2015
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1

Transverse Vibration for Nonuniform Timoshenko Nanobeams
https://macs.semnan.ac.ir/article_327.html
10.22075/macs.2015.327
1
In this paper, Eringen’s nonlocal elasticity and Timoshenko beam theories are implemented to analyze the bending vibration for nonuniform nanobeams. The governing equations and the boundary conditions are derived using Hamilton’s principle. A Generalized Differential Quadrature Method (GDQM) is utilized for solving the governing equations of nonuniform Timoshenko nanobeam for pinnedpinned, clamped–clamped, clamped–pinned, clamped–free, clamped–slide, and pinnedslide boundary conditions. The nondimensional natural frequencies and the normalized mode shapes are obtained for short and stubby nanobeams where influences varying crosssection area, small scale, shear deformation, rotational moment of inertia, acceleration gravity and the selfweight of the nonuniform Timoshenko nanobeam are discussed. The present study illustrates that the small scale effects are more significant for smaller size of nanobeam, larger nonlocal parameter and higher vibration modes. Further, the compression forces due to gravity and the selfweight of the nanobeam also like the small scale effect are reduced the magnitude of the frequencies of the nanobeam.
0

1
16


Keivan
Torabi
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
kvntrb@kashanu.ac.ir


Majid
Rahi
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
rahimajid@gmail.com


Hassan
Afshari
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
afshari_hasan@yahoo.com
Nonlocal elasticity
Gravity
Timoshenko
Nonuniform nanobeam
Generalized differential quadrature method
[[1] Wang LF, Hu HY. Flexural Wave Propagation in Singlewalled Carbon Nanotubes. Phys Rev B 2005; 71: 1–7.##[2] Eringen AC. Nonlocal Polar Elastic Continua. Int J Eng Sci 1972; 10: 1–16.##[3] Eringen AC, Edelen DGB. On Nonlocal Elasticity. Int J Eng Sci 1972; 10: 233–248.##[4] Eringen AC. On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves. J Appl Phys 1983; 54: 4703–4710.##[5] Eringen AC. Nonlocal Continuum Field Theories. SpringerVerlag; 2002.##[6] Lu P, Lee HP, Lu C, Zhang PQ. Dynamic Properties of Flexural Beams using a Nonlocal Elasticity Model. J Appl Phys 2006; 99: 073510.##[7] Peddieson J, Buchanan GG, McNitt RP. Application of Nonlocal Continuum Models to Nanotechnology. Int J Eng Sci 2003; 41: 305–312.##[8] Reddy JN, Wang CM. Deflection Relationships between Classical and Thirdorder Plate Theories. Acta Mech 1998; 130(3–4): 199–208.##[9] Wang Q. Wave Propagation in Carbon Nanotubes via Nonlocal Continuum Mechanics. J Appl Phys 2005; 98: 124301.##[10] Wang Q, Varadan VK. Vibration of Carbon Nanotubes Studied using Nonlocal Continuum Mechanics. Smart Mater Struct 2006; 15: 659–666.##[11] Wang CM, Zhang YY, Ramesh SS, Kitipornchai S. Buckling Analysis of Micro and Nanorods/tubes based on Nonlocal Timoshenko Beam Theory. J Phys D Appl Phys 2006; 39: 3904–3909.##[12] Reddy JN. Nonlocal Theories for Bending, Buckling and Vibration of Beams. Int J Eng Sci 2007; 45: 288–307.##[13] Wang CM, Zhang YY, He XQ. Vibration of Nonlocal Timoshenko Beams. Nanotechnology 2007; 18: 1–9.##[14] Murmu T, Pradhan SC. Buckling Analysis of a Singlewalled Carbon Nanotube Embedded in an Elastic Medium based on Nonlocal Elasticity and Timoshenko Beam Theory and using DQM. Physica E 2009; 41: 1232–1239.##[15] Şimşek M. Nonlocal Effects in The Forced Vibration of an Elastically Connected Doublecarbon Nanotube System under a Moving Nanoparticle. Comput Mater Sci 2011; 50: 2112–2123.##[16] Lu P, Lee HP, Lu C, Zhang PQ. Application of Nonlocal Beam Models for Carbon Nanotubes. Int J Solids Struct 2007; 44: 5289–5300.##[17] Reddy JN. Energy Principles and Variational Methods in Applied Mechanics. John Wiley & Sons; 2002.##[18] Reddy JN. Theory and Analysis of Elastic Plates and Shells. Taylor & Francis; 2007.##[19] Reddy JN, Pang SD. Nonlocal Continuum Theories of Beams for The Analysis of Carbon Nanotubes. J Appl Phys 2008; 103: 023511.##[20] Hutchinson JR. Shear Coefficients for Timoshenko Beam Theory. J Appl Mech 2001; 68: 1–6.##[21] Meirovitch L. Fundamentals of Vibrations. McGrawHill; 2001.##[22] Ke LL, Xiang Y, Yang J, Kitipornchai S. Nonlinear Free Vibration of Embedded Doublewalled Carbon Nanotubes based on Nonlocal Timoshenko Beam Theory. Comp Mater Sci 2009; 47: 409–417.##[23] Hijmissen JW, Horssen WTV. On Transverse Vibrations of a Vertical Timoshenko Beam. J Sound Vib 2008; 314: 161–179.##[24] Bellman R, Casti J. Differential Quadrature and Longterm Integration. J Math Anal Appl 1971; 34: 235–238.##[25] Bellman R, Kashef BG, Casti J. Differential Quadrature a Technique for The Rapid Solution of Nonlinear Partial Differential Equations. J Comput Phys 1972; 10: 40–52.##[26] Zong Z, Zhang Y. Advanced Differential Quadrature Methods. Chapman & Hall/CRC; 2009.##[27] Shu C. Differential Quadrature and Its Application in Engineering. Sprimger; 2000.##[28] Mestrovic M. Generalized Differential Quadrature Method for Timoshenko Beam. MIT Conf Comput Fluid Solid Mech 2003.##[29] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature Method to Structural Problems. J Num Meth Engrg 1994; 37: 1881–1896.##[30] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature to Vibration Analysis. J Sound Vib 1995; 181: 279–293.##[31] Mahmoud AA, Esmaeel RA, Nassar MM. Application of The Generalized Differential Quadrature Method to The Free Vibrations of Delaminated Beam Plates. J Eng Mech 2007; 14: 431–441.