Multistability and global dynamics of orthogonally coupled von Mises trusses with unilateral contact

Abstract

Abstract This work investigates the nonlinear dynamics of a system composed of two orthogonally coupled von Mises trusses connected through a unilateral elastic element. A discrete model is derived using an energy-based formulation, accounting for geometric nonlinearities and unilateral effects. The static response is analyzed to identify equilibrium configurations and assess the multistable nature of the system. The dynamic behavior under harmonic excitation is examined using numerical continuation techniques, allowing the construction of resonance curves and the identification of bifurcation phenomena associated with nonlinear modal coupling. The results show the coexistence of multiple dynamic regimes, including distinct attractors associated with different potential wells. The global response is further investigated through basin of attraction computations, which enable the identification of coexisting attractors and the characterization of their attraction regions. It is shown that variations in the excitation amplitude lead to a progressive reduction of these regions, indicating a qualitative loss of robustness of specific dynamical states. The main scientific contribution of this work lies in systematically establishing how contact-induced non-smooth nonlinearities modulate the multi-well potential energy landscape, demonstrating that state-dependent contact switching induces significant fragility in the boundaries of the basins of attraction. These findings fill a crucial gap regarding the global stability and safe operation boundaries of coupled structural systems under unilateral constraints.