2015
46
1
1
91
1

Nonlinear FlowInduced Flutter Instability of Double CNTs Using Reddy Beam Theory
https://jcamech.ut.ac.ir/article_53388.html
10.22059/jcamech.2015.53388
1
In this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (CNT) system have been investigated. The ViscoPasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. Both of the CNTs convey a viscose fluid and a uniform longitudinal magnetic field is applied to them. The fluid velocity is modified by smallsize effects on the bulk viscosity and the slip boundary conditions of nano flow through the Knudsen number (Kn). Using von Kármán geometric nonlinearity, Hamilton’s principle and considering longitudinal magnetic field, the nonlinear higher order governing equations for Reddy beam (RB) theory are derived. The differential quadrature method (DQM) is used to obtain the nonlinear frequency and critical fluid velocity (CFV) of the fluid conveying a coupled system. A detailed parametric study is conducted, focusing on the effects of parameters such as magnetic field strength, Knudsen number, aspect ratio, small scale and elastic foundation on the inphase and outofphase vibration of the nanotube. The results indicate that the natural frequency and the critical fluid velocity of double bonded Reddy beams increase with an increase in the longitudinal magnetic field and elastic medium module. Furthermore, the results of this study can be useful for designing and manufacturing micro/nano doublemechanical systems in advanced mechanics applications by controlling nonlinear frequency with an applied magnetic field.
0

1
12


Ali
Ghorbanpour Arani
Professor, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
aghorban@kashanu.ac.ir


Saeed
Amir
Assistant of professor, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
samir@kashanu.ac.ir


Abbas
Karamali Ravandia
MS Graduate, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
abbas_karamali2007@yahoo.com
conveying fluid
double nanosystem
flutter phenomena
Nonlinear vibration
Nonlocal Theory
Reddy beam
[[1].Reddy J.N., 2007, Nonlocal theories for bending, buckling and vibration of beams, Int. J. Sci. Technol. 45: 288307.##[2].Reddy J. N., Wang C. M., 2004, Dynamics of fluidconveying beams, Centre for Offshore Research and Engineering, National University of Singapore, CORE Report: 121.##[3].Wang L., Ni Q., 2008, On vibration and instability of carbon nanotubes conveying fluid, Comput. Mater. Sci. 43: 399402.##[4].Chang T.P., 2012, Thermalmechanical vibration and instability of a fluidconveying singlewalled carbon nanotubes embedded in an elastic medium based on nonlocal elasticity theory, Appl. Math. Modell. 36: 19641973.##[5].Ghorbanpour Arani A., Zarei M. Sh., Amir S., Khoddami Maraghi Z., 2013, nonlinear nonlocal vibration embedded DWCNT conveying fluid using shell model, Physica B. 410: 188196.##[6].GhorbanpourArani A., Amir S., 2014, Electrothermal vibration of viscoelastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory, Physica B. 419: 1–6.##[7].Murmu T., Adhikari S., 2011, Axial instability of doublenanobeamsystems, Phys. Lett. A. 375: 601608.##[8].Simsek M., 2011, Nonlocal effects in the forced vibration of an elastically connected doublecarbon nanotube system under a moving nanoparticle, Comput. Mater. Sci. 50: 21122123.##[9].Murmu T., Adhikari S., 2012, Nonlocal elasticity based vibration of initially prestressed coupled nanobeam systems, Eur. J. Mech. A. Solids 34: 5262.##[10]. Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of doublewalled carbon nanotubes conveying fluid, Comput. Mater. Sci. 45: 745756.##[11]. Wang H., Dong K., Men F., Yan Y.J., Wang X., 2010, Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix, Appl. Math. Modell. 34: 878889.##[12]. Wang L., Ni Q, 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscose fluid, Mech. Res. Commun. 36: 833837.##[13]. Beskok A., Karniadakis G.E., 1999, A model for flows in channels, pipes and ducts at micro and nano scale, Microscale Thermophys. Eng. 3: 4377.##[14]. Rashidi V., Mirdamadi H.R., Shirani E., 2012, A novel model for vibrations of nanotubes conveying nanoflow, Comput. Mater. Sci. 51: 347352.##[15]. Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys. 54: 4703 4710.##[16]. Ke L.L., Wang Y.Sh., 2011, Flowinduced vibration and instability of embedded doublewalled carbon nanotubes based on a modified couple stress theory, Physica E. 43: 10311039.##[17]. Karami G., Malekzadeh P., 2002, A new differential quadrature methodology for beam analysis and the associated differential quadrature element method, Comput. Methods Appl. Mech. Eng. 191: 35093526.##[18]. Ke L.L., Xiang Y., Yang J., Kitipornchai S., 2009, Nonlinear free vibration of embedded doublewalled carbon nanotubes based on nonlocal Timoshenko beam theory, Comput. Mater.Sci. 47: 409417.##[19]. Chang W. J., Lee H. L., 2009, Free vibration of a singlewalled carbon nanotube containing a fluid flow using the Timoshenko beam model, Phys. Lett. A. 373: 982985.##]
1

Numerical Simulation of Nugget Geometry and Temperature Distribution in Resistance Spot Welding
https://jcamech.ut.ac.ir/article_53389.html
10.22059/jcamech.2015.53389
1
Resistance spot welding is an important manufacturing process in the automotive industry for assembling bodies. The quality and strength of the welds and, by extension, the body is mainly defined by the quality of the weld nuggets. The most effective parameters in this process are sheet material, geometry of electrodes, electrode force, current intensity, welding time and sheet thickness. The present research examined the effect of process parameters on nugget formation. A mechanical/ electrical/ thermal coupled model was created in a finite element analysis environment. The effect of welding time and current, electrode force, contact resistivity and sheet thickness was simulated to investigate the effect of these parameters on temperature of the faying surface. The physical properties of the material were defined as nonlinear and temperature dependent. The shape and size of the weld nuggets were computed and compared with experimental results from published articles. The proposed methodology allows prediction of the quality and shape of the weld nuggets as process parameters are varied. It can assist in adjusting welding parameters that eliminates the need for costly experimentation. This process can be economically optimized to manufacture quality automotive bodies.
0

13
19


Mohsen
Hamedi
Associate Professor, School of Mechanical Engineering, University of Tehran, Tehran, Iran
Iran
mhamedi@ut.ac.ir