##[32] Wu T Y, Liu GR. A Differential Quadrature as a Numerical Method to Solve Differential Equations. Comput Mech 1999; 24: 197–205.##[33] Farchaly SH, Shebl MG. Exact Frequency and Mode Shape Formulae for Studying Vibration and Stability of Timoshenko Beam System. J Sound Vib 1995; 180: 205–227.##[34] Chen WR. Bending Vibration of Axially Loaded Timoshenko Beams with Locally Distributed KelvinVoigt Damping. J Sound Vib 2011; 330: 3040–3056.##[35] Arash B, Wang Q. A Review on The Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes. Comput Mater Sci 2012; 51: 303–313.##[36] Yang J, Ke LL, Kitipornchai S. Nonlinear Free Vibration of Singlewalled Carbon Nanotubes using Nonlocal Timoshenko Beam Theory. Physica E 2010; 42: 1727–1735.##[1] Wang LF, Hu HY. Flexural Wave Propagation in Singlewalled Carbon Nanotubes. Phys Rev B 2005; 71: 1–7.##[2] Eringen AC. Nonlocal Polar Elastic Continua. Int J Eng Sci 1972; 10: 1–16.##[3] Eringen AC, Edelen DGB. On Nonlocal Elasticity. Int J Eng Sci 1972; 10: 233–248.##[4] Eringen AC. On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves. J Appl Phys 1983; 54: 4703–4710.##[5] Eringen AC. Nonlocal Continuum Field Theories. SpringerVerlag; 2002.##[6] Lu P, Lee HP, Lu C, Zhang PQ. Dynamic Properties of Flexural Beams using a Nonlocal Elasticity Model. J Appl Phys 2006; 99: 073510.##[7] Peddieson J, Buchanan GG, McNitt RP. Application of Nonlocal Continuum Models to Nanotechnology. Int J Eng Sci 2003; 41: 305–312.##[8] Reddy JN, Wang CM. Deflection Relationships between Classical and Thirdorder Plate Theories. Acta Mech 1998; 130(3–4): 199–208.##[9] Wang Q. Wave Propagation in Carbon Nanotubes via Nonlocal Continuum Mechanics. J Appl Phys 2005; 98: 124301.##[10] Wang Q, Varadan VK. Vibration of Carbon Nanotubes Studied using Nonlocal Continuum Mechanics. Smart Mater Struct 2006; 15: 659–666.##[11] Wang CM, Zhang YY, Ramesh SS, Kitipornchai S. Buckling Analysis of Micro and Nanorods/tubes based on Nonlocal Timoshenko Beam Theory. J Phys D Appl Phys 2006; 39: 3904–3909.##[12] Reddy JN. Nonlocal Theories for Bending, Buckling and Vibration of Beams. Int J Eng Sci 2007; 45: 288–307.##[13] Wang CM, Zhang YY, He XQ. Vibration of Nonlocal Timoshenko Beams. Nanotechnology 2007; 18: 1–9.##[14] Murmu T, Pradhan SC. Buckling Analysis of a Singlewalled Carbon Nanotube Embedded in an Elastic Medium based on Nonlocal Elasticity and Timoshenko Beam Theory and using DQM. Physica E 2009; 41: 1232–1239.##[15] Şimşek M. Nonlocal Effects in The Forced Vibration of an Elastically Connected Doublecarbon Nanotube System under a Moving Nanoparticle. Comput Mater Sci 2011; 50: 2112–2123.##[16] Lu P, Lee HP, Lu C, Zhang PQ. Application of Nonlocal Beam Models for Carbon Nanotubes. Int J Solids Struct 2007; 44: 5289–5300.##[17] Reddy JN. Energy Principles and Variational Methods in Applied Mechanics. John Wiley & Sons; 2002.##[18] Reddy JN. Theory and Analysis of Elastic Plates and Shells. Taylor & Francis; 2007.##[19] Reddy JN, Pang SD. Nonlocal Continuum Theories of Beams for The Analysis of Carbon Nanotubes. J Appl Phys 2008; 103: 023511.##[20] Hutchinson JR. Shear Coefficients for Timoshenko Beam Theory. J Appl Mech 2001; 68: 1–6.##[21] Meirovitch L. Fundamentals of Vibrations. McGrawHill; 2001.##[22] Ke LL, Xiang Y, Yang J, Kitipornchai S. Nonlinear Free Vibration of Embedded Doublewalled Carbon Nanotubes based on Nonlocal Timoshenko Beam Theory. Comp Mater Sci 2009; 47: 409–417.##[23] Hijmissen JW, Horssen WTV. On Transverse Vibrations of a Vertical Timoshenko Beam. J Sound Vib 2008; 314: 161–179.##[24] Bellman R, Casti J. Differential Quadrature and Longterm Integration. J Math Anal Appl 1971; 34: 235–238.##[25] Bellman R, Kashef BG, Casti J. Differential Quadrature a Technique for The Rapid Solution of Nonlinear Partial Differential Equations. J Comput Phys 1972; 10: 40–52.##[26] Zong Z, Zhang Y. Advanced Differential Quadrature Methods. Chapman & Hall/CRC; 2009.##[27] Shu C. Differential Quadrature and Its Application in Engineering. Sprimger; 2000.##[28] Mestrovic M. Generalized Differential Quadrature Method for Timoshenko Beam. MIT Conf Comput Fluid Solid Mech 2003.##[29] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature Method to Structural Problems. J Num Meth Engrg 1994; 37: 1881–1896.##[30] Du H, Lim MK, Lin NR. Application of Generalized Differential Quadrature to Vibration Analysis. J Sound Vib 1995; 181: 279–293.##[31] Mahmoud AA, Esmaeel RA, Nassar MM. Application of The Generalized Differential Quadrature Method to The Free Vibrations of Delaminated Beam Plates. J Eng Mech 2007; 14: 431–441.##[32] Wu T Y, Liu GR. A Differential Quadrature as a Numerical Method to Solve Differential Equations. Comput Mech 1999; 24: 197–205.##[33] Farchaly SH, Shebl MG. Exact Frequency and Mode Shape Formulae for Studying Vibration and Stability of Timoshenko Beam System. J Sound Vib 1995; 180: 205–227.##[34] Chen WR. Bending Vibration of Axially Loaded Timoshenko Beams with Locally Distributed KelvinVoigt Damping. J Sound Vib 2011; 330: 3040–3056.##[35] Arash B, Wang Q. A Review on The Application of Nonlocal Elastic Models in Modeling of Carbon Nanotubes and Graphenes. Comput Mater Sci 2012; 51: 303–313.##[36] Yang J, Ke LL, Kitipornchai S. Nonlinear Free Vibration of Singlewalled Carbon Nanotubes using Nonlocal Timoshenko Beam Theory. Physica E 2010; 42: 1727–1735.##]
1

