Nonlinear dynamic behavior and instability of slender frames with semi-rigid connections

The free and forced nonlinear vibrations of slender frames with semi-rigid connections are studied in this work. Special attention is given to the influence of static pre-load on the natural frequencies and mode shapes, nonlinear frequency–amplitude relations, and resonance curves. An efficient nonlinear finite element program for buckling and vibration analysis of slender elastic frames with semi-rigid connections is developed. The equilibrium paths are obtained by continuation techniques, in combination with the Newton-Raphson method. The ordinary differential equations of motion of the discretized frame are solved by the Newmark implicit numerical integration method using adaptive time-step strategies. Three structural systems with important practical applications are analyzed: an L-frame, a shallow arch, and a pitched-roof frame. The results highlight the importance of the static pre-load and the stiffness of the semi-rigid connections on the buckling and vibration characteristics of these structures.