Hamid
Eisazadeh
MS Graduate, School of Mechanical Engineering, University of Tehran, Tehran, Iran
Iran
heisazadeh@gmail.com
nugget size
resistance spot welding
thermoelectromechanical analysis
[[1].Bentley K.P., Greenwood J. A., McK Knowlson P., 1963, Temperature distribution in spot welding, British Welding Journal 12: 613619.##[2].Greenwood J. A., 1963, Temperature in spot welding, British Welding Journal 6: 316322.##[3].Nagel Lee, Nagel G. L., 1988, Basic phenomena in resistance spot welding, Society of Automotive Engineers Technical Paper. No. 880277.##[4].Cho H. S., Cho Y. J., 1989, A study of the thermal behavior in resistance spot welds, Welding Journal 68: 236s244s.##[5].Kim E., Eager T. W., 1988, Transient thermal behavior in resistance spot welding, sheet metal, in: Welding Conference Ш, Detroit, MI.##[6].Nied H. A., 1984, The finite element modeling of the resistance spot welding process, Welding Journal 63(4): 123.##[7].Gould J. E., 1994, An examination of nugget development during spot welding using both experimental and analytical techniques, Welding Journal 66(1): 110.##[8].Tsai C. L., Jammal O. A., Dickinson D. W., 1992, Modeling of resistance spot weld nugget growth, Welding Journal 71(2): 47s54s.##[9].Tsai C. L., Jammal O. A., Dickinson D. W., 1989, Study of nugget formation in resistance spot welding using finite element method, Paper presented at the trends in welding research, in: 2nd International Conference. Materials Park, OH., USA.##[10]. Khan J.A., Xu L., Chao Y., Broach K., 2000, Numerical simulation of resistance spot welding process, Numerical Heat Transfer, Part A 37: 425–446.##[11]. Richard D., Fafard M., Lacroix R., Clery P., Maltais Y., 2003, Carbon to cast iron electrical contact resistance constitutive model for finite element analysis, J. Mater. Process. Technol. 132: 119–131.##[12]. Chang B. H., Zhou Y., 2003, Numerical study on the effect of electrode force in smallscale resistance spot welding, J. Mater. Process. Technol. 139 (1–3): 635–641.##[13]. Feulvarch E., Robin V., Bergheau J.M., 2004, Resistance spot welding simulation: a general finite element formulation of electrothermal contact conditions, J. Mater. Process. Technol. 153–154: 436–441.##[14]. Hou Z., Kim I., 2007, Finite element analysis for the mechanical features of resistance spot welding process, J. Mater. Process. Technol. 180: 160165.##]
1

Optimal Design of ShellandTube Heat Exchanger Based on Particle Swarm Optimization Technique
https://jcamech.ut.ac.ir/article_53390.html
10.22059/jcamech.2015.53390
1
The paper studies optimization of shellandtube heat exchangers using the particle swarm optimization technique. A total cost function is formulated based on initial and annual operating costs of the heat exchangers. Six variables – shell inside diameter, tube diameter, baffle spacing, baffle cut, number of tube passes and tube layouts (triangular or square) – are considered as the design parameters. The particle swarm optimization selects the parameters so that the system has minimum total cost. Although generalization is not possible for any case, for minimization of cost functions of the three different cases studied in this research, larger tube outer diameter, triangular layout, baffle cut equalling 0.25 of shell diameter and one pass for each tube result in optimum designs. The other two parameters show no fixed trend.
0

21
29


Seddigheh
Jalilirad
Department of Mechatronics Engineering, College of Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
Iran
s.jalilirad@hotmail.com


Mohammad Hassan
Cheraghali
Department of Mechatronics Engineering, College of Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
Iran
mhcheraghali@gmail.com


Hossein
Ahmadi Danesh Ashtiani
Department of Mechatronics Engineering, College of Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
Iran
hadashtiani@gmail.com
Heat exchanger
shell and tube
particle swarm optimization
[[1]. Selbas, R., Kizilkan, O., Reppich, M., “A new design approach for shellandtube heat exchangers using genetic algorithms from economic point of view”, Chem. Eng. Proc., 45, 268–275 (2006).##[2]. Muralikrishna K., Shenoy, U. V., “Heat exchanger design targets for minimum area and cost”, Institution of Chemical Engineers Trans IChemE, 78, 161167 (2000).##[3]. Ali Kara, Y., Guraras, O., “A computer program for designing of shellandtube heat exchangers”, Applied Thermal Engineering, 24, 1797–1805 (2004).##[4]. Serna, M., Jimenez, A., “A compact formulation of the belldelaware method for heat exchanger design and optimization”, Institution of Chemical Engineers Trans IChemE, 83, 539550 (2005).##[5]. Eryener, D., “Thermoeconomic optimization of baffle spacing for shell and tube heat exchanger”, Energy Conversion and Management 47, 1478–1489 (2006).##[6]. Ozcelik, Y., “Exergetic optimization of shell and tube heat exchangers Using a genetic based algorithm”, Applied Thermal Engineering, 27, 1849–1856 (2007).##[7]. Babu, B.V., Munawar, S. A., “Differential evolution Strategies for optimal design of shellandtube heat exchangers”, Chemical Engineering Science, 62, 3720 –3739 (2007).##[8]. Costa, A. L .H., Queiroz, E. M., “Design optimization of shellandtube heat exchangers”, Applied Thermal Engineering, 28, 1798–1805 (2008).##[9]. Guo, J., Cheng, L., Xu, M., “Optimization Design of ShellandTube Heat Exchanger by Entropy Generation Minimization and Genetic Algorithm”, Applied Thermal Engineering, 29, 2954–2960 (2009).##[10]. Engelbrecht, A. P., Computational Intelligence, John Wiley & Sons Ltd, USA (2007).##[11]. TEMA, Standard of tubular exchanger manufacturers association, Tarrytown, NY (1988).##[12]. Lee, P. S., Garimella, S.V., Liu, D., “Investigation of heat transfer in rectangular microchannels”, Int. J. of Heat and Mass Transfer, 48, 1688–1704 (2005).##[13]. Kern, D. Q., Process Heat Transfer, McGrawHill, New York (1950).##[14]. Hewitt, G.F., Heat Exchanger Design Handbook, Begell House, New York (1998).##[15]. Sinnott, R.K., Chemical Engineering Design, vol. 6, ButterworthHeinemann (2005).##[16]. Taal, M., Bulatov, I., Klemes, J., Stehlik, P., “Cost estimation and energy price forecast for economic evaluation of retrofit projects”, Applied Thermal Engineering, 23, 1819–1835 (2003).##[17]. Haupt, R., Haupt, S., Practical Genetic Algorithm, Wiley Publication, USA (2004).##[18]. R. Hassan, B. Cohanim, O. De Weck, and G. Venter, “A comparison of particle swarm optimization and the genetic algorithm,” in Proceedings of the 1st AIAA multidisciplinary design optimization specialist conference, 18–21 (2005).##[19]. J. Vesterstrom and R. Thomsen, “A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems,” in Evolutionary Computation, CEC2004. Congress, 2, 1980–1987 (2004).##[20]. S. Panda and N. P. Padhy, “Comparison of particle swarm optimization and genetic algorithm for FACTSbased controller design,” Applied soft computing, 8, 1418–1427 (2008).##[21]. Caputo, A. C., Pelagagge, P. M., Salini, P., “Heat exchanger design based on economic optimization”, Applied Thermal Engineering, 28, 1151–1159 (2008).##]
1

