ORIGINAL_ARTICLE
Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term
This paper presents the high order frequency-amplitude 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.
http://jacm.scu.ac.ir/article_10545_cdeea4bb07f2a3db61cf4e9502de142e.pdf
2014-06-01T11:23:20
2018-03-24T11:23:20
1
9
10.22055/jacm.2014.10545
Homotopy Perturbation Method with an auxiliary term
Non-linear vibrating beams
Frequency-amplitude relationship
Hamid M.
Sedighi
h.msedighi@scu.ac.ir
true
1
Shahid Chamran University, Faculty of Engineering, Mechanical Engineering Department, Ahvaz, Iran
Shahid Chamran University, Faculty of Engineering, Mechanical Engineering Department, Ahvaz, Iran
Shahid Chamran University, Faculty of Engineering, Mechanical Engineering Department, Ahvaz, Iran
LEAD_AUTHOR
Farhang
Daneshmand
farhang.daneshmand@mcgill.ca
true
2
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
AUTHOR
[1] Love, A.E.H.; 1927. A treatise on the Mathematical theory of Elasticity. New York: Dover Publications, Inc.
1
[2] Sedighi, H.M., Shirazi, K.H., and Noghrehabadi, A. Application of Recent Powerful Analytical Approaches on the Non-Linear Vibration of Cantilever Beams, Int. J. Nonlinear Sci. Numer. Simul., 2012; 13(7–8): 487-494, DOI: 10.1515/ijnsns-2012-0030.
2
[3] Barari, A.; Kaliji, H.D.; Ghadami, M.; Domairry, G.; 2011. Non-Linear Vibration of Euler-Bernoulli Beams. Latin American Journal of Solids and Structures. 8: 139-148.
3
[4] Sedighi, H.M.; Reza, A.; Zare, J.; 2011. Dynamic analysis of preload nonlinearity in nonlinear beam vibration, Journal of Vibroengineering. 13: 778-787.
4
[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): 8051-8056.
5
[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.
6
[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): 107-116.
7
[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), 443-451.
8
[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.
9
[10] Nikkhah Bahrami, M.; Khoshbayani Arani, M.; Rasekh Saleh, N.; 2011. Modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform beams. Scientia Iranica B, 18(5):1088–1094.
10
[11] Arvin, H.; Bakhtiari-Nejad, F.; 2011. Non-linear modal analysis of a rotating beam. International Journal of Non-Linear Mechanics, 46: 877–897.
11
[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.
12
[13] Freno, B.A.: Cizmas, P.G.A.; 2011. A computationally efficient non-linear beam model. International Journal of Non-Linear Mechanics, 46: 854-869.
13
[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.
14
[15] Andreaus, U.; Placidi, L.; Rega, G.; 2011. Soft impact dynamics of a cantilever beam: equivalent SDOF model versus infinite-dimensional system. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(10): 2444-2456. doi: 10.1177/0954406211414484.
15
[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 Non-Linear Mechanics, 46: 180–185.
16
[17] Sapountzakis, E.J.; Dikaros, I.C.; 2011. Non-linear flexural-torsional dynamic analysis of beams of arbitrary cross section by BEM. International Journal of Non-Linear Mechanics, 46: 782–794.
17
[18] Jang, T.S.; Baek, H.S.; Paik, J.K.; 2011. A new method for the non-linear deflection analysis of an infinite beam resting on a non-linear elastic foundation. International Journal of Non-Linear Mechanics, 46: 339–346.
18
[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): 2759-2764. Doi: 10.1177/0954406211417753.
19
[20] He, J.H., 2008. Max-Min Approach to Nonlinear Oscillators, International Journal of Nonlinear Sciences and Numerical Simulation, 9(2), 207-210.
20
[21] Liao, S.J. 2004. An analytic approximate approach for free oscillations of self-excited systems, International Journal of Non-Linear Mechanics, 39, 271-280.
21
[22] Sedighi, H.M.; Shirazi, K.H.; Zare, J.; 2012. An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method. International Journal of Non-Linear Mechanics, 47: 777- 784, DOI: 10.1016/j.ijnonlinmec.2012.04.008.
22
[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 Method-II, Journal of Mechanical Science and Technology, 27(11) 3433-3438.
