2015
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Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term
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This paper presents the high order frequencyamplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities, using Homotopy Perturbation Method with an auxiliary term (HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass, and quintic nonlinear beam are investigated to exhibit the reliability and ability of the proposed asymptotic approach. It is demonstrated that two terms in series expansions are sufficient to obtain a highly accurate periodic solutions. The integrity of the analytical solutions is verified by numerical results.
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Hamid M.
Sedighi
Shahid Chamran University, Faculty of Engineering, Mechanical Engineering Department, Ahvaz, Iran
Shahid Chamran University, Faculty of Engineering,
Iran
h.msedighi@scu.ac.ir


Farhang
Daneshmand
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Department of Mechanical Engineering, McGill
Iran
farhang.daneshmand@mcgill.ca
Homotopy Perturbation Method with an auxiliary term
Nonlinear vibrating beams
Frequencyamplitude relationship
[[1] Love, A.E.H.; 1927. A treatise on the Mathematical theory of Elasticity. New York: Dover Publications, Inc.##[2] Sedighi, H.M., Shirazi, K.H., and Noghrehabadi, A. Application of Recent Powerful Analytical Approaches on the NonLinear Vibration of Cantilever Beams, Int. J. Nonlinear Sci. Numer. Simul., 2012; 13(7–8): 487494, DOI: 10.1515/ijnsns20120030.##[3] Barari, A.; Kaliji, H.D.; Ghadami, M.; Domairry, G.; 2011. NonLinear Vibration of EulerBernoulli Beams. Latin American Journal of Solids and Structures. 8: 139148.##[4] Sedighi, H.M.; Reza, A.; Zare, J.; 2011. Dynamic analysis of preload nonlinearity in nonlinear beam vibration, Journal of Vibroengineering. 13: 778787.##[5] Sedighi, H.M.; Reza, A.; Zare, J.; 2011. Study on the frequency – amplitude relation of beam vibration, International Journal of the Physical Sciences. 6(36): 80518056.##[6] Sedighi, H.M.; Shirazi, K.H.; 2012. A new approach to analytical solution of cantilever beam vibration with nonlinear boundary condition, ASME Journal of Computational and Nonlinear Dynamics. 7: 034502. DOI:10.1115/1.4005924.##[7] Sedighi, H.M.; Shirazi, K.H.; Noghrehabadi, A.R.; Yildirim, A.; 2012. Asymptotic Investigation of Buckled Beam Nonlinear Vibration. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 36(M2): 107116.##[8] Sedighi, H.M.; Shirazi, K.H.; Zare, J.; 2012. Novel Equivalent Function for Deadzone Nonlinearity: Applied to Analytical Solution of Beam Vibration Using He’s Parameter Expanding Method. Latin American Journal of Solids and Structures, 9(4), 443451.##[9] Sedighi, H.M.; Shirazi, K.H.; Reza, A.; Zare, J.; 2012. Accurate modeling of preload discontinuity in the analytical approach of the nonlinear free vibration of beams. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 226(10), 2474–2484, DOI: 10.1177/0954406211435196.##[10] Nikkhah Bahrami, M.; Khoshbayani Arani, M.; Rasekh Saleh, N.; 2011. Modified wave approach for calculation of natural frequencies and mode shapes in arbitrary nonuniform beams. Scientia Iranica B, 18(5):1088–1094.##[11] Arvin, H.; BakhtiariNejad, F.; 2011. Nonlinear modal analysis of a rotating beam. International Journal of NonLinear Mechanics, 46: 877–897.##[12] Zohoor, H.; Kakavand, F.; Vibration of Euler–Bernoulli and Timoshenko beams in large overall motion on flying support using finite element method, Scientia Iranica B, in press, doi:10.1016/j.scient.2012.06.019.##[13] Freno, B.A.: Cizmas, P.G.A.; 2011. A computationally efficient nonlinear beam model. International Journal of NonLinear Mechanics, 46: 854869.##[14] Awrejcewicz, J.; Krysko, A.V.; Soldatov, V.; Krysko, V.A.; 2012. Analysis of the Nonlinear Dynamics of the Timoshenko Flexible Beams Using Wavelets. ASME Journal of Computational and Nonlinear Dynamics, 7(1): 011005.##[15] Andreaus, U.; Placidi, L.; Rega, G.; 2011. Soft impact dynamics of a cantilever beam: equivalent SDOF model versus infinitedimensional system. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(10): 24442456. doi: 10.1177/0954406211414484.