The Effects of the Moving Load and the Attached MassSpringDamper System Interactions on the Dynamic Responses of the Composite Plates: An Analytical Approach
https://macs.semnan.ac.ir/article_328.html
10.22075/macs.2015.328
1
In the current study, the effects of interactions of the moving loads and the attached massspringdamper systems of the composite plates on the resulting dynamic responses are investigated comprehensively, for the first time, using the classical plate theory. The solution of the coupled governing system of equations is accomplished through tracing the spatial variations using a Naviertype solution and the time variations by means of a Laplace transform. Therefore, the results are exact. The effects of various material, stiffness, and kinematic parameters of the system on the responses are investigated comprehensively and the results are illustrated graphically. Apart from the novelties presented in the modeling and solution stages, some practical conclusions have been drawn such as the fact that the amplitude of vibration increases for both the free and forced vibrations of the plate and the suspended mass, when the magnitude of suspended mass increases.
0

17
30


Sina
Fallahzadeh Rastehkenar
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Iran


Mohammad
Shariyat
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Iran
shariyat@kntu.ac.ir
Composite plate
Dynamic response
Laplace transform
Attached massspring system Moving load
[[1] Wong JY. Theory of Ground Vehicles. 3rd edition, John Wiley & Sons Inc.; 2001.##[2] Jazar RN. Vehicle Dynamics: Theory and Applications. Springer; 2008.##[3] Ellis BR, Ji T. HumanStructure Interaction in Vertical Vibrations. Proc Inst Civ Eng, Struct Build, 1997; 122: 1–9.##[4] Snowdon JC. Vibration of Cantilever Beams to Which Dynamic Absorbers Are Attached. J Acoust Soc Am 1966; 39: 878–886.##[5] Ranjan V, Ghosh MK. Forced Vibration Response of Thin Plate with Attached Discrete Dynamic Absorbers. ThinWall Struct 2005; 43: 1513–1533.##[6] Turhan O. On the Fundamental Frequency of Beams Carrying a Point Mass: Rayleigh Approximation Versus Exact Solutions. J Sound Vib 2000; 230(2): 449–459.##[7] Kompaz O, Telli S. Free Vibration of a Rectangular Plate Carrying Distributed Mass. J Sound Vib 2002; 251: 39–57.##[8] Wong WO. The Effect of Distributed Mass Loading on Plate Vibration Behavior. J Sound Vib 2002; 252: 577–583.##[9] Chiba M, Sugimoto T. Vibration Characteristics of a Cantilever Plate with Attached SpringMass System. J Sound Vib 2003; 260: 237–263.##[10] Li QS. An Exact Approach for Free Vibration Analysis of Rectangular Plates with Lineconcentrated Mass and Elastic LineSupport. Int J Mech Sci 2003; 45: 669–685.##[11] Zhou D, Ji T. Free Vibration of Rectangular Plates with Continuously Distributed SpringMass. Int J Solids Struct 2006; 43: 6502–6520.##[12] Éshmatov BK, Khodzhaev DA. Dynamic Stability of a Viscoelastic Plate with Concentrated Masses. Int Appl Mech 2008; 44(2): 208–216.##[13] Khodzhaev DA, Éshmatov BK. Nonlinear Vibrations of a Viscoelastic Plate with Concentrated Masses. J Appl Mech Tech Phys 2007; 48(6): 905–914.##[14] Ciancio PM, Rossit CA, Laura PAA. Approximate Study of the free Vibrations of a Cantilever Anisotropic Plate Carrying a Concentrated Mass. J Sound Vib 2997; 302: 621–628.##[15] Alibeigloo A, Shakeri M, Kari MR. Free Vibration Analysis of Antisymmetric Laminated Rectangular Plates with Distributed Patch Mass Using ThirdOrder Shear Deformation Theory. Ocean Eng 2007; 35: 183–190.##[16] Watkins RJ, Santillan S, Radice J, Barton Jr O. Vibration Response of an Elastically PointSupported Plate with Attached Masses. ThinWall Struct 2010; 48: 519–527.##[17] Malekzadeh K, Tafazoli S, Khalili SMR. Free Vibrations of Thick Rectangular Composite Plate with Uniformly Distributed Attached Mass Including Stiffness Effect. J Compos Mater 2010; 44: 2897–2918.##[18] Amabili M, Carra S. Experiments and Simulations for LargeAmplitude Vibrations of Rectangular Plates Carrying Concentrated Masses. J Sound Vib 2012; 331: 155–166.##[19] Agrawal OP, Stanisic MM, Saigal S. Dynamic Responses of Orthotropic Plates Under Moving Masses. Eng Arch 1988; 58: 9–14.##[20] Taheri MR, Ting EC. Dynamic Response of Plates to Moving Loads Finite Element Method. Comput Struct 1990; 34: 509–521.##[21] Zaman MM, Taheri R., Alavappillaix A. Dynamic Response of a Thick Plate on Viscoelastic Foundation to Moving Loads. Int J Numer Ana Meth Geomech 1991; 15: 627–647.##[22] de Faria AR, Oguamanam DCD. Finite Element Analysis of the Dynamic Response of Plates Under Traversing Loads Using Adaptive Meshes. ThinWall Struct 2004; 42: 1481–1493.##[23] Wu JJ. Dynamic analysis of a rectangular plate under a moving line load using scale beams and scaling laws. Comput Struct 2005; 83: 1646–1658.##[24] Sun L. Dynamics of plate generated by moving harmonic loads. J Appl Mech 2005; 72: 772–777.##[25] Malekzadeh P, Fiouz AR, Razi H. ThreeDimensional Dynamic Analysis of Laminated Composite Plates Subjected to Moving Load. Compos Struct 2009; 90: 105–114.##[26] Reddy JN. Mechanics of Laminated Composite Plate: Theory and Analysis. CRC Press; 1997.##[27] Spiegel MR. Advanced Mathematics for Engineers and Scientists. McGrawHill; 1971.##]
1

Atomic Simulation of Temperature Effect on the Mechanical Properties of Thin Films
https://macs.semnan.ac.ir/article_329.html
10.22075/macs.2015.329
1
The molecular dynamic technique was used to simulate the nanoindentation test on the thin films of silver, titanium, aluminum and copper which were coated on the silicone substrate. The mechanical properties of the selected thin films were studied in terms of the temperature. The temperature was changed from 193 K to 793 K with an increment of 100 K. To investigate the effect of temperature on the mechanical properties, two different ways including step by step and continuous ways, were used. The temperature in the indentation region was controlled and the effect of temperature increase due to the friction between the indenter and the film was taken into account. The temperature effects on the material structure, pilingup and sinkingin phenomena were also considered. The results show that the elasticity modulus and hardness of thin films decrease by increasing temperature. These mechanical properties also decreased due to the increase in temperature, in the indentation region, which in turn was due to the interaction between the indenter and the thin film.
0

31
38


M.R.
Ayatollahi
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Iran
m.ayat@iust.ac.ir


A.S.
Rahimi
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Iran
saleh_rahimi@mecheng.iust.ac.ir