23
[24] Bagheri, S.; Nikkar, A; Ghaffarzadeh, H; 2014. Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques, Latin American Journal of Solids and Structures, 11: 157-168.
24
[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: 347-353.
25
[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 pull-in instability of nano-actuators, Phys. Scr., 82: 045801. doi:10.1088/0031-8949/82/04/045801.
26
[27] Bayat, M.; Shahidi, M.; Barari, A.; Domairry, G.; 2011. Analytical evaluation of the nonlinear vibration of coupled oscillator systems. Zeitschrift fur Naturforschung A-A Journal of Physical Sciences, 66(1-2): 67–74.
27
[28] He, J.H., 2002. Preliminary report on the energy balance for nonlinear oscillations. Mech. Res. Commun., 29, 107-111.
28
[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.
29
[30] He, J.H; 2011. A short remark on fractional variational iteration method , PHYSICS LETTERS A, 375(38), 3362-3364, dio: 10.1016/j.physleta.2011.07.033.
30
[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.
31
[32] Hasanov, A.; 2011. Some new classes of inverse coefficient problems in non-linear mechanics and computational material science, International Journal of Non-Linear Mechanics, 46(5): 667-684.
32
[33] He, J.H.; 2010. Hamiltonian approach to nonlinear oscillators, Physics Letters A, 374(23): 2312-2314.
33
[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): 526-536. doi: 10.1243/09544062JMES2171.
34
[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): 312-325.
35
[36] He, J.H.; 2002. Modified Lindstedt-Poincare methods for some strongly non-linear oscillations Part I: expansion of a constant, International Journal of Non-linear Mechanics, 37(2): 309-314. DOI: 10.1016/S0020-7462(00)00116-5.
36
[37] He, J.H., Homotopy Perturbation Method with an Auxiliary Term, Abstract and Applied Analysis, 2012, Article ID 857612, doi:10.1155/2012/857612.
37
[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.
38
[39] M. R. M. Crespo da Silva & C. C. Glynn, Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion, Journal of Structural Mechanics, Volume 6, Issue 4, 1978, DOI: 10.1080/03601217808907348.
39
[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.
40
ORIGINAL_ARTICLE
Optimal Roll Center Height of Front McPherson Suspension System for a Conceptual Class A Vehicle
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.
http://jacm.scu.ac.ir/article_10578_3cdaf7097bd9f98624ec26e839b070d2.pdf
2014-06-01T11:23:20
2018-03-24T11:23:20
10
16
10.22055/jacm.2014.10578
Vehicle dynamics
Roll center height
McPherson suspension mechanism
Javad
Meshkatifar
j.meshkatifar@yahoo.com
true
1
Master Student, Department of Mechanical Engineering, Isfahan University of Technology
Master Student, Department of Mechanical Engineering, Isfahan University of Technology
Master Student, Department of Mechanical Engineering, Isfahan University of Technology
LEAD_AUTHOR
Mohsen
Esfahanian
mesf1964@cc.iut.ac.ir
true
2
Associate Professor, Department of Mechanical Engineering, Isfahan University of Technology
Associate Professor, Department of Mechanical Engineering, Isfahan University of Technology
Associate Professor, Department of Mechanical Engineering, Isfahan University of Technology
AUTHOR
[1] D.L. Cronin, 1981, “MacPherson Strut Kinematics”. Mechanism and machine theory, vol. 16, No.6, pp. 631-644.
1
[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.
2
[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.
3
[4] B. Nemeth, P. Gaspar, 2012, “Design of Variable-Geometry Suspension for Driver Assistance Systems”, Mediterranean Conference on Control & Automation (MED),Barcelona, Spain, July 3-6.
4
[5] J. C.Dixon, 1996, tires, suspension and handling, Society of Automotive Engineers.
5
[6] R. N.Jazar, 2008, vehicle dynamic theory and application, springer.
6
[7] J. Reimpell, H. Stoll, J.W.Betzler, 2001, the Automotive Chassis: Engineering Principles, Butterworth-Heinemann, Linacre House, Jordan Hill, Oxford.
7
[8] T. D.Gillespie, 1994, fundamentals of vehicle dynamics, Society of Automotive Engineers (SAE).
8
[9] ADAMS User Manual, 2013, M.S.C. Software Group.
