A fixed ended beam is subjected to a short pulse of transverse loading such that plastic deformations are imposed. Because of the end fixity, dynamic instabilities related to shallow arch action may occur. Anomalous phenomena (such a final deflections in the direction opposite that of the pulse and severe difficulty of prediction) have been studied in uniform beams (by finite element analysis) and in two-and single-degree of freedom special beam models. In the first two of these cases, indications of deterministic chaos appear. Their novelty and interest lie in their appearance with workless constraints and in the absence of harmonic or other sustained excitation. Research is proposed here which aims to confirm and amplify the preliminary results already obtained (outlined in the proposal), to gain deeper understanding by further analysis and extensions, and to provide methods for the estimation of parameter ranges in which they are likely to occur.