A.
Karimzadeh
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Iran
Thin film coatings
Molecular dynamic simulation
Nanoindentation test
Film temperature
Mechanical properties
[[1] Ashurst WR, Carraro C, Maboudian R, Frey W. Wafer Level AntiStiction Coatings for MEMS. Sens Actuators A 2003; 104: 213–221.##[2] Bourhis ELE. Indentation Mechanics and##its Application to Thin Film Characterization. Vacuum 2011; 82: 1353–1359.##[3] Radhakrishnan G, Robertson RE, Adams PM, Cole RC. Integrated TiC Coatings for Moving MEMS. Thin Solid Films 2002; 420: 553–564.##[4] Cao Y, Allameh SM, Nankivil D, Sethiaraj S, Otiti T, Soboyejo W. Nanoindentation Measurements of the Mechanical Properties of Polycrystalline Au and Ag Thin Films on Silicon Substrates: Effects of Grain Size and Film Thickness. Mater Sci Eng A 2006; 427: 232–240.##[5] Hong SH, Kim KS, Kim YM, Hahn JH, Lee CS, Park JH. Characterization of Elastic Moduli of Cu Thin Films using Nanoindentation Technique. Compos Sci Technol 2005; 65: 1401–1402.##[6] Sharpe WN, Yuan B, Edwards RL. A New Technique for Measuring the Mechanical Properties of Thin Films. J MicroElectroMechanical Syst 1997; 6 (3): 193–198.##[7] Minfray C, Martin JM, Esnouf C, Mogne T Le, Kersting R, Hagenhoff. A Multitechnique Approach of Tribofilm Characterization. Thin Solid Films 2004; 447: 272–277.##[8] Oliver WC, Pharr GM. An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation Experiments. J Mater Res 1992; 7(6): 1564–1583.##[9] Burnett PJ, Rickerby DS. The Mechanical Properties of Wear Resistant Coatings: Modeling of Hardness Behavior. Thin Solid Films 1987; 148: 51.##[10] Hay JL, Oliver WC, Bolshakov A, Pharr GM. Using the Ratio of Loading Slope and Elastic Stiffness to Predict Pileup and Constraint Factor during Indentation. MRS Symp Proc, Fundamentals of Nanoindentation and Nanotribiloy 1998.##[11] Hay JC, Pharr GM. Critical Issues in Measuring the Mechanical Properties of Hard Films on Soft Substrates by Nanoindentation Techniques. Mater Res Symp Proc 1998; 505: 65–70.##[12] Tang KC, Arnell RD. Determination of Coating Mechanical Properties using Spherical Indenters. Thin Solid Films 1999; 356: 263–269.##[13] Saha R, Xue ZY, Huang Y, Nix WD. Indentation of a Soft Metal Film on a Hard Substrate: Strain Gradient Hardening Effects. J Mech Phys Solids 2001; 49: 1997–2014.##[14] Saha R, Nix WD. Effects of The Substrate on The Determination of Thin Film Mechanical Properties by Nanoindentation. Acta Mater 2002; 50: 23–38.##[15] Seung Min Han , Ranjana Saha, William D. Nix. Determining Hardness of Thin Films in Elastically Mismatched Filmonsubstrate Systems using Nanoindentation. Acta Mater 2006; 54: 1571–1581.##[16] Szlufarska I, Kalia R, Nakano A, Vashishta P. Atomistic Mechanisms of Amorphization during Nanoindentation of SiC: A Molecular Dynamics Study. Phys Rev B 2005; 71: 1–11.##[17] Chen HP, Kalia RK, Nakano A, Vashishta P, Szlufarska I. Multimilionatom Nanoindentation Simulation of Crystalline Sillicon Carbide: Orientation Dependence and Anisotropic Pileup. J Appl Phys 2007; 102(6): 063514.##[18] Zaminpayma E. Computer Simulation on TiO2 Nanostructure Films and Experimental Study Using Sol–Gel Method. J Clust Sci 2009; 20: 641–649.##[19] Shi YF, Falk ML. Structural Transformation and Localization during Simulated Nanoindentation of A Noncrystalline Metal Film. Phys Rev Let 2005; 95: 1–5.##[20] Peng P, Liao G, Shi T, Tang Z, Gao Y. Molecular Dynamic Simulations of Nanoindentation in Aluminum Thin Film on Silicon Substrate. Appl Surf Sci 2010; 256: 6284–6290.##[21] Hwang SF, Li YH, Hong ZH. Molecular Dynamic Simulation for Cu Cluster Deposition on Si Substrate. Comput Mater Sci 2012; 56: 85–94.##[22] Gerolf Z, Alexander H, Herbert H. Pair vs Manybody Potentials: Influence on Elastic and Plastic Behavior in Nanoindentation of FCC Metals. J Mech Phys Solids 2009; 57: 1514–1526.##[23] Yan Y, Sun T, Dong S, Liang Y. Study on Effects of The Feed on AFMbased Nanolithography Process using MD Simulation. Comput Mater Sci 2007; 40: 1–5.##[24] Fang T, Wu J. Molecular Dynamics Simulations on Nanoindentation Mechanisms of Multilayered Films. Comput Mater Sci 2008; 43: 785–790.##[25] Tersoff J. Modeling SolidState Chemistry: Interatomic Potentials for Multicomponent Systems. Phys Rev 1989; 39: 5566.##[26] Ayatollahi MR, Rahimi A,Karimzadeh A. Study on Effect of Thickness of Thin Films on Mechanical Properties Measured by Nanoindentation and Comparison by The Molecular Dynamics (MD) Simulation. The BiAnnual International Conference on Experimental Solid Mechanics and Dynamics (XMech) Tehran, Iran; 2014.##[27] Dasilva J, Rino P. Atomistic Simulation of The Deformation Mechanism during Nanoindentation of Gamma Titanium Aluminide. Comput Mater Sci 2012; 62: 1–5.##[28] Wymyslowski A, Dowhan L. Application of Nanoindentation Technique for Investigation of Elastoplastic Properties of The Selected Thin Film Materials. MicroElectronics Reliab 2013; 53: 443–451.##[29] Bolshakov A, Pharr GM. Influences of Pileup on the Measurement of Mechanical Properties by Load and Depth Sensing Indentation Techniques. J Mater Res 1998; 13: 1049–1058.##[30] Liang L, Li M, Qin F, Wei Y. Temperature Effect on Elastic Modulus of Thin Films and Nanocrystals, Philos Mag 2013; 93(6): 574–583.##[31] Lebedev AB, Burenkov YA, Romanov AE, Kopylov VI, Filonenko VP, Gryaznov VG. Softening of The Elastic Modulus in Submicrocrystalline copper. Mater Sci Eng A 1995; 203: 165–170.