Stability problems of compound columns under an axial or eccentric load

Abstract

The conversion of an elastic system from stability to instability proceeds as a dynamic phenomenon. This is more pronouncedfor elastic systems subjected to follower loads. The loss of stability in such systems may be of flutter or divergence type, de-pending on the nature of boundary conditions. When these systems are of flutter type their limit of stability can be establishedonly by using the kinetic criterion, while if they are of divergence type their limit of stability can be determined by using astatic approach [1].In this work the divergence instability of a continuous two member system subjected to a partial follower force or aneccentric force P is studied. The members, discretely joined at their ends in both displacement and rotational senses, havedifferent flexural and axial stiffnesses. One end is supported against rotation by a spring of rigidity K. The physical modelsof the considered structure can comprise: a column made of two coaxial tubes, or a tube and a bar, or a planar frame madeof a strip located in the centre of the structure in which the second member is formed by two identical strips, symmetricallylocated at both sides of the central strip. The second model can be composed of more than three strips, creating a palisadestructure arranged in a two member co-axial system. For comparative purposes this geometrically non-linear system withdifferent methods of support and loading is also taken into consideration. Some static and dynamic features of such systemswere studied in [2-5].The problem of vibration and stability of geometrically non-linear structures of this type became especially important afterresearch on structures with piezoceramic or electrostrictive actuators, which are available in the form of plates, rods or patches[6]. Such actuators with comparable flexural stiffness are discretely mounted to the elements of the main structure for varioustype of control. The tube, bar or strip, considered here, can be an actuator mounted for the previously mentioned purposes.