##[16] Chen, J.S.; Chen, Y.K.; 2011. Steady state and stability of a beam on a damped tensionless foundation under a moving load. International Journal of NonLinear Mechanics, 46: 180–185.##[17] Sapountzakis, E.J.; Dikaros, I.C.; 2011. Nonlinear flexuraltorsional dynamic analysis of beams of arbitrary cross section by BEM. International Journal of NonLinear Mechanics, 46: 782–794.##[18] Jang, T.S.; Baek, H.S.; Paik, J.K.; 2011. A new method for the nonlinear deflection analysis of an infinite beam resting on a nonlinear elastic foundation. International Journal of NonLinear Mechanics, 46: 339–346. ##[19] Campanile, L.F.; Jähne, R.; Hasse, H.; 2011. Exact analysis of the bending of wide beams by a modified elastica approach, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(11): 27592764. Doi: 10.1177/0954406211417753.##[20] He, J.H., 2008. MaxMin Approach to Nonlinear Oscillators, International Journal of Nonlinear Sciences and Numerical Simulation, 9(2), 207210.##[21] Liao, S.J. 2004. An analytic approximate approach for free oscillations of selfexcited systems, International Journal of NonLinear Mechanics, 39, 271280.##[22] Sedighi, H.M.; Shirazi, K.H.; Zare, J.; 2012. An analytic solution of transversal oscillation of quintic nonlinear beam with homotopy analysis method. International Journal of NonLinear Mechanics, 47: 777 784, DOI: 10.1016/j.ijnonlinmec.2012.04.008.##[23] Ghaffarzadeh, H; Nikkar, A; 2013. Explicit solution to the large deformation of a cantilever beam under point load at the free tip using the Variational Iteration MethodII, Journal of Mechanical Science and Technology, 27(11) 34333438.##[24] Bagheri, S.; Nikkar, A; Ghaffarzadeh, H; 2014. Study of nonlinear vibration of EulerBernoulli beams by using analytical approximate techniques, Latin American Journal of Solids and Structures, 11: 157168.##[25] Shadloo, M.S.; Kimiaeifar, A.; 2011. Application of homotopy perturbation method to find an analytical solution for magneto hydrodynamic flows of viscoelastic fluids in converging/diverging channels. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225: 347353.##[26] Soroush, R.; Koochi, A.; Kazemi, A.S.; Noghrehabadi, A.; Haddadpour, H.; Abadyan, M.; 2010. Investigating the effect of Casimir and van der Waals attractions on the electrostatic pullin instability of nanoactuators, Phys. Scr., 82: 045801. doi:10.1088/00318949/82/04/045801.##[27] Bayat, M.; Shahidi, M.; Barari, A.; Domairry, G.; 2011. Analytical evaluation of the nonlinear vibration of coupled oscillator systems. Zeitschrift fur Naturforschung AA Journal of Physical Sciences, 66(12): 67–74.##[28] He, J.H., 2002. Preliminary report on the energy balance for nonlinear oscillations. Mech. Res. Commun., 29, 107111. ##[29] Evirgen, F.; Özdemir, N.; 2011. Multistage Adomian Decomposition Method for Solving NLP Problems Over a Nonlinear Fractional Dynamical System. ASME Journal of Computational and Nonlinear Dynamics, 6(2): 021003. Doi:10.1115/1.4002393.##[30] He, J.H; 2011. A short remark on fractional variational iteration method , PHYSICS LETTERS A, 375(38), 33623364, dio: 10.1016/j.physleta.2011.07.033.##[31] Khosrozadeh, A.; Hajabasi, M.A.; Fahham, H.R.; 2013. Analytical Approximations to Conservative Oscillators With Odd Nonlinearity Using the Variational Iteration Method, Journal of Computational and Nonlinear Dynamics, 8, 014502, DOI: 10.1115/1.4006789.##[32] Hasanov, A.; 2011. Some new classes of inverse coefficient problems in nonlinear mechanics and computational material science, International Journal of NonLinear Mechanics, 46(5): 667684.##[33] He, J.H.; 2010. Hamiltonian approach to nonlinear oscillators, Physics Letters A, 374(23): 23122314.##[34] Baferani, A.H.; Saidi, A.R.; Jomehzadeh, E.; 2011. An exact solution for free vibration of thin functionally graded rectangular plates. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(3): 526536. doi: 10.1243/09544062JMES2171.##[35] Naderi, A.; Saidi, A.R.; 2011. Buckling analysis of functionally graded annular sector plates resting on elastic foundations. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(2): 312325.##[36] He, J.H.; 2002. Modified LindstedtPoincare methods for some strongly nonlinear oscillations Part I: expansion of a constant, International Journal of Nonlinear Mechanics, 37(2): 309314. DOI: 10.1016/S00207462(00)001165.