Engineering Transactions, 13, 1, pp. 19-41, 1965

Stateczność Pręta Opływanego Równoległym Strumieniem Płynu przy Uwzględnieniu Oporu Czołowego

Z. Kordas
Politechnika Krakowska
Poland

The above problem concerns a bar (plate) clamped at one end. The load is composed of a front drag and lateral load acting after the stability loss. The introduction contains a brief survey of the literature concerning the stability analysis of elements in a fluid flow. It is found that this problem has hitherto been treated in an incomplete manner the front load or the lateral load being the only considered. The present paper presents a tentative analysis of the stability problem of a bar under the combined the hydraulic forces being. The main stress is laid on the stability analysis, the magnitude of the determined on the grounds of the theory of plane sections (Eq. 2.1). Sec. 2 contains the assumptions and the derivation of the fundamental equation small lateral vibration of the bar (Eq. 2.5). Sec. 3 is concerned with accurate stability analysis of the equation obtained in cases where the static criterion is sufficient. The range where the kinetic criterion is necessary is considered in Sec. 4. where the energy method is used. In this section the equation of the limit curve is obtained for an assumed form of the deflection line in the applicability range of
the static and kinetic stability criterion.
Next, the equations obtained are analysed in detail by describing the form of the limit curves using as coordinates the dimensionless flow velocity v and the dimensionless front drag s (Figs. 8, 9). Fig. 11 shows the form of the limit curves for various values of the "follow-up" parameter n and Fig. 10 – for various values of the parameter θ, characterizing the influence of the convection velocity of flow.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

H. ASHLEY, C. ZARTARIAN, Piston theory – a new aerodynamics tool for the aeroelastician, J. Aeronaut. Sci., 12, 23 (1956), 1109-1118.

M. BECK, Die Knicklast des eingeitig eingespannten tangential gedrückten Stabes, Z. angew. Math, Physik, 3, 3 (1952), 225.

M.A. BIOT, The divergence of supersonic wings including chord wize bending, Report Nr 67, Cornell Aeronautical Laboratory, 1954.

A. BOBESZKO, J. KACPRZYŃSKI, S. KALISKI, Vibration and stability of slender bodies in linearized supersonic flow, Proc. Vibr. Probl., 4 (1959).

[in Russian]

[in Russian]

H. K. CHENG, A variational method for the differential system arising from aeroelastic problems, dysertacja, Cornell University, 1950.

[in Russian]

W. H. DORRANCE, Nonsteady supersonic flow about pointed bodies of revolution, J.A.S., 8, 18 (1951), 505-511.

[in Russian]

J. M. HEDGEPETH, On the flutter of panels at high mach number, J.A.S., 6, 23 (1956), 609-610.

J. M. HEDGEPETH, Flutter of rectangular simply supperted panels at high supersonics speeds, J.A.S., 8, 24 (1957), 63-573.

[in Russian]

J. KACPRZYŃSKI, S. KALISKI, Flatter odkształcalnej rakiety w opływie naddźwiękowym, Biul. Wojsk. Akad. Techn. im. J. Dąbrowskiego, 8, 97 (1960), 3-19.

T. KÁRMÁN, M. A. BIOT, Metody matematyczne w technice, PWN, Warszawa 1958.

Z. KORDAS, M. ZYCZKOWSKI, Analiza dokładności metody energetycznej przy kinetycznym kryterium stateczności, Czasop. Techn., 9, 65 (1959), 1-8.

Z. KORDAS, M. ŻYCZKOWSKI, On the loss of stability of a rod under a super-tangential force, Arch. Mech. Stos., 1, 15 (1963), 7-31.

Z. KORDAS, Stateczność sprężyście utwierdzonego pręta w ogólnym przypadku zuchowania się obciążenia, Rozpr. Inz., 3, 11 (1963), 435-448.

J. W. MILES, On the aerodynamic instability of thin panels, J.A.S., 23 (1956).

[in Russian]

[in Russian]

A. PPLÜGER, Zur Stabilität des tangential gedrückten Stabes, Z. Angew. Math. Mech., 5, 35 (1955), 191.

A. PPLÜGER, Stabilitäts Probleme der Elastostatik, Springer-Verlag; 1950.

G. SEIFERT, A third-order boundary value problem arising in aeroelastic wing theory, Appl., Math., 2, 9 (1951).

, H. ZIEGLER, Ein nichtkonservatives Stabilitätsproblem, Z. angew Math. Mech., 8/9, 31 (1951), 265.

S. D. PONOMARIEW i inni, Współczesne metody obliczeń wytrzymałościowych w budowie maszyn, PWN, Warszawa 1957.