Static and dynamic nonlinear behavior of a multistable structural system

Resumo

The persistent search for new structural solutions has generated great interest from the scientific
community in understanding the static instability and nonlinear dynamics of multistable structural systems.
Structural multistability is achieved through structural arrangements that have several stable equilibrium
configurations and have a wide field of applications, such as: vibration control, self-deployable and collapsible
structures, dynamical systems with a periodic pattern and in the development of new materials (metamaterials),
among others. In this work we study the static and dynamic nonlinear behavior of a multistable structural system
formed by a sequence of von Mises trusses. For this, the non-linear equilibrium equations and equations of motion,
in their dimensionless forms, are obtained through the criterion of minimum potential energy and Hamilton’s
principle. Based on dimensionless parameters, equipotential energy surfaces and curves, non-linear equilibrium
paths, time responses, phase portraits and basins of attraction are obtained. Then a parametric analysis is conducted
to identify the influence of the dimensionless parameters on the quantity and stability of equilibrium positions.
From the results, the importance of geometric nonlinearity in the dynamics and stability in this new class of
structural systems is verified.