Energy Dissipation Rate Control Via a SemiAnalytical Pattern Generation Approach for Planar ThreeLegged Galloping Robot based on the Property of Passive Dynamic Walking
https://jcamech.ut.ac.ir/article_53391.html
10.22059/jcamech.2015.53391
1
In this paper an Energy Dissipation Rate Control (EDRC) method is introduced, which could provide stable walking or running gaits for legged robots. This method is realized by developing a semianalytical pattern generation approach for a robot during each Single Support Phase (SSP). As yet, several control methods based on passive dynamic walking have been proposed by researchers to provide an efficient humanlike biped walking robot. For most of these passive based controllers the main idea is to shape the robot’s energy level during each SSP to restore the mechanical energy which has been lost in the previous Impact Phases (IP); however, the EDRC method provides stable gaits for legged robots just by controlling the robot’s energy level during each IP. In this paper EDRC is applied to a SixLink ThreePoint Foot (6L3PF) model, to realize an active dynamic galloping gait on level ground. As the pointfoot contact assumption for the 6L3PF imposes one degree of underactuation in the ankle joint, it is not clear how to specify the forward kinematic defining the swing leg position and velocity as a function of actuated joint angles. So, a new strategy for solving the dynamic and kinematic equations of the robot is introduced for deriving suitable joint trajectories during each SSP. Simulation results show that the proposed methods in this paper are effective and the robot exhibits a stable dynamic galloping gait on level ground.
0

31
39


Mohsen
Azimi
M.Sc. Student, School of Mechanical Engineering College of Engineering, University of Tehran, Tehran, Iran
Iran
azimi_mohsen@ut.ac.ir


Mohammad Reza
Hairi Yazdi
Associate Professor, School of Mechanical Engineering College of Engineering, University of Tehran, Tehran, Iran
Iran
myazdi@ut.ac.ir
Inverted Pendulum Model (IPM)
passive dynamic walking
pointfoot contact assumption
semianalytical pattern generation
[[1].McGeer, T., 1990, “Passive Dynamic Walking,”##Int. J. Rob. Res., 9(2), pp. 62–82.##[2].McGeer, T., 1990, “Passive walking with##knees,” Robotics and Automation, 1990.##Proceedings., 1990 IEEE International##Conference on, IEEE, pp. 1640–1645.##[3].Kamath, a. K., and Singh, N. M., 2009, “Impact##dynamics based control of compass gait biped,”##2009 Am. Control Conf., (1), pp. 4357–4360.##[4].Farrell, M., “Control of the Compass Biped via##Hip Actuation and Weight Perturbation for##Small Angles and Level Ground Walking,”##media.mit.edu.##[5].Spong, M., 1999, “Passivity based control of the##compass gait biped,” Proc. IFAC World Congr.##Beijing, China, pp. 19–24.##[6].Spong, M. W., and Bhatia, G., 2003, “Further ##results on control of the compass gait biped,” Proc. 2003 IEEE/RSJ Int. Conf. Intell. Robot. Syst. (IROS 2003) (Cat. No.03CH37453), 2. [7].Asano, F., and Yamakita, M., 2001, “Virtual gravity and coupling control for robotic gait synthesis,” IEEE Trans. Syst. Man, Cybern.  Part A Syst. Humans, 31(6), pp. 2–7. [8].Asano, F., Yamakita, M., Kamamichi, N., and Luo, Z.W., 2004, “A Novel Gait Generation for Biped Walking Robots Based on Mechanical Energy Constraint,” IEEE Trans. Robot. Autom., 20(3), pp. 565–573. [9].Asano, F., and Yamakita, M., 2005, “Biped gait generation and control based on a unified property of passive dynamic walking,” IEEE Trans. Robot., 21(4), pp. 754–762. [10]. Asano, F., and Luo, Z., 2006, “On EnergyEfficient and HighSpeed Dynamic Biped Locomotion with Semicircular Feet,” 2006 IEEE/RSJ Int. Conf. Intell. Robot. Syst., pp. 5901–5906. [11]. Harata, Y., Asano, F., Luo, Z.W., Taji, K., and Uno, Y., 2007, “Biped gait generation based on parametric excitation by kneejoint actuation,” 2007 IEEE/RSJ Int. Conf. Intell. Robot. Syst., pp. 2198–2203.##[12]. Shkolnik, A., and Tedrake, R., 2007, “Inverse Kinematics for a PointFoot Quadruped Robot with Dynamic Redundancy Resolution,” Proc. 2007 IEEE Int. Conf. Robot. Autom., pp. 4331–4336. [13]. Kuo, A. D., 2007, “The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective,” Hum. Mov. Sci., 26(4), pp. 617–656. [14]. Griffin, T. M., Main, R. P., and Farley, C. T., 2004, “Biomechanics of quadrupedal walking: how do fourlegged animals achieve inverted pendulumlike movements?,” J. Exp. Biol., 207(Pt 20), pp. 3545–58. [15]. Mu, X., and Wu, Q., 2006, “On impact dynamics and contact events for biped robots via impact effects.,” IEEE Trans. Syst. Man. Cybern. B. Cybern., 36(6), pp. 1364–1372. [16]. Shah, S., Saha, S., and Dutt, J., 2012, “Modular framework for dynamic modeling and analyses of legged robots,” Mech. Mach. Theory, 49, pp. 234–255.##[17]. Wang, X., Li, M., Wang, P., Guo, W., and Sun, L., 2012, “BioInspired Controller for a Robot Cheetah with a Neural Mechanism Controlling Leg Muscles,” J. Bionic Eng., 9(3), pp. 282–293.##]
1

Aerodynamic Noise Computation of the Flow Field around NACA 0012 Airfoil Using Large Eddy Simulation and Acoustic Analogy
https://jcamech.ut.ac.ir/article_53392.html
10.22059/jcamech.2015.53392
1
The current study presents the results of the aerodynamic noise prediction of the flow field around a NACA 0012 airfoil at a chordbased Reynolds number of 100,000 and at 8.4 degree angle of attack. An incompressible Large Eddy Simulation (LES) turbulence model is applied to obtain the instantaneous turbulent flow field. The noise prediction is performed by the Ffowcs Williams and Hawkings (FWH) acoustic analogy. Both mean flow quantities and fluctuation statistics are studied. The behaviour of the turbulent vortical structures in the flow field from the perspective of the turbulent boundary layer development is visualized. Power spectral density of the lift coefficient is presented. The computed nondimensional mean velocity profiles in the boundary layer compared reasonably well with the theoretical predictions. The boundary layer transition from a laminar state to a turbulent state is also brought into focus. The skin friction coefficient and the urms streamwise velocity fluctuations predicted a transition zone from x/c=0.23 to x/c=0.45. Then, the research focuses on the broadband noises of the turbulent boundary layers and the tonal noises that arise from the vortex shedding generated by the laminar boundary layers. The spectra computed from the acoustic pressure are compared with the experimental data. The effect of observer location on the overall sound pressure level (OASPL) is investigated and the results indicate that the OASPL varies logarithmically with the receiver distance, as was expected.
0

