Abstract Summary
Recent decades have witnessed a new interest in the field of structural stability due to the use of multistable systems in several applications such as vibration control, energy harvesting, deployable and collapsible structures, micro- and nanocomponents and the development of metamaterials, among others. In many of these structures multistable behavior is attained by coupling bistable elements. The most basic example of bistable structure is the Von Mises truss, which presents two stable equilibrium configurations. In this work, the multistable be-havior of a sequence of Von Mises trusses connected through a flexible element is studied. This system has several stable and unstable equilibrium configurations resulting from the nonlinear coupling, which significantly influences its non-linear oscillations and dynamic stability. To obtain the equilibrium paths, the nonlinear equilibrium equations are derived in nondimensional form and solved by using the Newton-Raphson method and continuation techniques. Hamilton's principle is then employed to obtain the equations of motion around an equilibrium configuration. They are numerically integrated to obtain bifurcation diagrams and basins of attraction, which clarify the effect of load and system parameters on the nonlin-ear oscillations and instabilities of the coupled trusses, in particular the geometric nonlinear-ity and connection stiffness. This may help in the development of new engineering applica-tions where multistability is desired.
