Wpływ Więzów Geometrycznych I Dynamicznych Na Obszary Rezonansowe w Zagadnieniu Stateczności Dynamicznej Pręta Cienkościennego O Profilu Otwartym

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Authors

  • K. Piszczek Instytut Podstawowych Problemów Techniki PAN, Poland

Abstract

This paper seeks to determine the influence of the constraints referred to in the title on the dynamical stability of a straight thin-walled bar with hinged support end conditions. The problem is solved on the assumption of existence of a singIe symmetry axis of the cross-section, the force acting at an arbitrary point of that axis. The method of solution is based on Ref. [2] which is shown to be applicable to this problem. However, the method used in the present paper, seems to be more clear than that of Ref. [3]. The influence of rotation of the cross-sections is also taken into consideration. The notion of the geometrical and dynamical constraint is introduced. By geometrical constraint, we understand a conjugation concerning the geometry of the cross-section, the dynamical constraint being connected with the attachment point of the force. It is shown that the condition of existence of the most narrow resonance region is A2 = 0 where Ag denotes the expression (3.1).

References

[1] N. A. Artiemiew, Mietod opriedielenja charaktieristiczeskich pokazatielej pritozenja jewo k dwom zadaczam niebiesnoj miechaniki, Izw. AN SSSR,
Ser. mat., 1944.

[2] W. W. Bolotin, O paramietriczeskom wozbuzdient popieriecznych kolebanij. Popieriecznyje kolebanja kriticzeskije skorosti, Sborn, wtoroj, 1953.

[3] I. I. Goldienblat, Dinamiczeskij prodolnyj izgib tonkostiennych stierzniej. Inz. Sborn., t. 5, 1 (1948).

[4] R. Hielig, Torsions und Biegeschwingungen von dünnwandigen Trägern mit beliebiger offener Profilform mit Vorlasten, Ing. Archiv, t. 19, 1951.

[5] J. Naleszkiewicz, Zagadnienia stateczności sprężystej, WK, Warszawa 1953.

[6] K. Piszczek, Wpływ krzywizny W stanie naturalnym na obszary rezonansowe płaskiej postaci zginania, Arch. Mech. Stos. 2 (1957).

[7] S. D. Ponomariew i inni, Osnowy sowriemionnych mietodow rasczota na procznost w maszinostrojenji, Moskwa 1952.

[8] J. A. Pratusewicz, Wariacjonnyje mietody w stroitielnoj miechanikie, Moskwa-Leningrad 1948.