##[32] Hung Z, Gu LY, Weertman JR. Temperature Dependence of Hardness of Nanocrystalleve Copper in Lowtemperature Range. Scripta Materialia 1997; 37: 1071–1075.##[1] Ashurst WR, Carraro C, Maboudian R, Frey W. Wafer Level AntiStiction Coatings for MEMS. Sens Actuators A 2003; 104: 213–221.##[2] Bourhis ELE. Indentation Mechanics and##its Application to Thin Film Characterization. Vacuum 2011; 82: 1353–1359.##[3] Radhakrishnan G, Robertson RE, Adams PM, Cole RC. Integrated TiC Coatings for Moving MEMS. Thin Solid Films 2002; 420: 553–564.##[4] Cao Y, Allameh SM, Nankivil D, Sethiaraj S, Otiti T, Soboyejo W. Nanoindentation Measurements of the Mechanical Properties of Polycrystalline Au and Ag Thin Films on Silicon Substrates: Effects of Grain Size and Film Thickness. Mater Sci Eng A 2006; 427: 232–240.##[5] Hong SH, Kim KS, Kim YM, Hahn JH, Lee CS, Park JH. Characterization of Elastic Moduli of Cu Thin Films using Nanoindentation Technique. Compos Sci Technol 2005; 65: 1401–1402.##[6] Sharpe WN, Yuan B, Edwards RL. A New Technique for Measuring the Mechanical Properties of Thin Films. J MicroElectroMechanical Syst 1997; 6 (3): 193–198.##[7] Minfray C, Martin JM, Esnouf C, Mogne T Le, Kersting R, Hagenhoff. A Multitechnique Approach of Tribofilm Characterization. Thin Solid Films 2004; 447: 272–277.##[8] Oliver WC, Pharr GM. An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation Experiments. J Mater Res 1992; 7(6): 1564–1583.##[9] Burnett PJ, Rickerby DS. The Mechanical Properties of Wear Resistant Coatings: Modeling of Hardness Behavior. Thin Solid Films 1987; 148: 51.##[10] Hay JL, Oliver WC, Bolshakov A, Pharr GM. Using the Ratio of Loading Slope and Elastic Stiffness to Predict Pileup and Constraint Factor during Indentation. MRS Symp Proc, Fundamentals of Nanoindentation and Nanotribiloy 1998.##[11] Hay JC, Pharr GM. Critical Issues in Measuring the Mechanical Properties of Hard Films on Soft Substrates by Nanoindentation Techniques. Mater Res Symp Proc 1998; 505: 65–70.##[12] Tang KC, Arnell RD. Determination of Coating Mechanical Properties using Spherical Indenters. Thin Solid Films 1999; 356: 263–269.##[13] Saha R, Xue ZY, Huang Y, Nix WD. Indentation of a Soft Metal Film on a Hard Substrate: Strain Gradient Hardening Effects. J Mech Phys Solids 2001; 49: 1997–2014.##[14] Saha R, Nix WD. Effects of The Substrate on The Determination of Thin Film Mechanical Properties by Nanoindentation. Acta Mater 2002; 50: 23–38.##[15] Seung Min Han , Ranjana Saha, William D. Nix. Determining Hardness of Thin Films in Elastically Mismatched Filmonsubstrate Systems using Nanoindentation. Acta Mater 2006; 54: 1571–1581.##[16] Szlufarska I, Kalia R, Nakano A, Vashishta P. Atomistic Mechanisms of Amorphization during Nanoindentation of SiC: A Molecular Dynamics Study. Phys Rev B 2005; 71: 1–11.##[17] Chen HP, Kalia RK, Nakano A, Vashishta P, Szlufarska I. Multimilionatom Nanoindentation Simulation of Crystalline Sillicon Carbide: Orientation Dependence and Anisotropic Pileup. J Appl Phys 2007; 102(6): 063514.##[18] Zaminpayma E. Computer Simulation on TiO2 Nanostructure Films and Experimental Study Using Sol–Gel Method. J Clust Sci 2009; 20: 641–649.##[19] Shi YF, Falk ML. Structural Transformation and Localization during Simulated Nanoindentation of A Noncrystalline Metal Film. Phys Rev Let 2005; 95: 1–5.##[20] Peng P, Liao G, Shi T, Tang Z, Gao Y. Molecular Dynamic Simulations of Nanoindentation in Aluminum Thin Film on Silicon Substrate. Appl Surf Sci 2010; 256: 6284–6290.##[21] Hwang SF, Li YH, Hong ZH. Molecular Dynamic Simulation for Cu Cluster Deposition on Si Substrate. Comput Mater Sci 2012; 56: 85–94.##[22] Gerolf Z, Alexander H, Herbert H. Pair vs Manybody Potentials: Influence on Elastic and Plastic Behavior in Nanoindentation of FCC Metals. J Mech Phys Solids 2009; 57: 1514–1526.##[23] Yan Y, Sun T, Dong S, Liang Y. Study on Effects of The Feed on AFMbased Nanolithography Process using MD Simulation. Comput Mater Sci 2007; 40: 1–5.##[24] Fang T, Wu J. Molecular Dynamics Simulations on Nanoindentation Mechanisms of Multilayered Films. Comput Mater Sci 2008; 43: 785–790.##[25] Tersoff J. Modeling SolidState Chemistry: Interatomic Potentials for Multicomponent Systems. Phys Rev 1989; 39: 5566.##[26] Ayatollahi MR, Rahimi A,Karimzadeh A. Study on Effect of Thickness of Thin Films on Mechanical Properties Measured by Nanoindentation and Comparison by The Molecular Dynamics (MD) Simulation. The BiAnnual International Conference on Experimental Solid Mechanics and Dynamics (XMech) Tehran, Iran; 2014.##[27] Dasilva J, Rino P. Atomistic Simulation of The Deformation Mechanism during Nanoindentation of Gamma Titanium Aluminide. Comput Mater Sci 2012; 62: 1–5.##[28] Wymyslowski A, Dowhan L. Application of Nanoindentation Technique for Investigation of Elastoplastic Properties of The Selected Thin Film Materials. MicroElectronics Reliab 2013; 53: 443–451.##[29] Bolshakov A, Pharr GM. Influences of Pileup on the Measurement of Mechanical Properties by Load and Depth Sensing Indentation Techniques. J Mater Res 1998; 13: 1049–1058.##[30] Liang L, Li M, Qin F, Wei Y. Temperature Effect on Elastic Modulus of Thin Films and Nanocrystals, Philos Mag 2013; 93(6): 574–583.##[31] Lebedev AB, Burenkov YA, Romanov AE, Kopylov VI, Filonenko VP, Gryaznov VG.Softening of The Elastic Modulus in Submicrocrystalline copper. Mater Sci Eng A 1995; 203: 165–170.##[32]Hung Z, Gu LY, Weertman JR. Temperature Dependence of Hardness of Nanocrystalleve Copper in Lowtemperature Range. Scripta Materialia 1997; 37: 1071–1075.##]
1

