The effect of influence of conservative and tangential axial forces on transverse vibrations of tapered vertical columns

Jerzy Jaroszewicz



Leszek Radziszewski



Łukasz Dragun




Abstract

The Cauchy function and characteristic series were applied to solve the boundary value problem of free transverse vibrations of vertically mounted, elastically supported tapered cantilever columns. The columns can be subjected to universal axial point loads which considerate – conservative and follower /tangential/ forces, and to distributed loads along the cantilever length. The general form of characteristic equation was obtained taking into account the shape of tapered cantilever for attached and elastically secured. Bernstein-Kieropian double and higher estimators of natural frequency and critical loads were calculated based on the first few coefficients of the characteristic series. Good agreement was obtained between the calculated natural frequency and the exact values available in the literature.


Keywords:

transverse vibrations, vertical cantilever, boundary value problem


BIDERMAN V.L. 1972. Prikladnaja teorija mechaničeskich kolebanij. Vysšaja Škola, Moskva.   Google Scholar

HAŠČUK P., ZORYJ L.M. 1999. Linijni modeli diskretno-neperervnyh mechanicznych system. Lviv, Ukrainski technologii, 372.   Google Scholar

JAROSZEWICZ J. 1999. The effect of non-homogenous material properties on transverse vibration of elastic cantilever. JAM, Kiev, 35(6): 103–110.   Google Scholar

JAROSZEWICZ J., ZORYJ L. 1985. Free transversal vibrations of a cantilever beam with variable cross section. Eng. Trans., 33(4): 537–547.   Google Scholar

JAROSZEWICZ J., ZORYJ L. 1994. Transversal vibrations and stability of beams with variable parameters. Int. Appl. Mech.-Eng. Tr., 30(9): 713–720.   Google Scholar

JAROSZEWICZ J., ZORYJ L. 1996. Critical Euler load for a cantilever tapered beam. J. Theor. Appl. Mech., 4(34): 843–851.   Google Scholar

JAROSZEWICZ J., ZORYJ L.M. 1997. Metody analizy drgań i stateczności kontynualno-dyskretnych układów mechanicznych. Politechnika Białostocka, Białystok.   Google Scholar

JAROSZEWICZ J., ZORYJ L. 2000. Investigation of axial loads on transverse vibrations of vertical cantilevers of variable parameters. JAM, Kiev, 36(9): 1242–1251.   Google Scholar

JAROSZEWICZ J., ŻUR K., DRAGUN Ł. 2014. The influence function method in analysis of bending curve and relations of elastic supports of beam with variable parameters. Journal of Theoretical and Applied Mechanics, 52(1): 247–255.   Google Scholar

KUKLA S., SKALMIERSKI B. 1993. The effect of Axial Load on Transverse Vibrations of an Euler Bernoulli Beam. J. Theor. and Appl. Mech., 2(31).   Google Scholar

SOLECKI R., SZYMKIEWICZ J. 1964. Układy prętowe i powierzchniowe, obliczenia dynamiczne. Arkady, Warszawa.   Google Scholar

SZMIDLA J., KLUBA M. 2011. Stateczność i drgania swobodne niepryzmatycznego układu smukłego poddanego obciążeniu eulerowskiemu. Modelowanie Inżynierskie, 41: 385–394.   Google Scholar

ZORYJ L.M. 1982. Universal characteristic equations in problems on the vibrations and stability of elastic systems. Tverd. Tela, 6: 155–162.   Google Scholar

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Published
2017-08-16

Cited by

Jaroszewicz, J., Radziszewski, L., & Dragun, Łukasz. (2017). The effect of influence of conservative and tangential axial forces on transverse vibrations of tapered vertical columns. Technical Sciences, 20(4), 333–342. https://doi.org/10.31648/ts.5431

Jerzy Jaroszewicz 

Leszek Radziszewski 

Łukasz Dragun 








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