Non-linear torsional vibration of lengthy thin-walled simply supported beam of open section resting on Winkler foundation

2019 ◽  
Vol 155 ◽  
pp. 325-337
Author(s):  
Kameswara Rao Chellapilla ◽  
Bhaskara Rao Lokavarapu
Keyword(s):  
Torsional Vibration ◽  
Winkler Foundation ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Open Section ◽  
Non Linear ◽  
Thin Walled

The Torsional Vibration of Uniform Thin-Walled Beams of Open Section

1969 ◽  
Vol 73 (704) ◽  
pp. 672-674 ◽  
Author(s):  
J. B. Carr
Keyword(s):  
Torsional Vibration ◽  
Characteristic Functions ◽  
Shear Stresses ◽  
Simply Supported ◽  
Open Section ◽  
Torsional Resistance ◽  
Approximate Frequency ◽  
Thin Walled ◽  
Image Position ◽  
Fixed End

The pure torsional vibration of uniform thin-walled beams of open section, which is governed by the differential equation has been extensively analysed by Gere He derived the exact frequency equations for beams with a variety of end conditions. However, these equations are, in most cases, highly transcendental. This note uses an energy approach to obtain approximate frequency equations for the fixed-fixed and the fixed-simply-supported beams. A fixed end is one which allows no twist and no warping and a simply-supported end allows no twist but permits warping to take place freely. The approximating functions used are those corresponding to the exact solution of the problem if the torsional resistance caused by the St Venant system of shear stresses is zero. These functions are similar to the characteristic functions of simple beams in flexure.

Non-linear normal modes of a simply supported beam: continuous system and finite-element models

2004 ◽  
Vol 82 (31-32) ◽  
pp. 2683-2691 ◽  
Author(s):  
Carlos E.N. Mazzilli ◽  
Mário E.S. Soares ◽  
Odulpho G.P. Baracho Neto
Keyword(s):  
Finite Element ◽  
Normal Modes ◽  
Continuous System ◽  
Finite Element Models ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Non Linear

Non-linear GBT formulation for open-section thin-walled members with arbitrary support conditions

2011 ◽  
Vol 89 (21-22) ◽  
pp. 1906-1919 ◽  
Author(s):  
C. Basaglia ◽  
D. Camotim ◽  
N. Silvestre
Keyword(s):  
Open Section ◽  
Non Linear ◽  
Thin Walled ◽  
Support Conditions

Nonstandard Models for Thin-Walled Beams With a View to Applications

1996 ◽  
Vol 63 (2) ◽  
pp. 399-403 ◽  
Author(s):  
N. Rizzi ◽  
A. Tatone
Keyword(s):  
Cross Sections ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Lateral Buckling ◽  
Simply Supported Beam ◽  
One Dimensional ◽  
Simply Supported ◽  
Flexural Buckling ◽  
Nonstandard Models ◽  
Thin Walled

A direct theory of a one-dimensional structured continuum is introduced in order to study the postbuckling behavior of thin-walled beams. A simply supported beam bent by end couples is analyzed showing that, in the case of nonsymmetric cross sections, lateral buckling gives rise to imperfection sensitivity. Then an axially loaded beam is studied taking also into account the interaction between torsional and flexural buckling. The results obtained prove that in this case imperfection sensitivity, though slighter than in the previous case, arises also for symmetric cross sections.

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