ABSTRACT

This chapter describes the importance of investigating the strongly nonlinear mechanics and/or dynamics when there is a relationship between the multiple heteroclinic orbits and elastic instability in a basic folding model of a critical problem of a multifolding microstructures system, which has a bifurcation point. It demonstrates some more interesting models and results in the extended Duffing problem in nonlinear dynamics for a fundamental function of expanding and folding pantographic trusses, which have been going through structural instability of large and/or hierarchical snapthrough behaviors or subject cyclic loadings in the field of engineering science. The hilltop bifurcation phenomena in a pantographic truss are considered to be an appropriate chaotic model for determining advanced microstructure issues in multiple-well Duffing problems. The chapter considers the theoretical model of a simplified folding system with the rare hilltop bifurcation point and focus our analysis on the dynamic stability, convergence, static bifurcation, and oscillation of the system.