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

Abstract

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 preload and the stiffness of the semi-rigid connections on the buckling and vibration characteristics of these structures.

Dynamic Instability in Shallow Arches under Transversal Forces and Plane Frames with Semirigid Connections

“…Figure 14 indicates the results of the central node displacement. A considerable agreement with the results presented by Galvão [2] is observed. In the relations =P/h between 0.1 and 0.3 (Figures 14(a)-14(c)) the arch vibrates in its precritical configuration, around a constant value, equivalent to the static instability analysis.…”

“…Here, the proposed scheme to deal with elastic and viscoelastic connections is considerably simpler than the usual approach presented in Galvão et al [17] and Kassimali [18], based on variational principle of virtual work for static nonlinear analysis. Moreover, as presented in Greco et al [19], at critical points the positional formulation presents better reliability for the numerical calculation.…”

“…This problem was analyzed by Galvão [2], Silva [5], and Rosas [4], with different approaches. The amplitude of the arch is z 0 = 20mm.…”

“…Because they present considerable slenderness, they may present a dynamic instability called snap-through behavior. For a critical loading level below the ultimate load, the arch jumps from the potential prebuckling valley and the response converges to a stable postcritical solution with the arch assuming an inverted configuration [2]. This process leads to large stress inversions and frequencies that significantly increase the possibility of failure of the structure.…”

“…Rosas [4] conducted studies on a sine-shaped sine-arch subjected to uniformly distributed loading, considering support conditions as discrete rotational springs. This same model was also evaluated by Galvão [2] and Silva [5]. Zhou et al [6] demonstrated an analytical method to study the nonlinear stability and the disconnected equilibrium of shallow arches with asymmetric geometric imperfections.…”