The Structural and Mechanical Properties of Al2.5%wt. B4C Metal Matrix Nanocomposite Fabricated by the Mechanical Alloying
https://macs.semnan.ac.ir/article_330.html
10.22075/macs.2015.330
1
In this study, aluminum (Al) matrix reinforced with microparticles (30 µm) and nanoparticles (50 nm) boron carbide (B4C) were used to prepare Al2.5%wt., B4C nanocomposite and microcomposite, respectively, using mechanical alloying method. The mixed powders were mechanically milled at 5, 10, 15 and 20 hrs. The XRD results indicated that the crystallite sizes of both the microcomposite and nanocomposite matrix decreased with increasing milling time, showing 55 nm and 40 nm, respectively. Mechanical testing results showed an increase in the flexural strength from 98 to 164 and 115 to 180 MPa, and an increase in the hardness from 60 to 118 and 75 to 130 HV for microcomposite and nanocomposite, respectively. The results indicate that the strength and hardness of the nanocomposite are higher than those of the microcomposite due to the presence of the fine particles.
0

39
44


S.
Alalhessabi
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
Iran


S.A.
Manafi
Department of Materials Engineering, Islamic Azad University, Shahrood Branch, Shahrood, Iran
Iran


E.
Borhani
Department of NanoTechnology, Semnan University, Semnan, Iran
Iran
Mechanical properties
Al/B4C nanocomposite
Mechanical alloying
[[1] Fogagnolo JB, Robert MH, RuizNavas EM, Torralba JM. 6061 Al Reinforced with Zirconium Diboride Particles Processed by Conventional Powder Metallurgy and Mechanical Alloying. J Mater Sci 2004; 39: 127–132.##[2] Canakci A, Varol T. Production and Microstructure of AA2024B4C Metal Matrix Composites by Mechanical Alloying Method. Usak University J Mater Sci 2012; 1: 15–22.##[3] Fogagnolo JB, Velasco F, Robert MH, Torralba JM. Effect of Mechanical Alloying on The Morphology, Microstructure and Properties of Aluminium Matrix Composite Powders. Mater Sci Eng A 2003; 342: 131–143.##[4] Abdoli H, Salehi E, Faranoush H, Pourazarang K. Evolutions during Synthesis of AlAlN Nanostructured Composite Powder by Mechanical Alloying. J Alloy Compd 2008; 461: 166–172.##[5] Kaczmar JW, Pietrzak K, Wlosinsik W. The Production and Application of Metal Matrix Composite Materials. J Mater Process Technol 2000; 106: 58–67.##[6] Toptan F, Kilicarslan A, Karaaslan A, Cigdem M, Kreti I. Processing and Microstructural Characterisation of AA 1070 and AA 6063 Matrix B4Cp Reinforced Composites. Mater Des 2010; 31: 87–91.##[7] Mohanty RM, Balasubramanian K, Seshadri SK. Boron CarbideReinforced Alumnium 1100 Matrix Composites: Fabrication and Properties. Mater Sci Eng A 2008; 498: 42–52.##[8] Topcu I, Gulsov HO, Kadioglu N, Gulluoglu AN. Processing and Mechanical Properties of B4C Reinforced Al Matrix Composites. J Alloy Compd 2009; 482: 516–521.##[9] Shorowordi KM, Haseeb ASMA, Celis JP. Tribosurface Characteristics of AlB4C and AlSiC Composites Worn under Different Contact Pressures. Wear 2006; 261: 634–641.##[10] Lee KB, Sim HS, Cho SY, Kwon H. Tensile Properties of 5052 Al Matrix Composites Reinforced with B4C. Metall Mater Trans A 2001; 32: 2142–2147.##[11] Thevenot F. Boron Carbide: A Comprehensive Review. J Eur Ceram Soc 1990; 6: 205–225.##[12] Kleiner S, Bertocco F, Khalid FA, Beffort O. Decomposition of Process Control Agent during Mechanical Milling and Its Influence on Displacement Reactions in The AlTiO2 System. J Mater Chem Phys 2005; 89: 362–366. ##[13] Fathy A, Wagih A, Abd ElHamid M, Hassan AA. Effect of Mechanical Milling on the Morphology and Strutural Evaluation of AlAl2O3 Nanocomposite Powders. Int J Eng Trans A 2014, 27: 625–632.##[14] Sajjadi SA, Zebarjad SM. Influence of NanoSize Al2O3 Weight Percent on The Microstructure and Mechanical Properties of AlMatrix Nanocomposite. Powder Metall 2010; 471: 88–94.##[15] Khakbiz M, Akhlaghi F. Synthesis and Structural Characterization of AlB4C Nanocomposite Powders by Mechanical Alloying. J Alloy Compd 2009; 479: 334–341.##[16] Sharifi EM, Karimzadeh F, Enayati MH. Fabrication and Evaluation of Mechanical and Tribological Properties of Boron Carbide Reinforced Aluminum Matrix Nanocomposites. Mater Des 2011; 32: 3263–3271.##[17] Cvijovic I, Vilotijevic M, Milan TJ. Characterization of Prealloyed Copper Powders Treated in High Energy Ball Mill. Mater Charact 2006; 57: 94–99.##[18] Mahboob H, Sajjadi SA, Zebarjad SM. Nanocomposite by Mechanical Alloying and Evaluation of the Effect of Ball Milling Time on the Microstructure and Mechanical Properties. In: Proceedings of International Conference on MEMS and Nanotechnology; 2008.##[19] Hull D, Bacon DJ. Introduction to Dislocations, Butterworth Heinemann Ltd.; 2001.##[20] Alizadeh A, TaheriNassaj E,Baharvandi HR. Preparation and Investigation of Al4wt% B4C Nanocomposite Powders using Mechanical Milling. J Mater Sci 2011; 34: 1039–1048.##[21] Casati R, Vedani M. Metal Matrix Composites Reinforced by NanoParticles. J Metals 2014; 4: 65–83.##[22] Borhani E, Jafarian HR, Adachi H, Terada D, Tsuji N. Annealing Behaviour of Solution Treated and Aged Al0.2wt% Sc Deformed by ARB. Mater Sci Forum 2011; 667–669: 211–216.##[23] Moona M, Kim S, Jang J, Lee J. Orowan Strengthening Effect on The Nanoindentation Hardness of The Ferrite Matrix in Microalloyed Steels. Mater Sci Eng A 2008; 487(1–2): 552–557.##[1] Fogagnolo JB, Robert MH, RuizNavas EM, Torralba JM. 6061 Al Reinforced with Zirconium Diboride Particles Processed by Conventional Powder Metallurgy and Mechanical Alloying. J Mater Sci 2004; 39: 127–132.##[2] Canakci A, Varol T. Production and Microstructure of AA2024B4C Metal Matrix Composites by Mechanical Alloying Method. Usak University J Mater Sci 2012; 1: 15–22.##[3] Fogagnolo JB, Velasco F, Robert MH, Torralba JM. Effect of Mechanical Alloying on The Morphology, Microstructure and Properties of Aluminium Matrix Composite Powders. Mater Sci Eng A 2003; 342: 131–143.##[4] Abdoli H, Salehi E, Faranoush H, Pourazarang K. Evolutions during Synthesis of AlAlN Nanostructured Composite Powder by Mechanical Alloying. J Alloy Compd 2008; 461: 166–172.##[5] Kaczmar JW, Pietrzak K, Wlosinsik W. The Production and Application of Metal Matrix Composite Materials. J Mater Process Technol 2000; 106: 58–67.##[6] Toptan F, Kilicarslan A, Karaaslan A, Cigdem M, Kreti I. Processing and Microstructural Characterisation of AA 1070 and AA 6063 Matrix B4Cp Reinforced Composites. Mater Des 2010; 31: 87–91.##[7] Mohanty RM, Balasubramanian K, Seshadri SK. Boron CarbideReinforced Alumnium 1100 Matrix Composites: Fabrication and Properties. Mater Sci Eng A 2008; 498: 42–52.##[8] Topcu I, Gulsov HO, Kadioglu N, Gulluoglu AN. Processing and Mechanical Properties of B4C Reinforced Al Matrix Composites. J Alloy Compd 2009; 482: 516–521.##[9] Shorowordi KM, Haseeb ASMA, Celis JP. Tribosurface Characteristics of AlB4C and AlSiC Composites Worn under Different Contact Pressures. Wear 2006; 261: 634–641.##[10] Lee KB, Sim HS, Cho SY, Kwon H. Tensile Properties of 5052 Al Matrix Composites Reinforced with B4C. Metall Mater Trans A 2001; 32: 2142–2147.##[11] Thevenot F. Boron Carbide: A Comprehensive Review. J Eur Ceram Soc 1990; 6: 205–225.##[12] Kleiner S, Bertocco F, Khalid FA, Beffort O. Decomposition of Process Control Agent during Mechanical Milling and Its Influence on Displacement Reactions in The AlTiO2 System. J Mater Chem Phys 2005; 89: 362–366. ##[13] Fathy A, Wagih A, Abd ElHamid M, Hassan AA. Effect of Mechanical Milling on the Morphology and Strutural Evaluation of AlAl2O3 Nanocomposite Powders. Int J Eng Trans A 2014, 27: 625–632.##[14] Sajjadi SA, Zebarjad SM. Influence of NanoSize Al2O3 Weight Percent on The Microstructure and Mechanical Properties of AlMatrix Nanocomposite. Powder Metall 2010; 471: 88–94.##[15] Khakbiz M, Akhlaghi F. Synthesis and Structural Characterization of AlB4C Nanocomposite Powders by Mechanical Alloying. J Alloy Compd 2009; 479: 334–341.##[16] Sharifi EM, Karimzadeh F, Enayati MH. Fabrication and Evaluation of Mechanical and Tribological Properties of Boron Carbide Reinforced Aluminum Matrix Nanocomposites. Mater Des 2011; 32: 3263–3271.##[17] Cvijovic I, Vilotijevic M, Milan TJ. Characterization of Prealloyed Copper Powders Treated in High Energy Ball Mill. Mater Charact 2006; 57: 94–99.##[18] Mahboob H, Sajjadi SA, Zebarjad SM. Nanocomposite by Mechanical Alloying and Evaluation of the Effect of Ball Milling Time on the Microstructure and Mechanical Properties. In: Proceedings of International Conference on MEMS and Nanotechnology; 2008.##[19] Hull D, Bacon DJ. Introduction to Dislocations, Butterworth Heinemann Ltd.; 2001.##[20] Alizadeh A, TaheriNassaj E,Baharvandi HR. Preparation and Investigation of Al4wt% B4C Nanocomposite Powders using Mechanical Milling. J Mater Sci 2011; 34: 1039–1048.##[21] Casati R, Vedani M. Metal Matrix Composites Reinforced by NanoParticles. J Metals 2014; 4: 65–83.##[22] Borhani E, Jafarian HR, Adachi H, Terada D, Tsuji N. Annealing Behaviour of Solution Treated and Aged Al0.2wt% Sc Deformed by ARB. Mater Sci Forum 2011; 667–669: 211–216.##Moona M, Kim S, Jang J, Lee J. Orowan Strengthening Effect on The Nanoindentation Hardness of The Ferrite Matrix in Microalloyed Steels. Mater Sci Eng A 2008; 487(1–2): 552–557.##]
1

