Chaotic Behaviors of a Two-Member Truss

Abstract

In the literature, comparatively few research works have been conducted on the chaotic behaviors of civil engineering structures. By taking a symmetric two-member truss as an example in this paper, one can demonstrate that it is possible for the truss to display certain chaotic phenomena, considering only the effect of geometric nonlinearity. This paper starts with the derivation of the equation of motion for the truss subjected to a vertical harmonic load, which appears to be a general form of the Duffing equation. The fourth-order Runge-Kutta method is then employed to solve for the time-history response. Based on the following two facts, it is confirmed that chaos can occur with the truss under certain loading conditions: (1) the motion of the truss is very sensitive to small changes in initial conditions; (2) strange attracters can be identified using the Poincaré plot. Both the Lyapunov numbers and fractal dimensions calculated for the truss also confirm the occurrence of chaos. From the chaos boundary curves plotted for the truss, one observes that chaos can occur for a wide range of parameter values encountered.

Keywords

Chaos Duffing's equation fractal dimension geometric nonlinearity Poincaré plot strange attracter truss

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References

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