Method in calculating own vibration frequencies of open sections bars with thin walls

Abstract

Dynamic stability of thin-walled bars of open sections, as well as the stability of elastic systems dynamics in general, is studying closely with their vibrations. This, because, areas of dynamics instability is around twice the frequency of free vibration of the bar or elastic system in all cases excitation parametric, on the one hand, and on the other hand matrices involved in the matrix equation of free vibration are matrices of matrix equation of dynamic stability. In this paper we settled differential equations of parametric vibrations of thin-walled straight bars open sections constant as a system with a triple infinity of second order differential equations, linear coefficients homogeneous and periodicals. In the end of work, by customizing differential equations of forced vibration parameters have been obtained differential equations of own vibration of bars with thin wall and open sections as a system with a triple infinity of differential equations of second order, linear, homogeneous with constant coefficients and, using it, the algebraic equation of own vibrations pulsations.