Static Flexure of Soft Core Sandwich Beams using Trigonometric Shear Deformation Theory
https://macs.semnan.ac.ir/article_331.html
10.22075/macs.2015.331
1
This study deals with the applications of a trigonometric shear deformation theory considering the effect of the transverse shear deformation on the static flexural analysis of the soft core sandwich beams. The theory gives realistic variation of the transverse shear stress through the thickness, and satisfies the transverse shear stress free conditions at the top and bottom surfaces of the beam. The theory does not require a problemdependent shear correction factor. The governing differential equations and the associated boundary conditions of the present theory are obtained using the principle of the virtual work. The closedform solutions for the beams with simply supported boundary conditions are obtained using Navier solution technique. Several types of sandwich beams are considered for the detailed numerical study. The axial displacement, transverse displacement, normal and transverse shear stresses are presented in a nondimensional form and are compared with the previously published results. The transverse shear stress continuity is maintained at the layer interface, using the equilibrium equations of elasticity theory.
0

45
53


Atteshamuddin S.
Sayyad
Department of Civil Engineering, SRES’s College of Engineering, Savitribai Phule Pune University, Kopargaon, Maharashtra, India
Iran
attu_sayyad@yahoo.co.in


Y.M.
Ghugal
Department of Applied Mechanics, Government College of Engineering, Karad, Maharashtra, India
Iran
ghugal@rediffmail.com
Laminated beam
Soft core
Sandwich beam
Flexure
Trigonometric shear deformation theory
[[1] Timoshenko SP. On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars. Philos Mag 1921; 41(6): 742–746.##[2] Lo KH, Christensen RM, Wu EM. A Highorder Theory of Plate Deformation, Part1: Homogeneous Plates, ASME J Appl Mech 1977; 44: 663–668.##[3] Lo KH, Christensen RM, Wu EM. A Highorder Theory of Plate Deformation, Part2: Laminated Plates, ASME J Appl Mech 1977; 44: 669–676.##[4] Levinson M. A New Rectangular Beam Theory. J Sound Vib 1981; 74: 81–87.##[5] Reddy JN. A Simple Higher Order Theory for Laminated Composite Plates. ASME J Appl Mech 1984; 51: 745–752.##[6] Touratier M. An Efficient Standard Plate Theory. Int J Eng Sci 1991; 29(8): 901–916.##[7] Soldatos KP. A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates. Acta Mech 1992; 94: 195–200.##[8] Karama M, Afaq KS, Mistou S. A Refinement of Ambartsumian Multilayer Beam Theory. Comput Struct 2008; 86: 839–849.##[9] Sayyad AS. Comparison of Various Refined Beam Theories for the Bending and Free Vibration Analysis of Thick Beams. Appl Comput Mech 2011; 5: 217–230.##[10] Sayyad AS., Ghugal YM, Borkar RR. Flexural Analysis of Fibrous Composite Beams under Various Mechanical Loadings using Refined Shear Deformation Theories. Compos Mech Comput Appl 2014; 5(1): 1–19.##[11] Sayyad AS. Static Flexure and Free Vibration Analysis of Thick Isotropic Beams using Different Higher Order Shear Deformation Theories. Int J Appl Math Mech 2012; 8(14): 71–87.##[12] Mechab I, Tounsi A, Benatta MA, Bedia EAA. Deformation of Short Composite Beam using Refined Theories. J Math Anal Appl 2008; 346: 468–479.##[13] Carrera E, Giunta G. Refined Beam Theories based on A Unified Formulation, Int J Appl Mech 2010; 2(1): 117–143.##[14] Carrera E, Filippi M, Zappino E. Laminated Beam Analysis by Polynomial, Trigonometric, Exponential and Zigzag Theories. Eur J Mech A Solids 2013; 41: 58–69.##[15] Carrera E, Filippi M, Zappino E. Free Vibration Analysis of Laminated Beam by Polynomial, Trigonometric, Exponential and Zigzag Theories. J Compos Mater 2014; 48(19): 2299–2316.##[16] Giunta G, Metla N, Belouettar S, Ferreira AJM, Carrera E. A ThermoMechanical Analysis of Isotropic and Composite Beams via Collocation with Radial Basis Functions. J Therm Stresses 2013; 36: 1169–1199.##[17] Chakrabarti A, Chalak HD, Iqbal MA, Sheikh AH. A New FE Model based on Higher Order Zigzag Theory for the Analysis of Laminated Sandwich Beam with Soft Core. Compos Struct 2011; 93: 271–279.##[18] Chalak HD, Chakrabarti A, Iqbal MA, Sheikh AH. Vibration of Laminated Sandwich Beams Having Soft Core, J Vib Control 2011; 18(10): 1422–1435.##[19] Gherlone M, Tessler A, Sciuva MD. A C0 Beam Elements based on the Refined Zigzag Theory for Multilayered Composite and Sandwich Laminates. Compos Struct 2011; 93: 2882–2894.##[20] Shimpi RP, Ghugal YM. A New Layerwise Trigonometric Shear Deformation Theory for Twolayered Crossply Beams. Compos Sci Technol 2001; 61: 1271–1283.##[21] Ghugal YM, Shinde SB. Flexural Analysis of Crossply Laminated Beams using Layerwise Trigonometric Shear Deformation Theory. Latin Am J Solids Struct 2013; 10(4): 675–705.##[22] Arya H. A New Zigzag Model for Laminated Composite Beams: Free Vibration Analysis. J Sound Vib 2003; 264: 485–490.##[23] Sayyad AS, Ghugal YM. Effect of Transverse Shear and Transverse Normal Strain on Bending Analysis of Crossply Laminated Beams. Int J Appl Math Mech 2011; 7(12): 85–118.##[24] Mantari JL, Oktem AS, Soares CG. A New Trigonometric Shear Deformation Theory for Isotropic, Laminated Composite and Sandwich Plates. Int J Solids Struct 2012; 49(1): 43–53.##[25] Ferreira AJM, Roque CMC, Jorge RMN. Analysis of Composite Plates by Trigonometric Shear Deformation Theory and Multiquadrics. Comput Struct 2005; 83(27): 2225–2237.##[26] Zenkour AM. Benchmark Trigonometric and 3D Elasticity Solutions for an Exponentially Graded Thick Rectangular Plate. Arch Appl Mech 2007; 77: 197–214.##[27] Sayyad AS, Ghugal YM, Naik NS. Bending Analysis of Laminated Composite and Sandwich Beams according to Refined Trigonometric Beam Theory. Curved and Layered Struct 2015; 2: 279–289.##[28] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Procedia Eng 2013; 51: 1–7.##[29] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Int J Sci Res Publ 2012; 2(11): 1–7.##[30] Ghugal YM, Dahake AG. Flexure of Cantilever Thick Beams using Trigonometric Shear Deformation Theory. Int J Mech Aerosp Ind Mechatronic Manuf Eng 2013; 7(5): 380–389.##[31] Pagano NJ. Exact Solutions for Composite Laminates in Cylindrical Bending. Compos Mater 1969; 3: 398–411.##[1] Timoshenko SP. On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars. Philos Mag 1921; 41(6): 742–746.##[2] Lo KH, Christensen RM, Wu EM. A Highorder Theory of Plate Deformation, Part1: Homogeneous Plates, ASME J Appl Mech 1977; 44: 663–668.##[3] Lo KH, Christensen RM, Wu EM. A Highorder Theory of Plate Deformation, Part2: Laminated Plates, ASME J Appl Mech 1977; 44: 669–676.##[4] Levinson M. A New Rectangular Beam Theory. J Sound Vib 1981; 74: 81–87.##[5] Reddy JN. A Simple Higher Order Theory for Laminated Composite Plates. ASME J Appl Mech 1984; 51: 745–752.##[6] Touratier M. An Efficient Standard Plate Theory. Int J Eng Sci 1991; 29(8): 901–916.##[7] Soldatos KP. A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates. Acta Mech 1992; 94: 195–200.##[8] Karama M, Afaq KS, Mistou S. A Refinement of Ambartsumian Multilayer Beam Theory. Comput Struct 2008; 86: 839–849.##[9] Sayyad AS. Comparison of Various Refined Beam Theories for the Bending and Free Vibration Analysis of Thick Beams. Appl Comput Mech 2011; 5: 217–230.##[10] Sayyad AS., Ghugal YM, Borkar RR. Flexural Analysis of Fibrous Composite Beams under Various Mechanical Loadings using Refined Shear Deformation Theories. Compos Mech Comput Appl 2014; 5(1): 1–19.##[11] Sayyad AS. Static Flexure and Free Vibration Analysis of Thick Isotropic Beams using Different Higher Order Shear Deformation Theories. Int J Appl Math Mech 2012; 8(14): 71–87.##[12] Mechab I, Tounsi A, Benatta MA, Bedia EAA. Deformation of Short Composite Beam using Refined Theories. J Math Anal Appl 2008; 346: 468–479.##[13] Carrera E, Giunta G. Refined Beam Theories based on A Unified Formulation, Int J Appl Mech 2010; 2(1): 117–143.##[14] Carrera E, Filippi M, Zappino E. Laminated Beam Analysis by Polynomial, Trigonometric, Exponential and Zigzag Theories. Eur J Mech A Solids 2013; 41: 58–69.##[15] Carrera E, Filippi M, Zappino E. Free Vibration Analysis of Laminated Beam by Polynomial, Trigonometric, Exponential and Zigzag Theories. J Compos Mater 2014; 48(19): 2299–2316.##[16] Giunta G, Metla N, Belouettar S, Ferreira AJM, Carrera E. A ThermoMechanical Analysis of Isotropic and Composite Beams via Collocation with Radial Basis Functions. J Therm Stresses 2013; 36: 1169–1199.##[17] Chakrabarti A, Chalak HD, Iqbal MA, Sheikh AH. A New FE Model based on Higher Order Zigzag Theory for the Analysis of Laminated Sandwich Beam with Soft Core. Compos Struct 2011; 93: 271–279.##[18] Chalak HD, Chakrabarti A, Iqbal MA, Sheikh AH. Vibration of Laminated Sandwich Beams Having Soft Core, J Vib Control 2011; 18(10): 1422–1435.##[19] Gherlone M, Tessler A, Sciuva MD. A C0 Beam Elements based on the Refined Zigzag Theory for Multilayered Composite and Sandwich Laminates. Compos Struct 2011; 93: 2882–2894.##[20] Shimpi RP, Ghugal YM. A New Layerwise Trigonometric Shear Deformation Theory for Twolayered Crossply Beams. Compos Sci Technol 2001; 61: 1271–1283.##[21] Ghugal YM, Shinde SB. Flexural Analysis of Crossply Laminated Beams using Layerwise Trigonometric Shear Deformation Theory. Latin Am J Solids Struct2013; 10(4): 675–705.##[22] Arya H. A New Zigzag Model for Laminated Composite Beams: Free Vibration Analysis. J Sound Vib 2003; 264: 485–490.##[23] Sayyad AS, Ghugal YM. Effect of Transverse Shear and Transverse Normal Strain on Bending Analysis of Crossply Laminated Beams. Int J Appl Math Mech 2011; 7(12): 85–118.##[24] Mantari JL, Oktem AS, Soares CG. A New Trigonometric Shear Deformation Theory for Isotropic, Laminated Composite and Sandwich Plates. Int J Solids Struct 2012; 49(1): 43–53.##[25] Ferreira AJM, Roque CMC, Jorge RMN. Analysis of Composite Plates by Trigonometric Shear Deformation Theory and Multiquadrics. Comput Struct 2005; 83(27): 2225–2237.##[26] Zenkour AM. Benchmark Trigonometric and 3D Elasticity Solutions for an Exponentially Graded Thick Rectangular Plate. Arch Appl Mech 2007; 77: 197–214.##[27] Sayyad AS, Ghugal YM, Naik NS. Bending Analysis of Laminated Composite and Sandwich Beams according to Refined Trigonometric Beam Theory. Curved and Layered Struct 2015; 2: 279–289.##[28] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Procedia Eng 2013; 51: 1–7.##[29] Dahake AG, Ghugal YM. A Trigonometric Shear Deformation Theory for Flexure of Thick Beams. Int J Sci Res Publ 2012; 2(11): 1–7.##[30] Ghugal YM, Dahake AG. Flexure of Cantilever Thick Beams using Trigonometric Shear Deformation Theory. Int J Mech Aerosp Ind Mechatronic Manuf Eng2013; 7(5): 380–389.##[31] Pagano NJ. Exact Solutions for Composite Laminates in Cylindrical Bending. Compos Mater 1969; 3: 398–411.##]
1