9
ORIGINAL_ARTICLE
Pull-in behavior analysis of vibrating functionally graded micro-cantilevers under suddenly DC voltage
The present research attempts to explain dynamic pull-in instability of functionally graded micro-cantilevers actuated by step DC voltage while the fringing-field effect is taken into account in the vibrational equation of motion. By employing modern asymptotic approach namely Homotopy Perturbation Method with an auxiliary term, high-order frequency-amplitude relation is obtained, then the influences of material properties and actuation voltage on dynamic pull-in 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.
http://jacm.scu.ac.ir/article_10552_dc1efb081b26fc82c7ab2c8edeb51aa1.pdf
2014-06-01T11:23:20
2018-03-24T11:23:20
17
25
10.22055/jacm.2014.10552
Micro-actuator
Functionally graded material
Dynamic Pull-in instability
Homotopy Perturbation Method with an auxiliary term
Jamal
Zare
jamal.zare@hotmail.com
true
1
National Iranian South Oil Company (NISOC), Ahvaz, Iran
National Iranian South Oil Company (NISOC), Ahvaz, Iran
National Iranian South Oil Company (NISOC), Ahvaz, Iran
LEAD_AUTHOR
[1] Asghari, M., Ahmadian, M.T., Kahrobaiyan, M.H., Rahaeifard, M., “On the size-dependent behavior of functionally graded micro-beams”, Materials and Design, Vol. 31, pp. 2324–2329, 2010.
1
[2] Lü, C.F., Chen, W.Q., Lim, C.W., “Elastic mechanical behavior of nano-scaled FGM films incorporating surface energies”, Composites Science and Technology, Vol. 69, pp. 1124–1130, 2009.
2
[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.
3
[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.
4
[5] Fu, Y.Q., Du, H.J., “Huang WM, Zhang S, Hu M. TiNi-based thin films in MEMS applications: a review”, Sensors Actuat A, Vol. 112, No. (2–3), pp. 395-408, 2004.
5
[6] Witvrouw, A., Mehta, A., “The use of functionally graded poly-SiGe layers for MEMS applications, Functionally Graded Mater, Vol. 8, pp. 255–60, 2005.
6
[7] Lee, Z., Ophus, C., Fischer, L.M., et al. “Metallic NEMS components fabricated from nanocomposite Al-Mo films”, Nanotechnology, Vol. 17, No. 12, pp. 3063–70, 2006.
7
[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.
8
[9] Jafar, I., Sadeghi-Pournaki, Zamanzadeh, M.R., Shabani, R., Rezazadeh, G., “Mechanical Behavior of a FGM Capacitive Micro-Beam Subjected to a Heat Source”, Journal of Solid Mechanics, Vol. 3, No. 2, pp. 158-171, 2011.
9
[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.
10
[11] Sharafkhani, N., Rezazadeh, G., Shabani, R., “Study of mechanical behavior of circular FGM micro-plates under nonlinear electrostatic and mechanical shock loadings”, Acta Mech, Vol. 223, pp. 579–591, 2012.
11
[12] Das, K., Batra, R.C., “Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems,” J. Micromech. Microeng., Vol. 19, 035008, 2009. doi:10.1088/0960-1317/19/3/035008.
12
[13] Fu, Y., Zhang, J., “Size-dependent pull-in phenomena in electrically actuated nano beams incorporating surface energies,” Applied Mathematical Modelling, Vol. 35, pp. 941-951, 2011.
13
[14] Wang, Y.G., Lin, W.H., Feng, Z.J., Li, X.M., “Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations,” International Journal of Mechanical Sciences, Vol. 54, pp. 225–233, 2012.
14
[15] Jia, X.L., Yang, J., Kitipornchai, S., “Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces,” Acta Mech., Vol. 218, pp. 161-174, 2011. doi: 10.1007/s00707-010-0412-8.
15
[16] Sedighi, H.M., Shirazi, K.H., “Vibrations of micro-beams actuated by an electric field via Parameter Expansion Method,” Acta Astronautica, Vol. 85, pp. 19-24, 2013.
16
[17] Rahaeifard, M., Ahmadian, M.T., Firoozbakhsh, K., “Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage,” Proc IMechE Part C: J Mechanical Engineering Science, DOI: 10.1177/0954406213490376.
17
[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/S0894-9166(13)60003-8.