##[37] He, J.H., Homotopy Perturbation Method with an Auxiliary Term, Abstract and Applied Analysis, 2012, Article ID 857612, doi:10.1155/2012/857612.##[38] M.N. Hamden and N.H. Shabaneh, On the large amplitude free vibrations of a restrained uniform beam carrying an intermediate lumped mass, Journal of Sound and Vibration, 199(5) (1997), 711–736.##[39] M. R. M. Crespo da Silva & C. C. Glynn, Nonlinear FlexuralFlexuralTorsional Dynamics of Inextensional Beams. I. Equations of Motion, Journal of Structural Mechanics, Volume 6, Issue 4, 1978, DOI: 10.1080/03601217808907348.##[40] Lacarbonara, W. (1997). A theoretical and experimental investigation of nonlinear vibrations of buckled beams. Master Thesis, Virginia Polytechnic Institute and State University, Blacksburg Virginia.##]
Optimal Roll Center Height of Front McPherson Suspension System for a Conceptual Class A Vehicle
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In this paper, the effects of roll center height of McPherson suspension mechanism on dynamic behaviour of a vehicle are first studied, and then the optimum location of roll center of this suspension system is determined for a conceptual Class A vehicle. ADAMS/Car software was used for the analysis of vehicle dynamic behaviour in different positions of suspension roll center. Next, optimization process has been done using ADAMS/Insight. Results show significant effects of roll center location on body roll angle, body roll rate and steering response. Also, the contradiction between body roll and steering response can be observed.
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Javad
Meshkatifar
Master Student, Department of Mechanical Engineering, Isfahan University of Technology
Master Student, Department of Mechanical
Iran
j.meshkatifar@yahoo.com


Mohsen
Esfahanian
Associate Professor, Department of Mechanical Engineering, Isfahan University of Technology
Associate Professor, Department of Mechanical
Iran
mesf1964@cc.iut.ac.ir
Vehicle dynamics
Roll center height
McPherson suspension mechanism
[[1] D.L. Cronin, 1981, “MacPherson Strut Kinematics”. Mechanism and machine theory, vol. 16, No.6, pp. 631644. ##[2] A. Babaeian, R. Kazemi, S. Azadi, 2012, “sensitivity analysis and optimization of kinematics and elastokinematics behaviour of front suspension system”, 2nd conference on acoustics and vibration, Sharif university of technology, Tehran, Iran. ##[3] A. Mohammadi, M. Forouzan, M. Zoei, 2009, “optimization of suspension using TANGA method”, 17nd international conference on mechanical engineering, university of Tehran, Tehran, Iran. ##[4] B. Nemeth, P. Gaspar, 2012, “Design of VariableGeometry Suspension for Driver Assistance Systems”, Mediterranean Conference on Control & Automation (MED),Barcelona, Spain, July 36. ##[5] J. C.Dixon, 1996, tires, suspension and handling, Society of Automotive Engineers. ##[6] R. N.Jazar, 2008, vehicle dynamic theory and application, springer. ##[7] J. Reimpell, H. Stoll, J.W.Betzler, 2001, the Automotive Chassis: Engineering Principles, ButterworthHeinemann, Linacre House, Jordan Hill, Oxford. ##[8] T. D.Gillespie, 1994, fundamentals of vehicle dynamics, Society of Automotive Engineers (SAE). ##[9] ADAMS User Manual, 2013, M.S.C. Software Group.##]
Pullin behavior analysis of vibrating functionally graded microcantilevers under suddenly DC voltage
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The present research attempts to explain dynamic pullin instability of functionally graded microcantilevers actuated by step DC voltage while the fringingfield effect is taken into account in the vibrational equation of motion. By employing modern asymptotic approach namely Homotopy Perturbation Method with an auxiliary term, highorder frequencyamplitude relation is obtained, then the influences of material properties and actuation voltage on dynamic pullin behavior are investigated. It is demonstrated that the auxiliary term in the homotopy perturbation method is extremely effective for higher order approximation and two terms in series expansions are sufficient to produce an acceptable solution. The strength of this analytical procedure is verified through comparison with numerical results.
