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MOHAMED BELHAQ
Professor
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Professional Biography
Belhaq joined the University Hassan I I- Casablanca in 1982 after receiving his doctorate from the University Paul Sabatier, Toulouse, France. He was a visiting professor and lecturer several times at Free University of Berlin, University of Sevilla, University of L’Aquila, Italy, Ecole Centrale Lyon, INSA Lyon, University Complutence of Madrid, University of Cottbus, Germany, Military University of Warsaw, University of Munich, Cornell University, USA, Virginia Tech University, USA, Perdue university, USA and the Indiana State University, USA. Belhaq directed and co-supervised several Ph. D. theses. He received two Fulbright Scholarship awards for conducting research at Cornell University in 1997 and at Virginia Tech University in 2005. He is serving as a reviewer in several international journals (Journal of Sound and Vibration, Journal of Vibration and Control, Applied Mech. Rev, ASME, Nonlinear Dynamics, Int. J. Non-linear Mech., Int. J. Bif. Chaos, Mech. Res. Communications) and he is on the editorial boards of the International Journal of Applied Mathematics and Mechanics.
Research Interests
Current research focuses on investigating nonlinear dynamics of mechanical systems using perturbation methods, bifurcation analysis and numerical simulations. Current projects involve:
- Quasiperiodic parametric equations,
- Synchronization phenomena and control,
- High-frequency excitation of nonlinear oscillators,
Applications include control of hysteresis phenomena in nonlinear systems and in MEMS.
Selected Collaborative Funded Projects
- Morocco/USA (Cornell University, NY, USA), Fulbright Award 1997, with R.H. Rand.
- Morocco/Spain (University Complutence of Madrid) 1997-2000, with Manuel G. Velarde.
- CNRST/CNRi (Univerqsity of L’Aquila, Italy) 2005-2007, with F. Benedittini and G. Rega.
- Morocco/NSF, USA (Cornell University, NY, USA) 2000-2005, with R.H. Rand.
- Morocco/Spain (University of Sevilla) 1997-2000, with A.J. Rodriguez-Luis and E. Freire.
- CNRST Morocco / DFG (University of Cottbus, Germany) 2000-2003, with M. Besthorn.
- CNRST Morocco / DFG-GTZ (Free Univ. Berlin, Germany) 1994-1999, 2002-2005, with B. Fiedler.
- Morocco/USA (Virginia Tech & State University, USA), Fulbright Award 2005, with A.H. Nayfeh.
- NATO-Mediterranean Dialogue project: University Hassan II-Casablanca - Indiana State Univ., USA -Military University of Technology, Warsaw 2006-2008, with B. Bluykher and J. Malachowski.
- CNRST/ DFG (University of Munich, Germany) 2006-2009, with M. Effendiev.
- Morocco/USA (Cornell University, NY), Fulbright Cosupervisor Grant 2008-2009, with R.H. Rand.
- CNRST/CNRS (LaMCos, INSA Lyon) 2009-20011, with R. Dufour, J. Mahfoud, J. Der Hagopian.
Selected Publications (since 2000)
M. Belhaq, E. Freire, M. Houssni and A.J. Rodriguez-Luis,
Analytical prediction of the two first period-doubling in a three-dimensional system,
International Journal of Bifurcations and Chaos, vol. 10(6), p. 1497-1508, 2000. ( )
M. Belhaq, E. Freire, M. Houssni and A.J. Rodriguez-Luis,
Asymptotics of homoclinic bifurcation in a three-dimensional system,
Nonlinear Dynamics, vol. 21, p. 135-155, 2000.
M. Belhaq, B. Fiedler and F. Lakrad,
Homoclinic connections in strongly self-excited non-linear oscillators:
The Melnikov function and the elliptic Lindsted Poincaré method,
Nonlinear Dynamics, vol. 23, p. 67-86, 2000.
S. Aniss, M. Souhar and M. Belhaq,
Asymptotic study of the convective parametric instability in Hele-Shaw cell,
Physics of Fluids, vol. 12(2), p. 262-268, 2000.
M. Belhaq and F. Lakrad,
An elliptic multiple scales method for certain autonomous strongly nonlinear oscillators,
Journal of Sound and Vibration, vol. 234(3), p. 547-553, 2000.
M. Belhaq and F. Lakrad,
On the elliptic harmonic balance method for mixed parity non linear oscillators,
Journal of Sound and Vibration, vol. 233(5), p. 935-937, 2000.