18
[19] Towfighian, S., Heppler, G.R., Abdel-Rahman, E.M., “Analysis of a Chaotic Electrostatic Micro-Oscillator,” Journal of Computational and Nonlinear Dynamics, Vol. 6, No. 1, 011001, 2011.
19
[20] He, J.H., “Max-Min approach to nonlinear oscillators”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 9, pp. 207-210.
20
[21] Sedighi, H.M., Shirazi, K.H., Noghrehabadi, A., “Application of Recent Powerful Analytical Approaches on the Non-Linear Vibration of Cantilever Beams”, Int. J. Nonlinear Sci. Numer. Simul., Vol. 13, No. 7–8, pp. 487–494, 2012.
21
[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. 389-395, 2012.
22
[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 Non-Linear Mechanics, Vol. 47, pp. 777-784, 2012.
23
[24] Noghrehabadi, A., Ghalambaz, M., Ghanbarzadeh, A., “A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM–Padé technique”, Computers & Mathematics with Applications, Vol. 64, No. 9, pp. 2806–2815, 2012.
24
[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.
25
[26] Shou, D.H., He, J.H., “Application of parameter-expanding method to strongly nonlinear oscillators”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 8, No. (1), pp. 121-124, 2007.
26
[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. 107-116, 2012.
27
[28] He, J. H., “Hamiltonian approach to nonlinear oscillators”, Physics Letters A, Vol. 374, No. (23), pp. 2312-2314, 2010.
28
[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. 245-250, 2013.
29
[30] He, J.H., “Homotopy Perturbation Method with an Auxiliary Term”, Abstract and Applied Analysis, Vol. 2012, 857612, doi:10.1155/2012/857612.
30
[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. 600-612, 2008.
31
[32] He, J.H., “Homotopy perturbation method with two expanding parameters,” Ind. J. Phys., Vol. 88, No. 2, pp. 193-196, 2014.
32
ORIGINAL_ARTICLE
Global Finite Time Synchronization of Two Nonlinear Chaotic Gyros Using High Order Sliding Mode Control
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 second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order 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.
http://jacm.scu.ac.ir/article_10549_077192115381693b0d840d62b92b3586.pdf
2014-06-01T11:23:20
2018-03-24T11:23:20
26
34
10.22055/jacm.2014.10549
smooth second-order sliding mode (SSOSMC) control
chaos synchronization
chaotic gyros stability
Uncertainty
finite time converges
Mohammad Reza
Behjameh
rezabehjameh@yahoo.com
true
1
Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
LEAD_AUTHOR
Hadi
Delavari
hdelavari@gmail.com
true
2
Assistant Professor, Department of Electrical and Electronic Engineering, Hamedan University of Technology
Assistant Professor, Department of Electrical and Electronic Engineering, Hamedan University of Technology
Assistant Professor, Department of Electrical and Electronic Engineering, Hamedan University of Technology
AUTHOR
Ahmadreza
Vali
vali@mut.ac.ir
true
3
Assistant Professor, Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
Assistant Professor, Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
Assistant Professor, Faculty of Electrical and Electronic Engineering, Department of Control Engineering, Malek Ashtar University of Technology
AUTHOR
[1] Pecora, L.M., Carroll, T.L., 1990. “Synchronization in Chaotic Systems”, Physical Review Letters 64, 821–824.
1
[2] Nayfeh A.H., Applied Nonlinear Dynamics, Wiley, New York, 1995.
2
[3] Chen, G., Dong, X., From Chaos to Order: Methodologies, Perspectives and Applications, World Scientific, Singapore, 1998.
3
[4] Delavari, H., Ghaderi, R., Ranjbar A., Momani, S., 2010. “Fractional order control of a coupled tank,” Nonlinear Dynamics, 61, 383–397.
4
[5] Delavari, H., Ghaderi, R., Ranjbar, A., Momani, S., 2010. “Synchronization of chaotic nonlinear gyro using fractional order controller,” Berlin, Springer, 479–485.
5
[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), 1095-1101.
6
[7] Faieghi, M.R., Delavari, H., 2012, “Chaos in fractional-order Genesio–Tesi system and its synchronization,” Communications in Nonlinear Science and Numerical Simulation, 17, 731-741.
7
[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.
8
[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 18-20.
9
[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.
10
[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, 27-29.
11
[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 11-14.