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Jamal
Zare
National Iranian South Oil Company (NISOC), Ahvaz, Iran
National Iranian South Oil Company (NISOC),
Iran
jamal.zare@hotmail.com
Microactuator
Functionally graded material
Dynamic Pullin instability
Homotopy Perturbation Method with an auxiliary term
[[1] Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H., Rahaeifard, M., “On the sizedependent behavior of functionally graded microbeams”, Materials and Design, Vol. 31, pp. 2324–2329, 2010. ##[2] Lü, C.F., Chen, W.Q., Lim, C.W., “Elastic mechanical behavior of nanoscaled FGM films incorporating surface energies”, Composites Science and Technology, Vol. 69, pp. 1124–1130, 2009. ##[3] Craciunescu, C.M., Wuttig, M., “New ferromagnetic and functionally grade shape memory alloys”, J Optoelectron Adv Mater, Vol. 5, No. 1, pp. 139–46, 2003. ##[4] Fu, Y.Q., Du, H.J., Zhang, S., “Functionally graded TiN/TiNi shape memory alloy films”, Mater Lett, Vol. 57, No. 20, pp. 2995–9, 2003. ##[5] Fu, Y.Q., Du, H.J., “Huang WM, Zhang S, Hu M. TiNibased thin films in MEMS applications: a review”, Sensors Actuat A, Vol. 112, No. (2–3), pp. 395408, 2004. ##[6] Witvrouw, A., Mehta, A., “The use of functionally graded polySiGe layers for MEMS applications, Functionally Graded Mater, Vol. 8, pp. 255–60, 2005. ##[7] Lee, Z., Ophus, C., Fischer, L.M., et al. “Metallic NEMS components fabricated from nanocomposite AlMo films”, Nanotechnology, Vol. 17, No. 12, pp. 3063–70, 2006. ##[8] Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T., “The modified couple stress functionally graded Timoshenko beam formulation”, Materials and Design, Vol. 32, pp. 1435–1443, 2011. ##[9] Jafar, I., SadeghiPournaki, Zamanzadeh, M.R., Shabani, R., Rezazadeh, G., “Mechanical Behavior of a FGM Capacitive MicroBeam Subjected to a Heat Source”, Journal of Solid Mechanics, Vol. 3, No. 2, pp. 158171, 2011. ##[10] Ke, L.L., Wang, Y.S., “Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory”, Composite Structures, Vol. 93, pp. 342–350, 2011. ##[11] Sharafkhani, N., Rezazadeh, G., Shabani, R., “Study of mechanical behavior of circular FGM microplates under nonlinear electrostatic and mechanical shock loadings”, Acta Mech, Vol. 223, pp. 579–591, 2012. ##[12] Das, K., Batra, R.C., “Pullin and snapthrough instabilities in transient deformations of microelectromechanical systems,” J. Micromech. Microeng., Vol. 19, 035008, 2009. doi:10.1088/09601317/19/3/035008. ##[13] Fu, Y., Zhang, J., “Sizedependent pullin phenomena in electrically actuated nano beams incorporating surface energies,” Applied Mathematical Modelling, Vol. 35, pp. 941951, 2011. ##[14] Wang, Y.G., Lin, W.H., Feng, Z.J., Li, X.M., “Characterization of extensional multilayer microbeams in pullin phenomenon and vibrations,” International Journal of Mechanical Sciences, Vol. 54, pp. 225–233, 2012. ##[15] Jia, X.L., Yang, J., Kitipornchai, S., “Pullin instability of geometrically nonlinear microswitches under electrostatic and Casimir forces,” Acta Mech., Vol. 218, pp. 161174, 2011. doi: 10.1007/s0070701004128. ##[16] Sedighi, H.M., Shirazi, K.H., “Vibrations of microbeams actuated by an electric field via Parameter Expansion Method,” Acta Astronautica, Vol. 85, pp. 1924, 2013. ##[17] Rahaeifard, M., Ahmadian, M.T., Firoozbakhsh, K., “Sizedependent dynamic behavior of microcantilevers under suddenly applied DC voltage,” Proc IMechE Part C: J Mechanical Engineering Science, DOI: 10.1177/0954406213490376. ##[18] Rajabi, F., Ramezani, S., “A nonlinear microbeam model based on strain gradient elasticity theory,” Acta Mechanica Solida Sinica,Vol. 