41
50


Masoud
Ghasemian
Department of Mechanical Engineering, University of Tehran, Tehran, Iran
Iran
m_ghasemian@ut.ac.ir


Amir
Nejat
Department of Mechanical Engineering, University of Tehran, Tehran, Iran
Iran
nejat@ut.ac.ir
acoustic analogy
aerodynamic noise
boundary layer transition
turbulence
[[1]. Jianu, O., Rosen, M. A., and Naterer, G., 2012, "Noise Pollution Prevention in Wind Turbines: Status and Recent Advances," Sustainability, 4(6): 11041117.##[2]. Pedersen, E., and Waye, K. P., 2007, "Wind turbine noise, annoyance and selfreported health and wellbeing in different living environments," Occupational and environmental medicine, 64(7): 480486.##[3]. Wagner, S., Bareiss, R., Guidati, G., and WagnerBareißGuidati, 1996, "Wind turbine noise."##[4]. Oerlemans, S., Sijtsma, P., and Méndez López, B., 2007, "Location and quantification of noise sources on a wind turbine," Journal of sound and vibration, 299(4): 869883.##[5]. Brooks, T. F., Pope, D. S., and Marcolini, M. A., 1989, Airfoil selfnoise and prediction, National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division.##[6]. Wang, M., and Moin, P., 2000, "Computation of trailingedge flow and noise using largeeddy simulation," AIAA journal, 38(12): 22012209.##[7]. Williams, J., and Hall, L., 1970, "Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane," Journal of Fluid Mechanics, 40(04): 657670.##[8]. Singer, B. A., Brentner, K. S., Lockard, D. P., and Lilley, G. M., 2000, "Simulation of acoustic scattering from a trailing edge," Journal of Sound and Vibration, 230(3): 541560.##[9]. Shen, W. Z., Zhu, W., and Sørensen, J. N., 2009, "Aeroacoustic computations for turbulent airfoil flows," AIAA journal, 47(6): 15181527.##[10]. Jones, L. E., Sandham, N. D., and Sandberg, R. D., 2010, "Acoustic source identification for transitional airfoil flows using cross correlations," AIAA journal, 48(10): 22992312.##[11]. Kim, T., Lee, S., Kim, H., and Lee, S., 2010, "Design of low noise airfoil with high aerodynamic performance for use on small wind turbines," Science in China Series E: Technological Sciences, 53(1): 7579.##[12]. Göçmen, T., and Özerdem, B., 2012, "Airfoil optimization for noise emission problem and aerodynamic performance criterion on small scale wind turbines," Energy, 46(1): 6271.##[13]. Wolf, W. R., and Lele, S. K., 2012, "TrailingEdge Noise Predictions Using Compressible LargeEddy Simulation and Acoustic Analogy," AIAA journal, 50(11): 24232434.##[14]. Lilly, D. K., 1992, "A proposed modification of the Germano subgrid‐scale closure method," Physics of Fluids A: Fluid Dynamics (19891993), 4(3): 633635.##[15]. Williams, J. F., and Hawkings, D. L., 1969, "Sound generation by turbulence and surfaces in arbitrary motion," Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 264(1151): 321342.##[16]. Lighthill, M. J., 1952, "On sound generated aerodynamically. I. General theory," Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 211(1107): 564587.##[17]. Di Francescantonio, P., 1997, "A new boundary integral formulation for the prediction of sound radiation," Journal of Sound and Vibration, 202(4): 491509.##[18]. Morris, P. J., Long, L. N., and Brentner, K. S., "An aeroacoustic analysis of wind turbines," Proc. 23rd ASME Wind Energy Symposium, AIAA Paper: 58.##[19]. Farassat, F., and Succi, G. P., "The prediction of helicopter rotor discrete frequency noise," Proc. In: American Helicopter Society, Annual Forum, 38th, Anaheim, CA, May 47, 1982, Proceedings.(A8240505 2001) Washington, DC, American Helicopter Society, 1982: 497507.##[20]. Sheldahl, R. E., and Klimas, P. C., 1981, "Aerodynamic characteristics of seven symmetrical airfoil sections through 180degree angle of attack for use in aerodynamic analysis of vertical axis wind turbines," Sandia National Labs., Albuquerque, NM (USA).##[21]. Afzal, N., "Wake layer in a turbulent boundary layer with pressure gradient A new approach," Proc. IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers, Bochum, Germany: 95118.##[22]. Marsden, O., Bogey, C., and Bailly, C., 2008, "Direct noise computation of the turbulent flow around a zeroincidence airfoil," AIAA journal, 46(4): 874883.##[23]. Hoffmann, J. A., Kassir, S., and Larwood, S., 1989, "The influence of freestream turbulence on turbulent boundary layers with mild adverse pressure gradients."##[24]. Hunt, J. C., Wray, A., and Moin, P., "Eddies, streams, and convergence zones in turbulent flows," Proc. Studying Turbulence Using Numerical Simulation Databases, 2: 193208.##[25]. Chakraborty, P., Balachandar, S., and Adrian, R. J., 2005, "On the relationships between local vortex identification schemes," Journal of Fluid Mechanics, 535: 189214.##[26]. Kato, C., Iida, A., Takano, Y., Fujita, H., and Ikegawa, M., 1993, "Numerical prediction of aerodynamic noise radiated from low mach number turbulent wake," AIAA paper(930145).##]
1

Closedform Molecular Mechanics Formulations for the 3D Local Buckling and 2D Effective Young’s Modulus of the Nanosheets
https://jcamech.ut.ac.ir/article_53393.html
10.22059/jcamech.2015.53393
1
A closed form threedimensional solution is presented for determination of the local buckling (cell buckling) load of the nanosheets. Moreover, an expression is proposed for the effective 2D Young’s modulus of the unit cell of the nanosheet. In this regard, a threedimensional efficient spaceframelike geometrical model with angular and extensional compliances is considered to investigate stability and effective Young’s modulus of the nanosheet in terms of the generally possible relative movements of the atoms of the unit cell, in the Cartesian coordinates. The molecular dynamics approach is employed in development of the formulation, taking into account the force constants and bond characteristics. The governing equations are derived based on the principle of minimum total potential energy. Results of the special cases of each of the proposed expressions are verified by the results available in literature or results of the traditional approaches. Comparisons are made with various buckling results reported for different nanosheets, based on different approaches of determination of the stiffness parameters, and a good agreement is noticed.
0

