Coupled Vibrations of Thin-Walled Beams of Open Cross Section

1958 ◽  
Vol 25 (3) ◽  
pp. 373-378 ◽  
Author(s):  
J. M. Gere ◽  
Y. K. Lin
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Approximate Formula ◽  
Exact Method ◽  
End Conditions ◽  
Simple Supports ◽  
Thin Walled ◽  
Exact Calculations ◽  
Open Cross Section

Abstract The determination of coupled frequencies of free vibration for beams of nonsymmetric, open cross section is discussed in this paper. Beams with various end conditions, including simple supports, fixed ends and a cantilever, are considered. Results of both exact and approximate analyses are presented. For practical use, a simple approximate formula for determining frequencies of vibration for beams with any end conditions is given. The accuracy of the approximate formula is shown by comparison with results obtained by the exact method. The exact calculations were carried out on an IBM 605 Card Programmed Calculator.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

Torsional Vibrations of Beams of Thin-Walled Open Section

1954 ◽  
Vol 21 (4) ◽  
pp. 381-387
Author(s):  
J. M. Gere
Keyword(s):  
Cross Section ◽  
Normal Modes ◽  
Mode Shapes ◽  
Graphical Form ◽  
Torsional Vibrations ◽  
End Conditions ◽  
Modes Of Vibration ◽  
Thin Walled ◽  
Limiting Case ◽  
Open Cross Section

Abstract This analysis deals with the free torsional vibrations of bars of thin-walled open cross section for which the shear center and centroid coincide. Such sections include I-beams and Z-sections. The differential equation for torsional vibrations is derived and includes the effect of warping of the cross section. The effect of warping on the frequency of vibration and the shapes of the normal modes of vibration are determined for bars of single span with various end conditions. For a simply supported bar, a formula for the principal torsional frequencies and an expression for mode shape are derived. For other conditions of support, the frequency equations are derived and their solutions presented in graphical form. From these graphs the frequencies of vibration and the mode shapes may be obtained directly. The case of a cross section which does not warp is a limiting case of the general problem. For such shapes (for example, a cross-shaped or cruciform section) the formulas for torsional frequencies and modes of vibration are quite simple. These formulas also are valid for a circular shaft and may be used approximately for other solid sections.

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