26, No. 1, 2013, doi: 10.1016/S08949166(13)600038. ##[19] Towfighian, S., Heppler, G.R., AbdelRahman, E.M., “Analysis of a Chaotic Electrostatic MicroOscillator,” Journal of Computational and Nonlinear Dynamics, Vol. 6, No. 1, 011001, 2011. ##[20] He, J.H., “MaxMin approach to nonlinear oscillators”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 9, pp. 207210. ##[21] Sedighi, H.M., Shirazi, K.H., Noghrehabadi, A., “Application of Recent Powerful Analytical Approaches on the NonLinear Vibration of Cantilever Beams”, Int. J. Nonlinear Sci. Numer. Simul., Vol. 13, No. 7–8, pp. 487–494, 2012. ##[22] Ghadimi, M., Barari, A., Kaliji, H.D., Domairry, G., “Periodic solutions for highly nonlinear oscillation systems” Archives of Civil and Mechanical Engineering, Vol. 12, No. 3, pp. 389395, 2012. ##[23] Sedighi, H.M., Shirazi, K.H., Zare, J., “An analytic solution of transversal oscillation of quintic nonlinear beam with homotopy analysis method”, International Journal of NonLinear Mechanics, Vol. 47, pp. 777784, 2012. ##[24] Noghrehabadi, A., Ghalambaz, M., Ghanbarzadeh, A., “A new approach to the electrostatic pullin instability of nanocantilever actuators using the ADM–Padé technique”, Computers & Mathematics with Applications, Vol. 64, No. 9, pp. 2806–2815, 2012. ##[25] Kaliji, H.D., Ghadimi, M., Pashaei, M.H., “Study the behavior of an electrically exciting nanotube using optimal homotopy asymptotic method”, Int. J. Appl. Mechanics, Vol. 04, 1250004, 2012, DOI: 10.1142/S1758825112001336. ##[26] Shou, D.H., He, J.H., “Application of parameterexpanding method to strongly nonlinear oscillators”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8, No. (1), pp. 121124, 2007. ##[27] Sedighi, H.M., Shirazi, K.H., Noghrehabadi, A.R., Yildirim, A., “Asymptotic Investigation of Buckled Beam Nonlinear Vibration,” Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 36, No. (M2), pp. 107116, 2012. ##[28] He, J. H., “Hamiltonian approach to nonlinear oscillators”, Physics Letters A, Vol. 374, No. (23), pp. 23122314, 2010. ##[29] Sedighi, H.M., Shirazi, K.H., Attarzadeh, M.A., “A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches”, Acta Astronautica, Vol. 91, pp. 245250, 2013. ##[30] He, J.H., “Homotopy Perturbation Method with an Auxiliary Term”, Abstract and Applied Analysis, Vol. 2012, 857612, doi:10.1155/2012/857612. ##[31] Batra, R.C., Porfiri, M., Spinello, D., “Vibrations of narrow microbeams predeformed by an electric field”, Journal of Sound and Vibration, Vol. 309, pp. 600612, 2008. ##[32] He, J.H., “Homotopy perturbation method with two expanding parameters,” Ind. J. Phys., Vol. 88, No. 2, pp. 193196, 2014.##]
Global Finite Time Synchronization of Two Nonlinear Chaotic Gyros Using High Order Sliding Mode Control
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In this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of secondorder chaotic nonlinear gyros are achieved by considering a method of continuous smooth secondorder sliding mode control (HOAMSC). It is proved that the proposed controller is robust to mismatch parametric uncertainties. Also it is shown that the method have excellent performance and more accuracy in comparison with conventional sliding mode control. Based on Lyapunov stability theory, the proposed controller and some generic sufficient conditions for global finite time synchronization are designed such that the errors dynamic of two chaotic behaviour satisfy stability in the Lyapunov sense. The numerical results demonstrate the efficiency of the proposed scheme to synchronize the chaotic gyro systems using a single control input.