51
62


Z.
Sarvi
M.Sc., Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Iran
zsarvi@mail.kntu.ac.ir


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


M.
Asgari
Assistant Professor, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Iran
asgari@kntu.ac.ir
effective 2D Young’s modulus
local buckling load
molecular mechanics
unit cell of a nanosheet
[[1].Oberlin A., Endo M., Koyama T., 1976, Filamentous Growth of Carbon through Benzene Decomposition, Journal of Crystal Growth 32(3): 335349.##[2].Iljima S., 1991, Helical microtubules of graphitic carbon, Letters to Nature 354: 5658.##[3].Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A., 2004, Electric Field Effect in Atomically Thin Carbon Films, Science 306: 666669.##[4].Corso M., Auwarter W., Muntwiler M., Tamai A., Greber T., Osterwalder J., 2004, Boron Nitride Nanomesh, Science 303: 217220.##[5].CastellanosGomez A., Poot M., Steele G.A., van der Zant H.S.J., Agraït N., RubioBollinger G., 2012, Elastic Properties of Freely Suspended MoS2 Nanosheets, Advaced Materials 24(6): 772–775.##[6].Xu M., Liang T., Shi M., Chen H., 2013, GrapheneLike TwoDimensional Materials, Chemical Reviews 113(5): 3766–3798.##[7].Wang C.M., Zhang Y.Y., Ramesh S.S., Kitipornchai S., 2006, Buckling analysis of micro and nanorods/tubes based on nonlocal Timoshenko beam theory, Jouranl of Physics D: Applied Physics 39: 3904–3909,.##[8].Wanga Q., Duan W.H., Liew K.M., He X.Q., 2007, Inelastic buckling of carbon nanotubes, Applied Physics Letters 90: 033110.##[9].Sudak L.J., 2003, Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics, Journal of Applied Physics 94(11): 72817287.##[10]. Wang Q., Wang C.M., 2007, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology 18: 075702.##[11]. Lu P., Lee H.P., Lu C., Zhang P.Q., 2007, Application of nonlocal beam models for carbon nanotubes, International Journal of Solids and Structures 44: 5289–5300.##[12]. Shi M.X., Li Q.M., Liu B., Feng X.Q., Huang Y., 2009, Atomicscale finite element analysis of vibration mode transformation in carbon nanorings and singlewalled carbon nanotubes, International Journal of Solids and Structures 46: 4342–4360.##[13]. Moosavi H., Mohammadi M., Farajpour A., Shahidi S.H., 2011, Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory, Physica E 44: 135–140.##[14]. 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.##[15]. Aydogdu M., 2012, Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity, Mechanics Research Communications 43: 34–40.##[16]. Arash B., Wang Q., 2012, A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes, Computational Materials Science 51: 303–313.##[17]. 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.##[18]. Narendar S., 2011, Buckling analysis of micro/nanoscale plates based on twovariable refined plate theory incorporating nonlocal scale effects, Composite Structures 93: 3093–3103.##[19]. Samaeia A.T., Abbasion S., Mirsayar M.M., 2011, Buckling analysis of a singlelayer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory, Mechanics Research Communications 38: 481– 485.##[20]. Farajpour A., Mohammadi M., Shahidi A.R., Mahzoon M., 2011, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E 43: 1820–1825.##[21]. 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.##[22]. Narendar S., Gopalakrishnan S., 2012, Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal twovariable refined plate theory, Acta Mechanica 223: 395–413.##[23]. Ansari R., Rouhi S., Aryayi M., Mirnezhad M., 2012, On the buckling behavior of singlewalled silicon carbide nanotubes, Scientia Iranica 19(6): 1984–1990.##[24]. Tourki Samaei A., Hosseini Hashemi Sh., 2012, Buckling analysis of graphene nanosheets based on nonlocal elasticity theory, International Journal of Nano Dimension 2(4): 227232.##[25]. Ansari R., Rouhi S., Mirnezhad M., Aryayi M., 2013, Stability characteristics of singlelayered silicon carbide nanosheets under uniaxial compression, Physica E 53: 22–28.##[26]. Bedroud M., HosseiniHashemi S., Nazemnezhad R., 2013, Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mech 224(11): 26632676.##[27]. Sobhy M., 2015, Levytype solution for bending of singlelayered graphene sheets in thermal environment using the twovariable plate theory, International Journal of Mechanical Sciences 90: 171–178.##[28]. HosseiniHashemi S., Kermajani M., Nazemnezhad R., 2015, An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal thirdorder shear deformation plate theory, European Journal of Mechanics A/Solids 51: 2943.##[29]. Scarpa F., Adhikari S., Gil A.J., Remillat C., 2010, The bending of single layer graphene##sheets: the lattice versus continuum approach, Nanotechnology 21: 125702 (9pages).##[30]. Casewit C. J., Colwell K.S., Rappe A.K., 1992, Application of Universal Force Field to Organic Molecules, Journal of American Chemical Society 114(25): 1003510046.##[31]. Song L., Ci L., Lu H., Sorokin P.B., Jin Ch., Ni J., Kvashnin A.G., Kvashnin D.G., Lou J., Yakobson B.I., Ajayan P.M., 2010, Large Scale Growth and Characterization of Atomic Hexagonal Boron Nitride Layers, Nano Letters 10: 32093215.##[32]. Le M.Q., 2014, Prediction of Young’s modulus of hexagonal monolayer sheets based on molecular mechanics, International Journal of Mechanics and Materials in Design, DOI: 10.1007/s1099901492710.##[33]. Fitzpatrick R., 2012, An Introduction to Celestial Mechanics, Cambridge University Press.##[34]. Lee C., Wei X., Kysar J.W., Hone J., 2008, Measurement of the elastic properties and intrinsic strength of monolayer grapheme, Science 321: 385388.##[35]. Mortazavi B., Remond Y., 2012, Investigation of tensile response and thermal conductivity of boronnitride nanosheets using molecular dynamics simulation, Physica E 44: 18461852.##[36]. Panchal M. B., Upadhyay S. H., 2014, Boron nitride nanotubebased biosensor for acetone detection: molecular mechanicsbased simulation, Molecular Simulation 40(13): 10351042.##[37]. Akdim B., Kim S.N., Naik R.R., Maruyama B., Pender M.J., Pachter R., 2009, Understanding effects of molecular adsorption at a singlewall boron nitride nanotube interface from density functional theory calculations, Nanotechnology 20: 355705.##[38]. Erhart P., Albe K., 2005, Analytical potential for atomistic simulations of silicon, carbon, and silicon carbide, Physical Review B 71: 035211.##[39]. Chowdhurry R., Wang C.Y., Adhikari S., Scarpa F., 2010, Vibration and symmetrybreaking of boron nitride nanotubes, Nanotechnology 21: 365702.##[40]. Sahin H., Cahangirov S., Topsakal M., Bekaroglu E., Akturk E., Senger R.T., Ciraci S., 2009, Monolayer honeycomb structures of groupIV elements and IIIV binary compounds: firstprinciples calculations, Physical Review B 80: 155453.##[41]. Berinskii I.E., Krivtsov A.M., 2010, On using manyparticle interatomic potentials to compute elastic properties of graphene and diamond, Mechanics of Solids 45: 815.##[42]. Song L., Ci L., Lu H., Sorokin P.B., Jin Ch., Ni J., Kvashnin A.G., Kvashnin D.G., Lou J., Yakobson B.I., Ajayan P.M., 2010, Large Scale Growth and Characterization of Atomic Hexagonal Boron Nitride Layers, Nano Letters 10: 32093215.##[43]. Kudin K.N., Scuseria G.E., Yakobson B.I., 2001, C2F, BN, and C nanoshell elasticity from ab initio computations, Physical Review B 64: 235406.##[44]. Oh E.S., 2010, Elastic properties of boronnitride nanotubes through the continuum lattice approach, Materials Letters 64: 859–862.##[45]. Oh E.S., 2011, Elastic Properties of Various BoronNitride Structures, Metals and Materials International 17(1): 2127.##[46]. Boldrin L., Scarpa F., Chowdhury R., Adhikari S., 2011, Effective mechanical##properties of hexagonal boron nitride nanosheets, Nanotechnology 22: 505702.##[47]. Bosak A., Serrano J., Krisch M., Watanabe K., Taniguchi T., Kanda H., 2006, Elasticity of hexagonal boron nitride: Inelastic xray scattering measurements, Physical Review B 73: 041402.##[48]. Le M. Q., 2014, Atomistic study on the tensile properties of hexagonal AlN, BN, GaN, InN and SiC sheets, Journal of Computational and Theoretical Nanoscience 11: 1458–1464.##[49]. Li C., Chou T.W., 2003, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures 40: 24872499.##[50]. Mayo S.L., Olafson B.D., Goddard W.A., 1990, DREIDING: A Generic Force Field for Molecular Simulations, Journal Physical Chemistry 94(26): 88978909.##]
1

