. ##[5] Riha P., 1975, On the theory of heatconducting micropolar fluid with microtemperature, Acta Mechanica 23: 18. ##[6] Eringen A.C., Kafadar C.B.,1976, Polar Field Theories, In Continuum Physics ,Edited by A.C. Eringen, Vol. IV. Academic Press, New York. ##[7] Brulin O., 1982, Linear Micropolar Media, In Mechanics of Micropolar Media ,Edited by O. Brulin and R.K.T. HSIEH, World Scientific, Singapore. ##[8] Gorla R.S.R.,1989, Combined forced and free convection in the boundary layer flow of a micropolar fluid on a continuous moving vertical cylinder, International Journal of Engineering Science 27: 7786. ##[9] Eringen A.C., 1990, Theory of Microstretch and Bubbly Liquid, International Journal of Engineering Science 28: 133143. ##[10] Aydemir N.U., Venart J.E.S., 1990, Flow of a thermomicropolar fluid with stretch, International Journal of Engineering Science 28: 12111222. ##[11] Hsia S.Y., Cheng J.W., 2006, Longitudinal plane waves propagation in elastic micropolar porous media, Japanese Journal of Applied Physics 45: 17431748. ##[12] Hsia S.Y., Chiu S.M., Su C.C., Chen T.H., 2007, Propagation of transverse waves in elastic micropolar porous semispaces, Japanese Journal of Applied Physics 46: 73997405. ##[13] Biot M., 1956, Thermoelasticity and Irreversible Thermodynamics, Journal of Applied Physics 27: 240253. ##[14] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309. ##[15] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 17. ##[16] Dhaliwal R.S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India. ##[17] Ignaczak J., Starzewski M.O., 2010, Thermoelasticity with Finite Wave Speeds, Oxford Science Publisher. ##[18] Tomar S.K., Gogna M.L., 1992, Reflection and refraction of a longitudinal microrotational wave at an interface between two micropolar elastic solids in welded contact, International Journal of Engineering Science 30: 16371646. ##[19] Tomar S.K., Gogna M.L., 1995 a, Reflection and refraction of a longitudinal displacement wave at an interface between two micropolar elastic solids in welded contact, Journal of the Acoustical Society of America 97: 827830. ##[20] Tomar S.K., Gogna M.L., 1995 b, Reflection and refraction of a coupled transverse and microrotational waves at an interface between two different micropolar elastic solids in welded contact, International Journal of Engineering Science 30: 485496. ##[21] Kumar R., Sharma N., Ram P., 2008 a, Reflection and transmission of micropolar elastic waves at an imperfect boundary, Multidiscipline Modelling in Materials and Structures (MMMS) 4: 1536. ##[22] Kumar R., Sharma N., Ram P., 2008 b, Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media, Theoretical and Applied Fracture Mechanics 49: 305312. ##[23] Singh D., Tomar S. K., 2008, Longitudinal waves at a micropolar fluid/solid interface, International Journal of Solids And Structures 45: 225244. ##[24] Ciarletta M., 2001, Spatial decay estimates for heat conducting micropolar fluids, International Journal of Engineering Science 39: 655668.##]