Engineering Transactions, 8, 1, pp. 189-200, 1960

Układ o Jednym Stopniu Swobody o Silnie Nieliniowej Parzystej Charakterystyce Tłumienia

W. Bogusz

K. Szpunar

For qualitative investigation the method of the velocity hodograph is used. Analytic investigation is done by means of the method of analysis of the solution in the xx-plane. The results obtained by the two methods are in agreement. It is found that the equation under consideration has periodic solutions in the neighbourhood of the singular points and the solutions outside this region being unbounded. The form of the trajectory is determined in the entire phase plane. Equations for the period of the periodic solutions and the displacement amplitudes are obtained.

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S. ZIEMBA, Free Vibration with Damping of Marked Non-Linear Character, Arch. Mech. Stos., 5, 9 (1957), 525-548.

S. ZIEMBA, Free Vibration of Systems of One Degree of Freedom with Non-Linear Elastic Characteristic and Non-Linear Viscous-Type Damping, Arch. Mech. stos., 2, 10 (1958), 163-193.

J. SKOWROŃSKI, S. ZIEMBA, Zastosowanie metody delta do badania silnie nieliniowych mechanicznych układów drgających o skończonej liczbie stopni swobody [Application of the Delta Method for Investigation of Vibrating Systems of Finite Degree of Freedom and with Strong Non-Linearity],

Biul. WAT, 1, 1958.

W. BOGUSZ, Determination of Stability Regions of Dynamic Non-Linear System, Arch. Mech. stos, 6, 11 (1959).

K. SZPUNAR, Drgania swobodne układu o jednym stopniu swobody przy silnie nieliniowym tlumieniu [Free Vibration of System of One Degree of Freedom with Strong Non-Linear Damping]. Zesz. nauk. AGH (in print).