Issue 16 (4) 2017 pp. 5-14
Olga Szlachetka, Jacek Jaworski, Marek Chalecki
ANALYSIS OF FREE VIBRATIONS OF CANTILEVER BARS WITH PARABOLICALLY VARIABLE CROSS-SECTIONS USING THE RAYLEIGH’S METHOD
Keywords: cantilever bar, non-uniform section, first natural frequency, Rayleigh’s method
The Rayleigh’s method can be used to determine the first natural frequency of bars (beams or posts) with
non-uniform cross-section. The authors have analysed slender bars made of an elastic material and having the
shape of a solid of revolution: a curvilinear truncated cone and curvilinear conical pipe. It has been assumed
that the bar axis deflected during vibrations has a shape of a beam deflected by a static constant continuous
load. The Rayleigh’s method has been applied in the paper in aim to determine the first frequency of free
(transverse) vibrations of posts formed as a cantilever bars having the shape of solid and hollow curvilinear
truncated cone with the generatrix being a parabola which is convex in relation to the cone axis. The results
of calculations are very close to those obtained with finite element method (FEM).
http://www.architectura.actapol.net/volume16/issue4/16_4_5.pdf
MLA | Szlachetka, Olga, et al. "ANALYSIS OF FREE VIBRATIONS OF CANTILEVER BARS WITH PARABOLICALLY VARIABLE CROSS-SECTIONS USING THE RAYLEIGH’S METHOD." Acta Sci.Pol. Architectura 16.4 (2017): 5-14. |
APA | Szlachetka, O. et al. (2017). ANALYSIS OF FREE VIBRATIONS OF CANTILEVER BARS WITH PARABOLICALLY VARIABLE CROSS-SECTIONS USING THE RAYLEIGH’S METHOD. Acta Sci.Pol. Architectura, 16 (4), 5-14 |
ISO 690 | Szlachetka, Olga, Jaworski, Jacek, Chalecki, Marek. ANALYSIS OF FREE VIBRATIONS OF CANTILEVER BARS WITH PARABOLICALLY VARIABLE CROSS-SECTIONS USING THE RAYLEIGH’S METHOD. Acta Sci.Pol. Architectura, 2017, 16.4: 5-14. |
http://www.architectura.actapol.net/tom16/zeszyt4/abstrakt-5.html