NEW LEM ESTIMATIONS FOR THE UNDAMPED DÜFFING OSCILLATOR

Petre P. TEODORESCU, Ileana TOMA

Abstract


In a previous paper, the authors deduced a LEM representation for the damped Düffing oscillator with harmonic forcing, in null Cauchy conditions; the undamped case could not be obtained from this by canceling the damping coefficient. Therefore, in this paper they consider directly the harmonically forced undamped Düffing oscillator with nonzero initial conditions, establishing for it analytic LEM approximate solutions tested by using classical numerical methods. Some representative phase portraits are also presented.

Keywords: Düffing oscillator, linear equivalence method

Full Text:

PDF

References


.Düffing, Erzwungene Schwingungen bei verändlicher Eigenfrequenz, Vieweg, Braunschweig, 1918

Munteanu, L., Donescu, Ş., Introduction to the soliton theory, Applications to mechanics, Book Series: Fundamental Theories of Physics, Kluwer Academic Publishers, 2004

L Munteanu, D. Popa, C. Secara, V. Chiroiu, The analysis of a system of rigid bodies's dynamics by linear equivalence method, Proc. of the Roumanian Academy, series A, 8, 2, 2007

L Munteanu, T. Badea, V. Chiroiu, Linear equivalence method for the analysis of the double pendulum's motion, Complexity International Journal, 9, pp. 26-43, 2002

Patil, N.S, Mallik, A., Experimental investigation of the response of a harmonically excited hard Düffing oscillator, Pramana J. of Physics, 68, 1, pp. 99-104

Soare, M.V., Teodorescu, P.P., Toma, I., Ordinary differential equations with applications to mechanics, Springer, Dordrecht, 2007

J.C. Sprott, Some simple chaotic jerk functions, Am. J. Phys. 65, 6, June 1997, pp.537-543

Teodorescu, P.P., Mechanical systems. Classical models, Springer, Dordrecht, 2008

Teodorescu, P.P., Toma, I., A class of elastic structures with the same mathematical core, Honorary volume dedicated to professor emeritus Ioannis D. Mittas, Aristotle Univ. of Thessaloniki, Fac. of Eng., Dept. of Math, Phys.Sci., Division of Math., pp. 499-508, 2000

Teodorescu, P.P., Toma, I., Nonlinear damped pendulum treated by linear equivalence, Mech. Res. Comm, 27, 3, pp. 373-380, 2000

Teodorescu, P.P., Toma, I., New integral LEM formulae applied to the nonlinear bar, Mech. Res. Comm., 31, 1, pp. 161-168, 2004

Teodorescu, P.P., Toma, I., Nonlinear elastic deformations treated by LEM, Topics in Applied Mechanics, Ed. Academiei Române, Bucharest, eds. V. Chiroiu, T. Sireteanu, vol.II, pp.391-442, 2004

Teodorescu, P.P., Toma, I., Applying LEM to Düffing’s oscillator, UPB Sci. Bull., series D: Mechanical Engineering, 72, 3, 2010, pp.3-12

J.M.T. Thompson, H.B. Stewart, Nonlinear dynamics and chaos, 2nd edition, John Wiley & Sons, 2002

Toma, I., On polynomial differential equations, Bull. Math. Soc. Sci. Math. de la Roumanie, 24(72), 4, pp. 417-424, 1980

Toma, I., Normal LEM representations for the non-linear forced pendulum, II NNMAE, Thessaloniki, Greece, 7-8.07.2006, pp.329-332, 2006

Toma, I., Specific LEM techniques for some polynomial dynamical systems, Topics in Applied Mechanics, Ed. Academiei Române, eds. V. Chiroiu, T. Sireteanu, vol.III, pp. 427-459, 2006

Toma, I., The nonlinear pendulum from a LEM perspective, Research Trends in Mechanics, Ed. Academiei Române, eds. D.Popa, V. Chiroiu, I.Toma, vol.I, pp.395-422, 2007

Toma, I., LEM solutions in mechanics and engineering, Proc. of ICTCAM, 20-23.06.2007, Bucharest, Romania, pp.123-128, 2007

Toma, I., Extensions of LEM to non-autonomous systems, Research Trends in Mechanics, Ed. Academiei Române, eds. D.Popa, V. Chiroiu, I.Toma, vol.II, pp.361-378, 2008

Toma, I., Metoda echivalenţei lineare şi aplicaţiile ei în mecanică, Ed. Tehnică, Bucureşti, 2008

Toma, I., New periodic LEM solutions for the nonlinear pendulum, Rev. Roum. des Sci. Techn., série de Mécanique Appliquée, vol. 53, nr.2, pp. 135-146, 2008, ISSN 0035-4074

Ueda, Y., The road to chaos, Aerial Press, 1992

Virgin, L.N., Introduction to experimental nonlinear dynamics: A case study in mechanical vibration, Cambridge University Press, Cambridge, 2000

Voinea,R., Stroe, I., Introducere în teoria sistemelor dinamice, Ed. Academiei Române, Bucureşti, 2000

Zeeman, Chr., Düffing’s equation: catastrophic jumps of amplitude and phase, conference, Univ. of Texas at San Antonio, 31.03.2000


Refbacks

  • There are currently no refbacks.


JOURNAL INDEXED IN :