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Mohammad Reza
Behjameh
Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
Faculty of Electrical and Electronic Engineering,
Iran
rezabehjameh@yahoo.com


Hadi
Delavari
Assistant Professor, Department of Electrical and Electronic Engineering, Hamedan University of Technology
Assistant Professor, Department of Electrical
Iran
hdelavari@gmail.com


Ahmadreza
Vali
Assistant Professor, Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
Assistant Professor, Faculty of Electrical
Iran
vali@mut.ac.ir
smooth secondorder sliding mode (SSOSMC) control
chaos synchronization
chaotic gyros stability
Uncertainty
finite time converges
[[1] Pecora, L.M., Carroll, T.L., 1990. “Synchronization in Chaotic Systems”, Physical Review Letters 64, 821–824. ##[2] Nayfeh A.H., Applied Nonlinear Dynamics, Wiley, New York, 1995. ##[3] Chen, G., Dong, X., From Chaos to Order: Methodologies, Perspectives and Applications, World Scientific, Singapore, 1998. ##[4] Delavari, H., Ghaderi, R., Ranjbar A., Momani, S., 2010. “Fractional order control of a coupled tank,” Nonlinear Dynamics, 61, 383–397. ##[5] Delavari, H., Ghaderi, R., Ranjbar, A., Momani, S., 2010. “Synchronization of chaotic nonlinear gyro using fractional order controller,” Berlin, Springer, 479–485. ##[6] Delavari, H., Mohammadi Senejohnny, D., Baleanu, D., 2012. “Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter,” Central European Journal of Physics ,10(5), 10951101. ##[7] Faieghi, M.R., Delavari, H., 2012, “Chaos in fractionalorder Genesio–Tesi system and its synchronization,” Communications in Nonlinear Science and Numerical Simulation, 17, 731741. ##[8] Delavari, H., Lanusse, P., Sabatier, J., 2013. “Fractional Order Controller Design for a Flexible Link Manipulator Robot,” Asian Journal of Control, 15(3), 783–795. ##[9] Delavari, H., Ghaderi, R., Ranjbar, A., Momani, S., 2010. “A Study on the Stability of Fractional Order Systems,” FDA2010, University of Extremadura, Badajoz, Spain, October 1820. ##[10] Salarieh, H., Alastyisc, A., 2008. “Chaos synchronization of nonlinear gyros in presence of stochastic excitation via sliding mode control,” Journal of Sound and Vibration, 313, 760–771. ##[11] Che, Y.Q., Wang, J., Chan, W., Tsang, K.M., Wei, X.L., Deng, B., 2009. “Chaos Synchronization of Gyro Systems via Variable Universe Adaptive Fuzzy Sliding Mode Control,” Proceedings of the 7th Asian Control Conference, 2729. ##[12] Chen, T.U., Zhan, W.I., Lin, C.M., Yeung, D.S., 2010. “Chaos Synchronization of Two Uncertain Chaotic Nonlinear Gyros Using Rotary Sliding Mode Control,” Proceedings of the Ninth International Conference on Machine Learning and Cybernetics, July 1114. ##[13] Yang, C.C., Ouech, C.J., 2013. “Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros,” Commun Nonlinear Sci Numer Simulat., 18, 682–691. ##[14] Lei, Y., Xu, W., Zheng, H., 2005. “Synchronization of two chaotic nonlinear gyros using active control,” Physics Letters A, 343, 153–158. ##[15] Chen, H.K. 2002. “Chaos and chaos synchronization of a symmetric gyro with linearpluscubic damping,” Journal of Sound and Vibration, 255, 719–740. ##[16] Tanaka, K., Ikeda, T., Wang, H.O., 1998. “A unified approach to controlling chaos via LMIbased fuzzy control system design,” IEEE Transactions on Circuits and Systems I, 45, 1021–1040. ##[17] Feng, G., Chen, G., 2005. “Adaptive control of discretetime chaotic systems: a fuzzy control approach,” Chaos Solitons & Fractals, 23, 459–467. ##[18] Xue, Y.J., Yang, S.Y., 2003. “Synchronization of generalized Henon map by using adaptive fuzzy controller,” Chaos Solitons & Fractals, 17, 717–722. ##[19] Kaveh, P., Shtessel, Y.B., 2008. “Blood glucose regulation using higherorder sliding mode control,” International Journal of Robust and Nonlinear Control, 18(45), 557–569. ##[20] Levant, A. 2007. “Principles of 2slidingmode design,” Automatica, 43, 576586. ##[21] Mondal, S., Mahanta, Ch. 2011. “Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems,” Commun Nonlinear Sci Numer Simulat, 16, 3760–3769. ##[22] Evangelista, C. Puleston, P., Valenciaga, F., 2010. “Wind turbine efﬁciency optimization. Comparative study of controllers based on second order sliding modes,” International Journal of Hydrogen Energy, 35, 5934–5939. ##[23] Filippov, A. “Differential equations with discontinuous righthand side,” Dordrecht, Netherlands: Kluwer Academic Publishers, 1988. ##[24] Slotine, J. J. E., Li, W., Applied Nonlinear Control, PrenticeHall, Upper Saddle River, NJ, pp. 276309. 