S. K. A. Shah, A. Soleiman Fallah and L. A Louca
The Journal of Mechanical Science and Technology, vol. 26, no. 6, pp.1697-1709, 2012

Abstract : This paper presents a comprehensive study on counter-intuitive or chaotic dynamic response of prototype discrete parameter models of single or multiple degrees of freedom subject to blast or impact loading. Non-linear dynamic behaviour of a typical single degree-offreedom (SDOF) and multi-degree-of-freedom (MDOF) systems are studied by taking into account cubic and quintic non-linearities, elastic perfect-plastic, and elastic-plastic-hardening and softening behaviours. The first part is founded on Duffing’s equation and Ueda‘s work on strange attractors which indicates the presence of chaos in deterministic systems by using chaos detection techniques such as Poincare’s mapping and Lyapunov’s exponents and in some cases by fractal dimensions. In these deterministic problems, the system hesitates to settle between two different possible settling regimes despite the fact that the input parameters to the system are deterministic. In a SDOF model with elastic perfectly-plastic or elastic-plastic-hardening resistance function the sign of the permanent plastic deformation may or may not coincide with that of loading direction hence chaotic behaviour can be observed. For an elastic-plastic-softening system, subjected to blast loading, the problem is sensitive to the ratio of post yield stiffness to initial stiffness and for certain ranges of this parameter a small change can replicate into an abrupt change in response. Examples are included of finite elements models with many degrees of freedom of beams and plates. As most intricate engineering structures are composed of these structural elements the existence of component chaos can imply global counter-intuitive behaviour.

Keyword : Chaos; Counter-intuitive response; Discrete parameter model; Dynamic loading; Non-linearity; SDOF and MDOF systems