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IssuesArchive of Issues2015-1pp.33-43

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G.T. Aldoshin and S.P. Yakovlev, "Analytic Model of Vibrations of a Carbon Dioxide Molecule. Fermi Resonance," Mech. Solids. 50 (1), 33-43 (2015)
Year 2015 Volume 50 Number 1 Pages 33-43
DOI 10.3103/S0025654415010045
Title Analytic Model of Vibrations of a Carbon Dioxide Molecule. Fermi Resonance
Author(s) G.T. Aldoshin (Ustinov Baltic State Technical University "Voenmekh," ul. 1-ya Krasnoarmeyskaya 1, St. Petersburg, 190005 Russia, kaf_b3@bstu.spb.su)
S.P. Yakovlev (Ustinov Baltic State Technical University "Voenmekh," ul. 1-ya Krasnoarmeyskaya 1, St. Petersburg, 190005 Russia, yakovlev_sp@mail.ru)
Abstract We use the invariant normalization method to study nonlinear autonomous vibrations of a CO2 molecule near its stable configuration. If the frequencies of symmetric and deformation vibrations are related as 2:1, then a third-order resonance occurs in the molecule. The simulation discovered the following two nonlinear effects: the energy transfer between modes of longitudinal and transverse vibration modes which participate in the resonance and the frequency splitting in the molecule spectrum; namely, instead of one line of symmetric vibration, there is a group of four closely located lines. These effects are known as the Fermi resonance phenomenon.
Keywords carbon dioxide molecule, nonlinear vibrations, Fermi resonance, invariant normalization
References
1.  M. V. Volkenshtein, M. A. El'shevich, and B. I. Stepanov, Molecule Oscillations (Gostechizdat, Moscow-Leningrad, 1949) [in Russian].
2.  G. Herzberg, Oscillatory and Rotational Spectra of Polyatomic Molecules (Izd-vo Inostr. Lit., Moscow, 1949) [in Russian].
3.  E. Fermi, "Über den Ramaneffekt des Kohlendioxyds," Zs. für Physik 71, 250 (1931).
4.  A. Vitt and G. Gorelik, "Elastic Pendulum Oscillations as an Example of Oscillations of Two Parametrically Connected Linear Systems," Zh. Tekhn. Fiz. 3 (2-3), 294-307 (1933).
5.  A. L. Kunitsyn and A. P. Markeev, "Stability in Resonance Cases," in Progress in Science and Technology. General Mechanics, Vol. 4 (VINITI, Moscow, 1979), pp. 58-139 [in Russian].
6.  G. T. Aldoshin, "To the Problem of Linearization of Lagrange Equations," in Fifth Polyakhov Readings. Selected Proc. Intern. Conf. in Mechanics (St. Petersburg, 2009) [in Russian].
7.  A. G. Petrov and M. M. Shunderyuk, "On Nonlinear Vibrations of a Heavy Mass Point on a Spring," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 27-40 (2010) [Mech. Solids (Enggl. Transl.) 45 (2), 176-186 (2010)].
8.  L. D. Landau and E. M. Lifshits, Theoretical Physics. Vol. 3: Mechanics (Nauka, Moscow, 1965) [in Russian].
9.  E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge Univ. Press, Cambridge, 1927; ONTI, Moscow-Leningrad, 1937).
10.  D. J. Korteweg, "Sur Certaines Vibrations d'Ordre Superrierur et d'Intensile Anomale," Areh. Neeri Sci. Exactes et Natur, Ser. 2, 1, 229-260 (1898).
11.  M. Born, Lectures in Atomic Mechanics (ONTI, Kharkov-Kiev, 1934), Vol. 1 [in Russian].
12.  K. S. Krasnov, N. V. Filippenko, V. A. Bobkova, et al., Molecular Constants of Nonorganic Compounds. Reference Book, Ed. by K. S. Krasnov (Khimiya, Leningrad. Otd., Leningrad, 1979) [in Russian].
13.  A. G. Petrov, "Nonlinear Vibrations of a Swinging Spring at Resonance," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 18-28 (2006) [Mech. Solids (Engl. Transl.) 41 (5), 13-22 (2006)].
14.  G. T. Aldoshin and S. P. Yakovlev, "Dynamics of a Swinging Spring With Moving Support," Vestnik St. Peterburg. Univ. Ser. 1, No. 4, 45-52 (2012).
15.  L. A. Gribov, Oscillations of Molecules (KomKniga, Moscow, 2009) [in Russian].
16.  G. T. Aldoshin, Theory of Linear and Nonlinear Oscillations. A Manual (Lan', St.Petersburg, 2013) [in Russian].
Received 12 March 2013
Link to Fulltext http://link.springer.com/article/10.3103/S0025654415010045
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