Analysis of 3D Passive Walking Including Turning Motions for the Finitewidth Rimless Wheel
https://jcamech.ut.ac.ir/article_53394.html
10.22059/jcamech.2015.53394
1
The focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. In this paper, the passive motions of a finite width rimless wheel as the simplest 3D model of passive biped walkers was investigated with a focus on turning motions. For this purpose, the hybrid model of the system consisting of continuous and discontinuous phases of motion was derived with respect to a vertical fixed frame that was independent of the surface profile. A Poincaré map corresponding to a step is one of the common methods used for the determination of periodic motions (limit cycles) and their specifications. In this study, it was emphasized that the Poincaré map has only one fixed point, indicating only one stable periodic motion that is parallel to the steepest slope surface. It is also shown that if the wheel is released from an orientation other than the steepest slope, the wheel turns towards the slope surface and eventually, its motion continues on the only existing stable limit cycle (passive limited turning). The effect of variation among some parameters of the initial conditions on rotational behaviour and its convergence were investigated.
0

63
68
امیر
جابری
Amir
Jaberi
Research assistant in control laboratory
Iran
a.jaberi@ut.ac.ir
محمدرضا
حائری یزدی
Mohammad Reza
Hairi Yazdi
Associate professor, School of Mechanical Engineering, University of Tehran, Iran
Iran
myazdi@ut.ac.ir
محمدرضا
سبع پور
Mohammad Reza
Sabaapour
PhD student, School of Mechanical Engineering, University of Tehran, Iran.
Iran
sabaapour@ut.ac.ir
biped robot
finitewidth rimless wheel
limit cycle
Passive walking
Steering
Turning
[[1]. McGeer, T., 1990, Passive dynamic walking,##The International Journal of Robotics Reseach,##9(2), pp. 6282.##[2]. Coleman, M.J. 1998, A stability study of a##threedimensional passive dynamic model of##human gait, Cornell University, PhD thesis.##[3]. Coleman, M.J., Chatterjee, A. and Ruina, A.,##1997, Motions of a rimless spoked wheel: a##simple threedimensional system with impacts,##Dynamics and Stability of Systems, 12(3), pp.##[4]. Smith, A. C. and Berkemeier, M. D., 1998, The##motion of a finitewidth rimless wheel in 3D, in##Robotics and Automation Proceedings IEEE##International Conference, Leuven, Belgium.##[5]. Sabaapour, M.R., HairiYazdi, M.R. and##Beigzadeh, B., 2014, Towards passive turning in##biped walkers, Procedia Technology, 12, pp. 98##[6]. Sabaapour, M. R., HairiYazdi, M. R., and##Beigzadeh, B., 2014, Passive turning motion of##3D rimless wheel: novel periodic gaits for##bipedal curved walking, Submitted to Advanced##[7]. Spong, M. W., and Bullo, F., 2002, Controlled##symmetries and passive walking, in in Proc.##15th Triennial World Congress..##[8]. Goswami, A., Espiau, B., and Keramane, A.,##1997, Limit cycles in a passive compass gait##biped and passivitymimicking control laws,##Autonomous Robots, 4(3), pp. 273286.##[9]. Shih, C., Grizzle, J.W. and Chevallereau, C.,##2009, Asymptotically stable walking and##steering of a 3D bipedal robot with passive point##feet, IEEE Transactions on Robotics.##]
1

Fractional Order PID Controller for Diabetes Patients
https://jcamech.ut.ac.ir/article_53395.html
10.22059/jcamech.2015.53395
1
This paper proposes an optimized control policy over type one diabetes. Type one diabetes is taken into consideration as a nonlinear model (Augmented Minimal Model), which is implemented in MATLABSIMULINK. This Model is developed in consideration of the patient's conditions. There are some uncertainties in the regarded model due to factors such as blood glucose concentration, daily meals or sudden stresses. Moreover, there are distinct approaches toward the elimination of these uncertainties. In here, a meal is fed to the model as an input in order to omit these uncertainties. Also, different control methods could be chosen to monitor the blood glucose level. In this paper, a Fractional Order PID is utilized as the control method. Thereafter, the control method and parameters are tuned by conducting genetic algorithm, as a powerful evolutionary algorithm. Finally, the output of the optimized Fractional order PID and traditional PID control method, which had the same parameters as the Fractional PID except the fractions, are compared. At the end, it is concluded by utilizing Fractional Order PID, not only the controller performance improved considerably, but also, unlike the traditional PID, the blood glucose concentration is maintained in the desired range.
0

