Nonlinear static and dynamic behavior of a multistable structure formed by elastically connected trusses

Resumo

Multistable systems have proved to be important in several engineering areas, from nano to
macrostructures. Important applications can be found in vibration control, deployable and collapsible structures,
dynamic systems with a periodic pattern and in the development of new materials (metamaterials), among others.
However, there is a need to investigate the static and dynamic behavior of these eminently non-linear systems.
The most basic example of multistable structures is the classic Von Mises truss, which presents two
configurations of stable equilibrium, that is, a bistable behavior. In this work, the multistable behavior of a
sequence of Von Mises trusses connected through the insertion of a flexible element represented by a linear
elastic spring is studied. This system has multiple equilibrium configurations, both stable and unstable, which
significantly influences its non-linear static and dynamic behavior. For analysis, the nonlinear equilibrium and
motion equations, in their dimensionless forms, are obtained through the criterion of minimum potential energy
and Hamilton's principle. Their behavior is then investigated through the use of equipotential energy surfaces
and curves, nonlinear equilibrium paths, phase planes and basins of attraction. The parametric analysis
investigates the effect of the connection stiffness and the physical and geometric parameters of the trusses on the
behavior of the system. Through the results, it is possible to observe the importance of geometric nonlinearity
and connection stiffness in the dynamics and stability of this new class of structures.