The Impact of Chaos on Science and Society (UNU, 1997, 415 pages)
 14. The impact of chaos on engineering
 (introduction...) Introduction The role of geometrical theory in applied mechanics Transient failure The influence of chaotic transients Conclusions Acknowledgements References

### Transient failure

To safeguard against collapse when designing a new structure or system, an engineer must first evaluate the possible modes of failure for that particular system. Having done so, the design can then be adapted so that these modes can be avoided during all imaginable operations. Thus as well as having to calculate long-term behaviour, to understand any particular failure mechanism we have to investigate transient dynamics. To illustrate this we again return to the problem of ship capsize, though the generic form of potential wells encountered enables us to apply the following techniques to other, wider fields.

In Canada during the 1970s several fishing vessels capsized off the west coast in conditions that were not thought to be particularly hazardous. To account for these unusual events a report was commissioned to determine the nature of the stability of the common designs used at the time (see Miller et al. 1986). Using a specific hull form, full dynamic analysis of the ship's motions was calculated in the six degrees of freedom taking into account wave diffraction theory, fluid forces on the vessel etc., to calculate the nonlinear time history. Three separate mechanisms of capsize corresponding to resonant and subharmonic rolling in beam seas and loss of stability at a wave crest were highlighted in their report. The latter of these mechanisms is particularly disturbing since there is little or no warning of the impending capsize. Figure 6 shows a printout from the computer simulations and the wave crest can be seen amidship when the time t=95 seconds, leading up to t=103 seconds at which time the ship capsizes. Plots of the roll, pitch, and yaw displacements of the vessel that display no prior warning of the impending disaster are also shown in this figure.

Fig. 6 Schematic representation of the phase diagrams for driven systems with a single and two-well potential energy function. For small values of the forcing the basins resemble those in figure 5 (autonomous with time dependence) except attracting equilibrium points are now periodic and basins are obtained by a projection of the sampled phase space

Further mechanisms for capsize have been established, one of which is due to a rolling motion induced by a parametric resonance in head waves studied by Nayfeh (1988) and de Kat and Paulling (1989). Of course new insights are constantly being offered into the complex way in which ship motions can be modelled. Recent investigations into a single degree of freedom model of ship roll in beam seas have highlighted how new theories of dynamical systems can be used to examine qualitative long-term, and transient, behaviour (McRobie and Thompson 1990).