69
76


Masoud
Goharimanesh
Department of Mechanical Engineering, Ferdowsi University of Mashhad
Iran
ma.goharimanesh@stumail.um.ac.ir
علی
لشکری پور
Ali
Lashkaripour
Department of Life Science Engineering, University of Tehran
Iran
a.lashkaripour@ut.ac.ir


Ali
Abouei Mehrizi
Department of life science engineering, University of Tehran
Iran
abouei@ut.ac.ir
diabetes
fractional order PID
Genetic Algorithm
[[1]. CentersforDiseaseControlPrevention, National diabetes fact sheet: national estimates and general information on diabetes and prediabetes in the United States, 2011. Atlanta, GA: US Department of Health and Human Services, Centers for Disease Control and Prevention, 2011. 201.##[2]. Wild, S., et al., Global prevalence of diabetes estimates for the year 2000 and projections for 2030. Diabetes care, 2004. 27(5): pp. 10471053.##[3]. AmericanDiabetesAssociation, Standards of medical care in diabetes—2013. Diabetes care, 2013. 36(Suppl 1): p. S11.##[4]. Tchobroutsky, G., Relation of diabetic control to development of microvascular complications. Diabetologia, 1978. 15(3): pp. 143152.##[5]. Pietri, A., F.L. Dunn, and P. Raskin, The effect of improved diabetic control on plasma lipid and lipoprotein levels: a comparison of conventional therapy and continuous subcutaneous insulin infusion. Diabetes, 1980. 29(12): pp. 10011005.##[6]. Cobelli, C., et al., Diabetes: models, signals, and control. Biomedical Engineering, IEEE Reviews in, 2009. 2: pp. 5496.##[7]. M. Goharimanesh, A. Lashkaripour, S. Shariatnia, A. Akbari, Diabetic Control Using Genetic FuzzyPI Controller. International Journal of Fuzzy Systems, 2014. 16(2): pp. 133139.##[8]. Ǻström, K.J. and T. Hägglund, PID controllers: theory, design, and tuning. Instrument Society of America, Research Triangle Park, NC, 1995.##[9]. Cominos, P. and N. Munro, PID controllers: recent tuning methods and design to specification. IEE ProceedingsControl Theory and Applications, 2002. 149(1): pp. 4653.##[10]. Åström, K.J. and T. Hägglund, Advanced PID control. 2006: ISAThe Instrumentation, Systems, and Automation Society; Research Triangle Park, NC 27709.##[11]. Åström, K.J. and T. Hagglund, Automatic tuning of PID controllers. 1988: Instrumentation, Systems, and Automation Society.##[12]. Zhuang, M. and D. Atherton. Automatic tuning of optimum PID controllers. in Control Theory and Applications, IEE Proceedings D. 1993. IET.##[13]. Pan, I., S. Das, and A. Gupta, Tuning of an optimal fuzzy PID controller with stochastic algorithms for networked control systems with random time delay. ISA transactions, 2011. 50(1): pp. 2836.##[14]. Padula, F. and A. Visioli, Tuning rules for optimal PID and fractionalorder PID controllers. Journal of Process Control, 2011. 21(1): pp. 6981.##[15]. Cao, J. Y., J. Liang, and B.G. Cao. Optimization of fractional order PID controllers based on genetic algorithms. in Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on. 2005. IEEE.##[16]. Ramprasad, Y., G. Rangaiah, and S. Lakshminarayanan, Robust PID controller for blood glucose regulation in type I diabetics. Industrial & engineering chemistry research, 2004. 43(26): pp. 82578268.##[17]. Ibbini, M., A PIfuzzy logic controller for the regulation of blood glucose level in diabetic patients. Journal of medical engineering & technology, 2006. 30(2): pp. 8392.##[18]. Markakis, M.G., G.D. Mitsis, and V.Z. Marmarelis. Computational study of an augmented minimal model for glycaemia control. in Engineering in Medicine and Biology Society, 2008. EMBS 2008. 30th Annual International Conference of the IEEE. 2008. IEEE.##[19]. Brunner, G.A., et al., Validation of home blood glucose meters with respect to clinical and analytical approaches. Diabetes Care, 1998. 21(4): pp. 585590.##[20]. Podlubny, I., Fractionalorder systems and fractionalorder controllers. The Academy of Sciences Institute of Experimental Physics, UEF0394, Kosice, Slovak Republic, 1994.##[21]. Podlubny, I., Fractionalorder systems and PI/sup/spl lambda//D/sup/spl mu//controllers. Automatic Control, IEEE Transactions on, 1999. 44(1): pp. 208214.##[22]. Oustaloup, A., et al., Frequencyband complex noninteger differentiator: characterization and synthesis. Circuits and##Systems I: Fundamental Theory and Applications, IEEE Transactions on, 2000. 47(1): pp. 2539.##]
1

3node Basic Displacement Functions in Analysis of NonPrismatic Beams
https://jcamech.ut.ac.ir/article_53396.html
10.22059/jcamech.2015.53396
1
Purpose– Analysis of nonprismatic beams has been focused of attention due to wide use in complex structures such as aircraft, turbine blades and space vehicles. Apart from aesthetic aspect, optimization of strength and weight is achieved in use of this type of structures. The purpose of this paper is to present new shape functions, namely 3node Basic Displacement Functions (BDFs) for derivation of structural matrices for general nonprismatic EulerBernoulli beam elements. Design/methodology/approach– Static analysis and free transverse vibration of nonprismatic beams are extracted studied from a mechanical point of view. Following structural/mechanical principles, new static shape functions are in terms of BDFs, which are obtained using unitdummyload method. All types of crosssections and crosssectional dimensions of the beam element could be considered in this method. Findings– According to the outcome of static analysis, it is verified that exact results are obtained by applying one or a few elements. Furthermore, it is observed that results from both static and free transverse vibration analysis are in good agreement with the previous published once in the literature. Research limitations/implications– The method can be extended to structural analysis of curved and Timoshenko beams as well as plates and shells. Furthermore, exact dynamic shape functions can be derived using BDFs by solving the governing equation for transverse vibration of beams. Originality/value– The present investigation introduces new shape functions, namely 3node Basic Displacement Functions (BDFs) extended from 2node functions, and then compares its performance with previous element.
0

77
91


Ahmad
Modarakar Haghighi
School of Civil Engineering, College of Engineering, University of Tehran, Tehran P.O. Box 113654563, Iran
Iran
za57190@gmail.com


Mohammad
Zakeri
Assistant Professor, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
mohammad_zakeri@ut.ac.ir