Adaptive Tunable Vibration Absorber using Shape Memory Alloy
https://macs.semnan.ac.ir/article_332.html
10.22075/macs.2015.332
1
This study presents a new approach to control the nonlinear dynamics of an adaptive absorber using shape memory alloy (SMA) element. Shape memory alloys are classified as smart materials that can remember their original shape after deformation. Stress and temperatureinduced phase transformations are two typical behaviors of shape memory alloys. Changing the stiffness associated with phase transformations causes these properties of SMA. A thermomechanical model (based on the transformation strain which is a measure of strain indicating the phase transformation) is used to constrain the general thermomechanical features of the SMA. Here, the onedimensional SMA model is adopted to calculate both the pseudoelastic response and the shape memory effects. The dynamic behavior of shape memory alloys is then investigated, and a Newmark method is adopted to analyze the nonlinear dynamic equations. Results demonstrate that the vibration of an initial system can be tuned using the SMA absorber in a wide range of frequencies. Therefore, SMAs as adaptive tuned vibration absorbers provide an excellent performance to control vibrations.
0

55
60


Shirko
Faroughi
Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
Iran
sh.faroughi@uut.ac.ir
Shape memory alloy
Vibration absorber
Phase transformation
Nonlinear dynamic
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1

Free Vibration of Lattice Cylindrical Composite Shell Reinforced with Carbon Nanotubes
https://macs.semnan.ac.ir/article_333.html
10.22075/macs.2015.333
1
The free vibration of the lattice cylindrical composite shell reinforced with Carbon Nanotubes (CNTs) was studied in this study. The theoretical formulations are based on the Firstorder Shear Deformation Theory (FSDT) and then by enforcing the Galerkin method, natural frequencies are obtained. In order to estimate the material properties of the reinforced polymer with nanotubes, the modified HalpinTsai equations were used and the results were checked with an experimental investigation. Also, the smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of the shell in order to obtain the equivalent stiffness of the whole structure. The effect of the weight fraction of the CNTs and also the ribs angle on the natural frequency of the structure is investigated in two types of length to diameter ratios in the current study. Finally, the results which are obtained from the analytical solution are checked with the FEM method using ABAQUS CAE software, and a good agreement has been seen between the FEM and the analytical results.
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J.
Emami
Composite Materials and Technology Center, MalekAshtar University of Technology, Tehran, Iran
Iran
javademami90@gmail.com


J.
Eskandari Jam
Composite Materials and Technology Center, MalekAshtar University of Technology, Tehran, Iran
Iran
eskandari@mut.ac.ir


M.R.
Zamani
Composite Materials and Technology Center, MalekAshtar University of Technology, Tehran, Iran
Iran


A.
Davar
Composite Materials and Technology Center, MalekAshtar University of Technology, Tehran, Iran
Iran
Carbon nanotubes
Lattice structures
Modified HalpinTsai equations
Free vibration
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