12
[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.
13
[14] Lei, Y., Xu, W., Zheng, H., 2005. “Synchronization of two chaotic nonlinear gyros using active control,” Physics Letters A, 343, 153–158.
14
[15] Chen, H.K. 2002. “Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping,” Journal of Sound and Vibration, 255, 719–740.
15
[16] Tanaka, K., Ikeda, T., Wang, H.O., 1998. “A unified approach to controlling chaos via LMI-based fuzzy control system design,” IEEE Transactions on Circuits and Systems I, 45, 1021–1040.
16
[17] Feng, G., Chen, G., 2005. “Adaptive control of discrete-time chaotic systems: a fuzzy control approach,” Chaos Solitons & Fractals, 23, 459–467.
17
[18] Xue, Y.J., Yang, S.Y., 2003. “Synchronization of generalized Henon map by using adaptive fuzzy controller,” Chaos Solitons & Fractals, 17, 717–722.
18
[19] Kaveh, P., Shtessel, Y.B., 2008. “Blood glucose regulation using higher-order sliding mode control,” International Journal of Robust and Nonlinear Control, 18(4-5), 557–569.
19
[20] Levant, A. 2007. “Principles of 2-slidingmode design,” Automatica, 43, 576-586.
20
[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.
21
[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.
22
[23] Filippov, A. “Differential equations with discontinuous right-hand side,” Dordrecht, Netherlands: Kluwer Academic Publishers, 1988.
23
[24] Slotine, J. J. E., Li, W., Applied Nonlinear Control, Prentice-Hall, Upper Saddle River, NJ, pp. 276-309. 1991.
24
[25] Lawrence, A., Modern Internal Technology, navigation, guidance and control, Springer, TL, 588.L38, 1988.
25
ORIGINAL_ARTICLE
Bearing Fault Detection Based on Maximum Likelihood Estimation and Optimized ANN Using the Bees Algorithm
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.
http://jacm.scu.ac.ir/article_10547_decbdc01b7f1970b36a9b83382e1f020.pdf
2014-06-01T11:23:20
2018-03-24T11:23:20
35
43
10.22055/jacm.2014.10547
Fault Diagnosis
MLE distributions
RBF neural network
Bees Algorithm
Behrooz
Attaran
attaranbehrooz@yahoo.com
true
1
MSc., Mechanical Engineering, Shahid Chamran University of Ahvaz
MSc., Mechanical Engineering, Shahid Chamran University of Ahvaz
MSc., Mechanical Engineering, Shahid Chamran University of Ahvaz
LEAD_AUTHOR
Afshin
Ghanbarzadeh
ghanbarzadeh.a@scu.ac.ir
true
2
Assistant Professor, Mechanical Engineering Department, Shahid Chamran University of Ahvaz
Assistant Professor, Mechanical Engineering Department, Shahid Chamran University of Ahvaz
Assistant Professor, Mechanical Engineering Department, Shahid Chamran University of Ahvaz
AUTHOR
[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. 4891-4903, 2014.
1
[2] Thomas, M., and Fiabilite, 2003, “Maintenance Predictive”, et Vibration de Machines, Publications ETS, Montreal, Qc, Can, p. 616.
2
[3] Archambault, J., Archambault, R. and Thomas, M., 2002, “Time domain descriptors for rolling-element bearing fault detection”, Proceedings of the 20th seminar on machinery vibration, CMVA, Québec, p. 10.
3
[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. 21.1-21.12.
4
[5] Gluzman, D., 2000, “The use of log scales to analyse bearing failures”, J. Vibrations, 16 (3), pp. 3-5.
5
[6] Randall, R. B., Antoni, J., “Rolling Element Bearing Diagnostics _ A Tutorial”, Mechanical Systems and Signal Processing, Vol. 25, No. 2, pp. 485-520, 2011.
6
[7] Yan, R., Gao, R. X., “Multi-Scale Enveloping Spectrogram for Vibration Analysis in Bearing Defect Diagnosis”, Tribology International, Vol. 42, No. 2, pp. 293-302, 2009.
7
[8] Loutas, T. H., Roulias, D., Pauly, E., Kostopoulos, V., “The Combined Use of Vibration, Acoustic Emission and Oil Debris On-line Monitoring Towards a More Effective Condition Monitoring of Rotating Machinery”, Mechanical Systems and Signal Processing, Vol. 25, No. 4, pp. 1339-1352, 2011.
