Engineering Transactions, 14, 2, pp. 216-230, 1966

Drgania Wymuszone Parametrycznie w Układzie z Nieliniowa Bezwładnością

R. Gryboś
Politechnika Śląska

The conditions of main subharmonic resonance excited parametrically by a harmonic force are studied for a system with nonlinear inertion. First is solved the case when the excitation frequency is twice as great as the natural frequency of the linear system (i.e. without the concentrated mass at the end of the bar). The stability of the solution is investigated. The next case under consideration is that of any excitation frequency. This problem is solved, by means of the perturbation method combined with the method of variation of constants, Solution is found in the first approximation. The stability of the solution is investigated.
The case of nonlinear elasticity is also considered.

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A. J. BELLIN, Non-autonomous systems, Advances in Appl. Mech. vol. 3, New York 1953.

В. В, Болотин, Динамическая устойчивость упругих систем, Москва 1956.

W. J. CUNINGHAM, Introduction to nonlinear analisys, New York 1958.

R. GRYBOS, Drgania swobodne układu z nieliniową bezwładnością, Rozp. Inżyn., 1, 13 (1965).

CH, HAYASHI, Forced oscillations in nonlinear systems, Osaka 1953.

Y. H. KU, YANG Tsu-Te, Analisys of parametrically excited systems J. of the Franklin Inst. 274, nr 6, 1962.

И. Г. Малкин, Некоторые задачи теории нелинейных колебаний, Москва 1956.

N. W. Mc LACHLAN, Ordinary nonlinear differential equations in engineering and physical sciences, Oxford 1956.

N. W. Mc LACHLAN, Theory and Applications of Mathieu Functions, Oxford 1951.

N. MINORSKY, Modern trends in nonlinear mechanics, Advences in Appl. Mech., vol. 1. New-York 1948.

G. SCHMIDT, Über die Biegeschwingungen des gelenking gelagerten axial pulsierend belasteten Stabes, Math. Nachr., z. 2, 1961.

R. A. STRUBLE, S. M. YIONOULIS, General perturbational solution of the harmonically forced Duffing equation, Arch. for Rational Mechanics and Analysis, 9, nr 5/1962.

F. WEIDENHAMMER, Nichtlineare Biegeschwingungen des axial pulsierend belasteten Stabes. Ing. Arch., 5, 20 (1962).