Flutter and divergence instability regions of a column subjected to the load realized by means of a jet engine with an additional guiding structure

Abstract

In this paper, a new slender system is considered — a column that is subjected to a compressive follower load. The studied structure uses a system of rigid transoms guiding the loaded end of the column with the limitation of their mutual rotation by means of rotational springs. This additional element does not transfer the compressive load but affects guidance of the loaded end of the column. In the presented form, the solution used to guide the end of the column was not previously taken into account. The boundary problem was formulated on the basis of Hamilton’s principle, taking into account (due to the non-linearity) the small parameter method. The theoretical, numerical, and experimental studies were conducted by determining an influence of the system parameters (in particular the element guiding the loaded end) on the instability type. On the basis of the kinetic stability criterion, critical divergence and flutter loads as well as limit values of parameters in the system were determined, at which instability occurs. The research was limited to the determination of the first linear component of vibration frequency. As a part of numerical research, detailed considerations were made on characteristic curves. It has been shown that with an appropriate selection of the parameters of the guiding system, a new shape of the characteristic curves can be obtained. This new feature shows that in the boundary case (instability change from flutter to divergence) the critical divergence load is greater than the critical flutter. In order to confirm the correctness of the mathematical model and thus the results of numerical tests concerning the occurrence of flutter and divergence areas the experimental tests were carried out consisting of recording the behavior of the system with a quick camera when it was loaded with a model jet engine. The correctness of the shape of characteristic curves was confirmed by the experimental frequency analysis of considered columns at different jet engine thrust magnitudes. The conducted research may be of great importance in the control of the flutter phenomenon of slender systems exposed to follower forces, including those resulting from the action of the wind.