Reza
Attarnejad
MS Graduate, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Iran
attarnjd@ut.ac.ir
3node basic displacement functions
free transverse vibration
nonprismatic beam
shape functions
Static analysis
[[1]. Gunda J.B., Ganguli R., 2008, New rational##interpolation functions for finite element##analysis of rotating beams, Int. J. Mech. Sci. 50:##[2]. Caruntu D.I., 2009, Dynamic modal##characteristics of transverse vibrations of##cantilevers of parabolic thickness, Mech. Res.##Commun. 36: 391–404.##[3]. Gallagher R.H., Lee C.H., 1970, Matrix##dynamic and instability analysis with nonuniform##elements, J. Numer. Meth. Eng. 2: 265##[4]. Karabalis D.L., Beskos D.E., 1983, Static,##dynamic and stability analysis of structures ##composed of tapered beams, Comput. Struct. 16: 731748.##[5]. Eisenberger M., Reich Y., 1989, Static, vibration and stability analysis of nonuniform beams, Comput. Struct. 31: 563571.##[6]. Eisenberger M., 1986, An exact element method, Int. J. Numer. Meth. Eng. 30: 363370.##[7]. Eisenberger M., 1991, Exact solution for general variable crosssection members, Comput. Struct. 41: 765772.##[8]. Banerjee J.R., Williams F.W., 1985, Exact BernoulliEuler dynamic stiffness matrix for a range of tapered beam, J. Numer. Meth. Eng. 21: 22892302.##[9]. Mou Y., Han R.S.P., Shah A.H., 1997, Exact dynamic stiffness matrix for beams of arbitrarily varying cross sections, Int. J. Numer. Meth. Eng. 40: 233250.##[10]. Chambers J.J., Almudhafar S., Stenger F., 2003, Effect of reduced beam section frame elements on stiffness of moment frames, J. Struct. Eng. 129: 383393.##[11]. Kim K.D., Engelhardt M.D., 2007, Nonprismatic beam element for beams with RBS connections in steel moment frames, J. Struct. Eng. 133: 176184.##[12]. Ece M.C., Aydogdu M., Taskin V., 2007, Vibration of a variable crosssection beam, Mech. Res. Commun. 34: 7884.##[13]. Banerjee J.R., 2000, Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method. J. Sound Vib. 233: 857875.##[14]. Wang G., Wereley N.M., 2004, Free vibration analysis of rotating blades with uniform tapers, J. AIAA 42: 24292437.##[15]. Banerjee J.R., Su H., 2006, Jackson D.R., Free vibration of rotating tapered beams using the dynamic stiffness method, J. Sound Vib. 298: 10341054.##[16]. Ruta P., 1999, Application of Chebyshev series to solution of nonprismatic beam vibration problems, J. Sound Vib. 227: 449467.##[17]. Auciello N.M., Ercolano A., 2004, A general solution for dynamic response of axially loaded nonuniform Timoshenko beams, Int. J. Solids Struct. 41: 4861–4874.##[18]. Ho S.H., Chen C.K., 1998, Analysis of general elastically end restrained nonuniform beams using differential transform, Appl. Math. Model. 22: 219–234.##[19]. Zeng H., Bert C.W., 2001, Vibration analysis of a tapered bar by differential transformation, J. Sound Vib. 242: 737–739.##[20]. Ozdemir O., Kaya M.O., 2006, Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method, J. Sound Vib. 289: 413–420.##[21]. Ozdemir O., Kaya M.O., 2006, Flapwise bending vibration analysis of double tapere rotating Euler–Bernoulli beam by using the differential transform method, Meccanica 40: 661–670.##[22]. Seval C., 2008, Solution of free vibration equations of beam on elastic soil by using differential transform method, Appl. Math. Model 32: 17441757.##[23]. Balkaya M., Kaya M.O., Saglamer A., 2009, Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method, Arch. Appl. Mech. 79: 135–146.##[24]. Catal S., 2008, Solution of free vibration equations of beam on elastic soil by using differential transform method, Appl. Math. Model. 32: 1744–1757.##[25]. Yesilce Y., Catal S., 2009, Free vibration of axially loaded ReddyBickford beam on elastic soil using the differential transform method, Struct. Eng. Mech. 31: 453–476.##[26]. Yesilce Y., 2010, DTM and DQEM for free vibration of axially loaded and semirigidconnected ReddyBickford beam, Commun. Numer. Meth. Eng. 27: 666693.##[27]. Attarnejad R., Shahba A., 2008, Application of differential transform method in free vibration analysis of rotating nonprismatic beams, World Appl. Sci. J. 5: 441448.##[28]. Shahba A., Rajasekaran S., 2012, Free vibration and stability of tapered EulerBernoulli beams made of axially functionally graded materials, Appl. Math. Model. 36: 30943111.##[29]. Attarnejad R., 2000, On the derivation of the geometric stiffness and consistent mass matrices for nonprismatic EulerBernoulli beam elements, Barcelona, Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering.##[30]. Attarnejad R., 2002, Free vibration of nonprismatic beams, New York, Proceedings of 15th ASCE Engineering Mechanics Conference.##[31]. Attarnejad R., 2010, Basic displacement functions in analysis of nonprismatic beams, Eng. Comput. 27: 733776.##[32]. Attarnejad R., Shahba A., 2011, Basic displacement functions in analysis of centrifugally stiffened tapered beams, AJSE 36: 841853.##[33]. Attarnejad R., Shahba A., Semnani S.J., 2011, Analysis of nonprismatic Timoshenko beams using basic displacement functions, Adv. Struct. Eng. 14: 319332.##[34]. Attarnejad R., Shahba A., 2010, Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered ##beams; a mechanical solution, Meccanica 46:##12671281.##[35]. Attarnejad R., Shahba A., 2011, Basic##displacement functions for centrifugally##stiffened tapered beams, Commun. Numer.##Meth. Eng. 27: 13851397.##[36]. Attarnejad R., Semnani S.J., Shahba A., 2010,##Basic displacement functions for free vibration##analysis of nonprismatic Timoshenko beams,##Finite Elem. Anal. Des. 46: 916929.##[37]. Attarnejad R., Shahba A., Eslaminia M., 2011,##Dynamic basic displacement functions for free##vibration analysis of tapered beams, J. Vib.##Control 17: 22222238.##[38]. Franciosi C., Mecca M., 1998, Some finite##elements for the static analysis of beams with##varying cross section, Comput. Struct. 69: 191##[39]. Cranch E.T., Adler A.A., 1956, Bending##vibration of variable section beams, J. Appl.##Mech. 23: 103–108.##[40]. Tong X., Tabarrok B., 1995, Vibration##analysis of Timoshenko beams with nonhomogeneity##and varying crosssection, J.##Sound Vib. 186: 821–835.##]