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IssuesArchive of Issues2007-1pp.12-18

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D. A. Sukhoruchkin, "On the precession of a standing wave in a string with fixed ends," Mech. Solids. 42 (1), 12-18 (2007)
Year 2007 Volume 42 Number 1 Pages 12-18
Title On the precession of a standing wave in a string with fixed ends
Author(s) D. A. Sukhoruchkin (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, sukhor@ipmnet.ru)
Abstract Nonlinear differential equations of motion of a string are derived. In the single-mode approximation, the evolution of a transverse standing wave is studied. The dependence of the precession velocity and the correction to the vibration frequency on the semiaxes of the ellipse along which the string midpoint moves is determined.
References
1.  W. H. Quick, "Theory of Vibrating Strings as an Angular Motion Sensor," Trans. ASME. Ser. E. J. Appl. Mech. 31 (3), 523-534 (1964).
2.  D. A. Sukhoruchkin, "On the String Implementation of a Generalized Foucault Pendulum," in Mechanics of Solids (In-t Prikl. Mat. Mech. Nat. Acad. Sci. Ukraine, Donetsk, 2000), No. 30, pp. 125-131.
3.  V. Ph. Zhuravlev, "A Controlled Foucault Pendulum as a Model of a Class of Free Gyros," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 27-35 (1997) [Mech. Solids (Engl. Transl.)].
4.  V. Ph. Zhuravlev and D. M. Klimov, Wave Solid-State Gyro (Nauka, Moscow, 1985) [in Russian].
5.  A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1977) [in Russian].
6.  L. I. Sedov, Continuum Mechanics. Vol. 1 (Nauka, Moscow, 1994) [in Russian].
7.  L. D. Akulenko, S. V. Nesterov, "Nonlinear Vibration of a String," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 87-92 (1993) [Mech. Solids (Engl. Transl.)].
Received 02 July 2004
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