A linear one-dimensional model for the flexural-torsional vibrations of tapered thin-walled bars with open cross-sections

摘要

The physical significance of a newly developed one-dimensional model for tapered thin-walledrnbars with open cross-sections is discussed by means of an illustrative example – the (undamped) free torsionalrnmotion of a family of doubly symmetric and linearly web-tapered I-section cantilevers. The shortcomings ofrnstepped (piecewise prismatic) models, which become particularly noticeable when restrained warping plays anrnimportant part in the torsional behaviour, are highlighted. It is also shown that the approach to non-uniformrntorsion pioneered by Timoshenko – i.e., regarding each plated component of the bar as an Euler-Bernoullirnmember undergoing stretching and bending –, when correctly applied to the tapered case, leads to identicalrnresults.