M. Belhaq, K. Guennoun and M. Houssni,
Asymptotic solutions for a nonlinear quasi-periodic Mathieu equation,
International Journal of Non-Linear Mechanics, vol. 37(3), p. 445-460, 2002. ()
F. Lakrad and M. Belhaq,
An elliptic multiple scales method for autonomous strongly nonlinear oscillators,
Journal of Sound and Vibration, vol. 258(4), p. 677-700, 2002.
M. Belhaq and F. Lakrad,
Analytics of homoclinic bifurcations in three-dimensional systems,
International Journal of Bifurcations and Chaos, vol. 12(11), p. 2479-2486, 2002. ()
R.H. Rand, K. Guennoun and M. Belhaq,
2:2:1 Resonance in the quasi-periodic Mathieu equation,
Nonlinear Dynamics, vol. 31 (4), p. 367-374, 2003. ()
N. Abouhazim, M. Belhaq and F. Lakrad,
Three-period quasi-periodic oscillations in a self-excited quasi-periodic Mathieu equation,
Nonlinear Dynamics, vol. 39(4), p. 395-409, 2005.
F. Lakrad, N. Abouhazim, A Azouani and M. Belhaq,
Bursters and quasi-periodic solutions of a self-excited quasi-periodic Mathieu oscillator,
Chaos, Solitons & Fractals, vol. 24(3), p. 813-824, 2005.
S. Aniss, M. Belhaq, M. Souhar and M. G. Velarde,
Effect of the surface temperature modulation on the onset of Rayleigh-Bénard convection in Hele-Shaw cell,
Physica Scripta, vol. 71, p. 1-7, 2005.
N. Abouhazim R.H. Rand, and M. Belhaq,
The damped nonlinear quasiperiodic Mathieu equation near 2:2:1 resonance,
Nonlinear Dynamics, vol. 45(3-4), p. 237-247, 2006. ()
N. Abouhazim, M. Belhaq and R.H. Rand,
Two models for the parametric forcing of a nonlinear oscillator,
Nonlinear Dynamics, vol. 50, p. 147-160, 2007.
R. Bourkha and M. Belhaq,
Effect of fast harmonic excitation on a self-excited motion in Van der Pol oscillator,
Chaos, Solitons and Fractals,vol. 34(2), p. 621-627, 2007.
T. Boulal, A. Aniss, M. Belhaq and R.H. Rand,
Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer,
Physical Review E 76, 056320, 2007. ()
M. Rougui, A. Karimin and M. Belhaq,
Nonlinear flexural vibration of a circular ring. A single mode approach,
Chaos, Solitons and Fractals, vol. 37(4), p. 1143-1152, 2008.
M. Sah and M. Belhaq,
Effect of vertical high-frequency parametric excitation on self-excited motion in a delayed van der Pol oscillator,
Chaos, Soliton and Fractals, vol. 37(5), p. 1489-1496, 2008. ()
M. Belhaq and M. Sah,
Horizontal fast excitation in delayed van der Pol oscillator,
Communications in Nonlinear Science and Numerical Simulation, vol. 13, p. 1706-1713, 2008.
M. Belhaq and A. Fahsi,
2:1 and 1:1 frequency-locking in fast excited van der Pol-Mathieu-Duffing oscillator,
Nonlinear Dynamics, vol. 53(1-2), p. 139-152, 2008. ()
S.M. Sah, G. Recktenwald, R.H. Rand and M. Belhaq,
Autoparametric quasiperiodic excitation,
International Journal of Non-Linear Mechanics, vol. 43(4), pp. 320-327, 2008. ()
T. Boulal, S. Aniss, M. Belhaq and A. Azouani,
Effect of quasi-periodic gravitational modulation on the convective instability in Hele-Shaw cell,
International Journal of Non-Linear Mechanics, vol. 43(9), pp. 852-857, 2008. ()
A. Fahsi and M. Belhaq,
Effect of fast harmonic excitation on frequency-locking in a van der Pol-Mathieu-Duffing oscillator,
Communications in Nonlinear Science and Numerical Simulation, vol. 14(1), p. 244-253, 2009. ()
Fahsi, F. Lakrad and M. Belhaq,
Suppression of hysteresis in a forced van der Pol-Duffing oscillator,
Communications in Nonlinear Science and Numerical Simulation, vol. 14(4), p. 1609-1616, 2009. ()
F. Lakrad and M. Belhaq,
Quasi-periodic solutions and periodic bursters in quasiperiodically driven oscillators,
Communications in Nonlinear Science and Numerical Simulation, vol. 14(5), p. 2426-2433, 2009.()
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