On the dynamic buckling of very slender structures to self-weight

¹ Federal University of ABC, São Bernardo do Campo, SP, Brazil
² UNOESTE, Presidente Prudente, SP, Brazil

^* Corresponding author: reyolando.brasil@ufabc.edu.br

Abstract

We present a mathematical and experimental study of the dynamic buckling of very slender structures due to their self-weight. Modern materials and powerful new analysis methods are leading to the design of very slender tall structures that may be prone to instability issues. Elastic stability of such structures is a problem inside the scope of the Non-Linear Dynamics Analysis Methods. An indicator of instability is when the structure’s free vibration frequency approaches null value. Two main factors affect these frequency results. First the stiffness, composed of elastic stiffness, always positive and non-zero, that diminishes rapidly with height, and the geometric stiffness, negative for compressive forces, whose absolute value grows as the structure gets taller and heavier. Second, the mass, that also grows with the height of the structures. To access this behaviour, we first present a simple one-degree-of-freedom mathematical model derived with Rayleigh’s Method, adopting a cubic polynomial as shape function. Next, comparisons are made with results of an experimental set up composed of a variable length cantilever vertical aluminium bar. These models reasonably agree with analytical close solutions available in the literature.