The free vibrations and optimization of the shape of a column subjected to a load by a follower force directed towards the positive pole applying the variational method

• Autorzy: Szmidla J. , Yatsenko D.
• Konferencja: Jubilee Symposium Vibrations In Physical Systems (25 ; 15-19.05.2012 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

The results of numerical computations and theoretical research into optimization of the shape and the free vibrations of a cantilever column subjected to a load by the follower force directed towards the positive pole are presented in this paper. The systems of equations: of motion and of cross-sectional area of the considered column were determined on the basis of the total mechanical energy and Hamilton’s principle. Taking into account the formulated boundary conditions, optimized shapes of the systems were determined for the chosen values of geometrical parameter of a head subjected to a load. The values of natural frequency of the considered system were obtained taking into account distribution of flexural rigidity along the column length while the values of critical load of optimized column were obtained on the basis of curves of changes in the basic natural frequency in relation to external load. The results of numerical computations were presented in the case of one from three classes of the systems – versatile uniformly convergence column for the assumed criterion of constant volume of the system.

Słowa kluczowe

EN

column; specific load; free vibrations; optimization

PL

kolumna; obciążenie swoiste; drgania swobodne; optymalizacja

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2012
• Tom: Vol. 25
• Strony: 393--398
• Opis fizyczny: Bibliogr. 7 poz., rys., wykr.

Twórcy

autor

Szmidla J.

• Częstochowa University of Technology, Institute of Mechanics and Machine Design Foundations ul. Dąbrowskiego 73, 42-200 Częstochowa

autor

Yatsenko D.

• Częstochowa University of Technology, Institute of Mechanics and Machine Design Foundations ul. Dąbrowskiego 73, 42-200 Częstochowa

Bibliografia

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• 2. Ziegler H., Principles of Structural Stability, Waltham 1968.
• 3. Prager W., Taylor I. E., Problems of optimal structural design, Journal of Applied Mechanics, 35 (1968) 102-106.
• 4. Langthjem M. A., Sugiyama Y., Optimum design of cantilevered columns under the combined action of conservative and nonconservative loads. Part I: The undamped case; Computers and Structures, 74(4) (2000) 385-398.
• 5. Szmidla J., Drgania swobodne i stateczność układów smukłych poddanych obciążeniu swoistemu, Seria Monografie, Nr 165, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2009.
• 6. Tomski, L., Obciążenia układów oraz układy swoiste. Rozdział 1: Drgania swobodne i stateczność obiektów smukłych jako układów liniowych lub nieliniowych. Praca zbiorowa wykonana pod kierunkiem naukowym i redakcją L. Tomskiego, WNT, Fundacja „Książka Naukowo-Techniczna”, Warszawa 2007, 17-46.
• 7. Gajewski A., Życzkowski M., Optimal shaping of an elastic homogeneous bar compressed by polar force, Biulletyn de L`Academie Polonaise des Sciences, 17, 10 (1969) 479-488.