1991. ##[25] Lawrence, A., Modern Internal Technology, navigation, guidance and control, Springer, TL, 588.L38, 1988.##]
Bearing Fault Detection Based on Maximum Likelihood Estimation and Optimized ANN Using the Bees Algorithm
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2
Rotating machinery is the most common machinery in industry. The root of the faults in rotating machinery is often faulty rolling element bearings. This paper presents a technique using optimized artificial neural network by the Bees Algorithm for automated diagnosis of localized faults in rolling element bearings. The inputs of this technique are a number of features (maximum likelihood estimation values), which are derived from the vibration signals of test data. The results show that the performance of the proposed optimized system is better than most previous studies, even though it uses only two features. Effectiveness of the above method is illustrated using obtained bearing vibration data.
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43


Behrooz
Attaran
MSc., Mechanical Engineering, Shahid Chamran University of Ahvaz
MSc., Mechanical Engineering, Shahid Chamran
Iran
attaranbehrooz@yahoo.com


Afshin
Ghanbarzadeh
Assistant Professor, Mechanical Engineering Department, Shahid Chamran University of Ahvaz
Assistant Professor, Mechanical Engineering
Iran
ghanbarzadeh.a@scu.ac.ir
Fault Diagnosis
MLE distributions
RBF neural network
Bees Algorithm
[[1] Seera, M., Lim, CH. P., Nahavandi, S., Loo, CH. K., “Condition Monitoring of Induction Motors: A Review and an Application of an Ensemble of Hybrid Intelligent Models”, Expert Systems with Applications, Vol. 41, No. 10, pp. 48914903, 2014. ##[2] Thomas, M., and Fiabilite, 2003, “Maintenance Predictive”, et Vibration de Machines, Publications ETS, Montreal, Qc, Can, p. 616. ##[3] Archambault, J., Archambault, R. and Thomas, M., 2002, “Time domain descriptors for rollingelement bearing fault detection”, Proceedings of the 20th seminar on machinery vibration, CMVA, Québec, p. 10. ##[4] Thomas, M., Archambault, R., and Archambault, J., 2003, “Modified Julien index as a shock detector: its application to detect rolling element bearing defect”, Proceedings of the 21th seminar on machinery vibration, CMVA, Halifax (N.S.), pp. 21.121.12. ##[5] Gluzman, D., 2000, “The use of log scales to analyse bearing failures”, J. Vibrations, 16 (3), pp. 35. ##[6] Randall, R. 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Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method
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In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this method is effective and convenient. Also, it is predicated that MIPM can be potentially used in the analysis of strongly nonlinear oscillation problems accurately.
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Mohammad
Mashinchi Joubari
Dept. of Mechanical Engineering, Babol University of Technology, Babol, Iran
Dept. of Mechanical Engineering, Babol University
Iran
mmmjouybari@gmail.com


Davood
Ganji
Assistant Professor, Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
Assistant Professor, Department of Mechanical
Iran
mirgang@nit.ac.ir


Hamid
Javanian Jouybari
Department of Mechanical Engineering, Semnan University, Iran
Department of Mechanical Engineering, Semnan
Iran
hamidjavaniyan@gmail.com
Periodic behavior
Tapered beam
Modified Iteration Perturbation Method (MIPM)
Nonlinear ordinary differential equation
Nonlinear oscillation
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