8
[9] Hamel, M., Addali, A., Mba, D., “Investigation of the Influence of Oil Film Thickness on Helical Gear Defect Detection Using Acoustic Emission”, Applied Acoustic, Vol. 79, pp. 42-46, 2014.
9
[10] Safizadeh, M.S., Lakis, A.A., and Thomas, M., 2002, “Time-Frequency distributions and their Application to Machinery Fault Detection”, J. International Journal of Condition Monitoring and Diagnosis Engineering Management, 5 (2), pp. 41-56.
10
[11] Khemili, I., Chouchane, M., “Detection of Rolling Element Bearing Defects by Adaptive Filtering”, European Journal of Mechanics – A/Solids, Vol. 24, No. 2, pp. 293-303, 2005.
11
[12] Wang, H., Chen, P., “Intelligent Diagnosis Method for Rolling Element Bearing Faults Using Possibility Theory and Neural Network”, Computers & Industrial Engineering, Vol. 60, No. 4, pp. 511-518, 2011.
12
[13] Castejon, C., Lara, O., Garcia-Prada J. C., “Automated Diagnosis of Rolling Bearings Using MRA and Neural Networks”, Mechanical Systems and Signal Processing, Vol. 24, No. 1, pp. 289-299, 2010.
13
[14] Dong, G., Chen, J., “Noise Resistant Time Frequency Analysis and Application in Fault Diagnosis of Rolling Element Bearings”, Mechanical Systems and Signal Processing, Vol. 33, pp. 212-236, 2012.
14
[15] Pham, D.T., Ghanbarzadeh, A., Koc, E., Otri, S., Rahim, S. and Zaidi, M., 2006, “The Bees Algorithm. A novel tool for complex optimization problems”, In Proceedings of the 2nd International Virtual Conference on Intelligent production machines and systems (IPROMS 2006), pp. 454–459 (Elsevier, Oxford), see also URL http://www.iproms.org/
15
[16] Samanta, B., and Al-Balushi, K.R., 2003, “Artificial neural network based fault diagnostics of rolling element bearings using time-domain features”, J. Mechanical Systems and Signal Processing, 17 (2), pp. 317-328.
16
[17] Abbasion, S., Rafsanjani, A., Farshidianfar, A., and Irani, N., 2007, “Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine”, J. Mechanical Systems and Signal Processing, 21, pp. 2933-2945.
17
[18] Sassi, S., Badri, B., and Thmoas, M., 2006, “"TALAF" and "THIKAT" as innovative time domain indicators for tracking BALL bearings”, Proceedings of the 24nd Seminar on machinery vibration, Canadian Machinery Vibration Association, éditeur M. Thomas, Montréal, Canada, pp.404-419.
18
[19] Loparo, K.A., Bearings vibration data set, 2003, Case Western Reserve University, available from <http://www.eecs.cwru.edu/laboratory/bearing/download.htm>.
19
[20] Nelwamondo, F.V., Marwala, T., and Mahola, U., 2006, “Early classifications of bearing faults using hidden markov models, Gaussian mixture models, mel-frequency cepstral coefficients and fractals”, J. International Journal of Innovative Computing, Information and Control, 2 (6), pp. 1281-1299.
20
[21] Marwala, T., and Vilakazi, C.B., 2007, “Computational intelligence for condition monitoring”, CoRR.
21
[22] Yang, J., Zhang, Y., and Zhu, Y., 2007, “Intelligent fault diagnosis of rolling element bearing based on SVMs and fractal dimension”, J. Mechanical Systems and Signal Processing, 21, pp. 2012-2024.
22
[23] Sreejith, B., Verma, A.K., and Srividya, A., 2008, “Fault diagnosis of rolling element bearing using time-domain features and neural network”, IEEE region 10 Colloquium and the ICIIS, Kharagpur, India, No. 409.
23
[24] Xu, Z., Xuan, J., Shi, T., Wu, B., and Hu, Y., 2009, “A novel fault diagnosis method of bearing based on improved fuzzy ARTMAP and modified distance discriminant technique”, J. Expert Systems with Applications, 36, pp. 11801-11807.
