Ds. Sophianopoulos et An. Kounadis, DYNAMIC STABILITY OF IMPERFECT FRAMES UNDER JOINT DISPLACEMENTS, Journal of engineering mechanics, 120(8), 1994, pp. 1661-1674
In this investigation a nonlinear dynamic-stability analysis is perfor
med on a two-bar geometrically imperfect frame subjected to an axial d
isplacement of its joint, either suddenly applied or time dependent. T
he dynamic response of the frame is governed by a coupled system of tw
o one-dimensional partial differential equations for the axial and lat
eral motion of each bar. One and two-mode solutions are thoroughly dis
cussed for various geometric configurations of the frame. Dynamic buck
ling occurs when the corresponding frame under static loading loses it
s stability through a limit point. This happens for initial bar curvat
ures above a certain critical value; below this value the frame is dyn
amically stable. Numerical results are obtained by using Galerkin's me
thod in connection with the seventh-order Runge-Kutta-Verner scheme wi
th appropriate step size. The results of the one-mode solution are fou
nd to be in excellent agreement with those of previous analyses.