24
[25] Wang, Q., Zhang, Y., and Zhu, Y., 2010, “Neural network Compact Ensemble and Its Application”, Chinese Journal of Mechanical Engineering, 23(2).
25
ORIGINAL_ARTICLE
Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method
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.
http://jacm.scu.ac.ir/article_10729_d9d4b6eb88c9bf486ec1ad1fad40136f.pdf
2014-06-01T11:23:20
2018-03-24T11:23:20
44
51
10.22055/jacm.2014.10729
Periodic behavior
Tapered beam
Modified Iteration Perturbation Method (MIPM)
Nonlinear ordinary differential equation
Nonlinear oscillation
Mohammad
Mashinchi Joubari
mmmjouybari@gmail.com
true
1
Dept. of Mechanical Engineering, Babol University of Technology, Babol, Iran
Dept. of Mechanical Engineering, Babol University of Technology, Babol, Iran
Dept. of Mechanical Engineering, Babol University of Technology, Babol, Iran
LEAD_AUTHOR
Davood
Ganji
mirgang@nit.ac.ir
true
2
Assistant Professor, Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
Assistant Professor, Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
Assistant Professor, Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
AUTHOR
Hamid
Javanian Jouybari
hamidjavaniyan@gmail.com
true
3
Department of Mechanical Engineering, Semnan University, Iran
Department of Mechanical Engineering, Semnan University, Iran
Department of Mechanical Engineering, Semnan University, Iran
AUTHOR
[1] Sarma, B.S., Varadan, T.K., “Lagrange-type formulation for finite element analysis of nonlinear beam vibrations”, J. Sound Vib, Vol. 86, pp. 61–70, 1983.
1
[2] Shi, Y., Mei, C.A., “Finite element time domain model formulation for large amplitude free vibrations of beams and plates”, J. Sound Vib, Vol. 193, pp. 453–465, 1996.
2
[3] Azrar, L., Benamar, R., White, R.G., “A semi-analytical approach to the non-linear dynamic response problem of S-S and C-C beams at large vibration amplitudes part I: general theory and application to the single mode approach to free and forced vibration analysis”, J. Sound Vib, Vol. 224, pp. 183–207, 1999.
3
[4] Qaisi, M.I., “Application of the harmonic balance principle to the nonlinear free vibration of beams”, Appl. Acoust, Vol. 40, pp. 141–151, 1993.
4
[5] Mashinchi Joubari, M., Asghari, R., “Analytical Solution for Nonlinear Vibration of Micro-Electro-Mechanical System (MEMS) by Frequency-Amplitude Formulation Method”, Journal of Mathematics and Computer Science, Vol. 4, No. 3, pp. 371 – 379, 2012.
5
[6] Baghani, M., Fattahi, M., Amjadian, A., “Application of the variational iteration method for nonlinear free vibration of conservative oscillators”, Scientia Iranica B, Vol. 19, No. 3, pp. 513-518, 2012.
6
[7] Rafei, M., Ganji, D.D., Daniali, H., Pashaei, H., “The variational iteration method for nonlinear oscillators with discontinuities”, Journal of Sound and Vibration, Vol. 305, pp. 614-620, 2007.
7
[8] He, J.H., “Some Asymptotic Methods for Strongly Nonlinear Equations”, International Journal of Modern Physics B, Vol. 20, No. 10, pp. 1141-1199, 2006.
8
[9] He, J.H., “Iteration perturbation method for strongly nonlinear oscillations”, Journal of Vibration and Control, Vol. 7, pp. 631-642, 2001.
9
[10] Özis, Turgut., Yıldırım, Ahmet., “Generating the periodic solutions for forcing van der Pol oscillators by the Iteration Perturbation method”, Nonlinear Analysis: Real World Applications, Vol. 10, pp. 1984–1989, 2009.
10
[11] Younesian, Davood., Yazdi, Mohammad Kalami., Askari, Hassan., Saadatnia, Zia., “Frequency Analysis of Higher-order Duffing Oscillator using Homotopy and Iteration-Perturbation Techniques”, 18th Annual International Conference on Mechanical Engineering-ISME, 2010.
11
[12] Ganji, D.D., “The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer” Physics Letters A, Vol. 355, pp. 337-341, 2006.
12
[13] He, J.H., “The homotopy perturbation method for non-linear oscillators with discontinuities”, Appl Math Comput, Vol. 151, pp. 287–92, 2004.
13
[14] Barari, A., Kaliji, H.D., Ghadimi, M., Domairry, G., “Non-linear vibration of Euler-Bernoulli beams”, Latin American Journal of Solids and Structures, Vol. 8, pp. 139 – 148, 2011.
14
[15] Ganji, S.S., Barari, A., Ganji, D.D., “Approximate analyses of two mass-spring systems and buckling of a column”, Computers & Mathematics with Applications, Vol. 61, No. 4, pp. 1088–1095, 2011.
15
[16] Azami, R., Ganji, D.D., Babazadeh, H., “He’s Max-Min method for the relativistic oscillator and high order duffing equation”, International journal of modern physics B, Vol. 32, pp. 5915-5927, 2009.
16
[17] He, J.H., “Max-Min Approach to Nonlinear Oscillators”, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 9, No. 2, pp. 207-210, 2008.
17
[18] Wu, B.S., Sun, W.P., Lim, C.W., “An analytical approximate technique for a class of strongly non-linear oscillators”, International Journal of Non-Linear Mechanics, Vol. 41, pp. 766-774, 2006.
18
[19] Mashinchi Joubari, M., Asghari, R., Zareian Jahromy, M., “Investigation of the Dynamic Behavior of Periodic Systems with Newton Harmonic Balance Method”, Journal of Mathematics and Computer Science, Vol. 4, No. 3, pp. 418 – 427, 2012.
19
[20] Joneidi, A.A., Ganji, D.D., Babaelahi, M., “Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity”, International Communications in Heat and Mass Transfer, Vol. 36, pp. 757–762, 2009.
20
[21] Momeni, M., Jamshidi, N., Barari, A., Ganji, D.D., “Application of He’s Energy Balance Method to Duffing Harmonic Oscillators”, International Journal of Computer Mathematics, Vol. 88, No. 1, pp. 135–144, 2010.
21
[22] Mehdipour, I., Ganji, D.D., Mozaffari, M., “Application of the energy balance method to nonlinear vibrating equations”, Current Applied Physics, Vol. 10, pp. 104–112, 2010.
22
[23] He, J.H., “Asymptotic Methods for Solitary Solutions and Compactons”, Abstract and Applied Analysis, Article ID 916793, 2012.
23
[24] Goorman, D.J., “Free vibrations of beams and shafts”, ASME Appl. Mech, Vol. 18, pp. 135–139, 1975.
24
[25] Evensen, D.A., “nonlinear vibration of beams with various boundary conditions”, AIAAJ, Vol. 6, pp. 370-372, 1968.
25
[26] Pillai, S.R.R., Rao, B.N., “On nonlinear free vibrations of simply supported uniform beams”, J. Sound Vib, Vol. 159, pp. 527–531, 1992.
26
[27] Barari, A., Kimiaeifar, A., Domairry, G., Moghimi, M., “Analytical evaluation of beam deformation problem using approximate methods”, Songklanakarin Journal of Science and Technology, Vol. 32, No. 3, pp. 207–326, 2010.
27
[28] Klein, L., “Transverse vibrations of non-uniform beam”, J. Sound Vib, Vol. 37, pp. 491–505, 1974.
28
[29] Sato, K., “Transverse vibrations of linearly tapered beams with ends restrained elastically against rotation subjected to axial force”, Int. J. Mech. Sci, Vol. 22, pp. 109–115, 1980.
29
[30] Marinca, V., Herisanu, N., “A modified iteration perturbation method for some nonlinear oscillation problems”, Acta Mechanica, Vol. 184, pp. 231-242, 2006.
30
[31] Lim, C.W., Wu, B.S., “A modified Mickens procedure for certain non-linear oscillators”, J. Sound Vib, Vol. 257, pp. 202-206, 2002.
31
[32] Shahidi, M., Bayat, M., Pakar, I., Abdollahzadeh, G.R., “Solution of free non-linear vibration of beams”, International Journal of Physical Sciences, Vol. 6, No. 7, pp. 1628-1634, 2011.
32
[33] Bayat, M., Pakar, I., M., Bayat, “Analytical study on the vibration frequencies of tapered beams”, Latin American Journal of Solids and Structures, Vol. 8, pp. 149–162, 2011.
33